3.14159 26535 89793 23846 26433 83279 50288 41971 69399 37510 58209 74944 59230 78164 06286 20899 86280 34825 34211 70679 82148 08651 32823 06647 09384 46095 50582 23172 53594 08128 48111 74502 84102 70193 85211 05559 64462 29489 54930 38196 44288 10975 66593 34461 28475 64823 37867 83165 27120 19091 45648 56692 34603 48610 45432 66482 13393 60726 02491 41273 72458 70066 06315 58817 48815 20920 96282 92540 91715 36436 78925 90360 01133 05305 48820 46652 13841 46951 94151 16094 33057 27036 57595 91953 09218 61173 81932 61179 31051 18548 07446 23799 62749 56735 18857 52724 89122 79381 83011 94912 98336 73362 44065 66430 86021 39494 63952 24737 19070 21798 60943 70277 05392 17176 29317 67523 84674 81846 76694 05132 00056 81271 45263 56082 77857 71342 75778 96091 73637 17872 14684 40901 22495 34301 46549 58537 10507 92279 68925 89235 42019 95611 21290 21960 86403 44181 59813 62977 47713 09960 51870 72113 49999 99837 29780 49951 05973 17328 16096 31859 50244 59455 34690 83026 42522 30825 33446 85035 26193 11881 71010 00313 78387 52886 58753 32083 81420 61717 76691 47303 59825 34904 28755 46873 11595 62863 88235 37875 93751 95778 18577 80532 17122 68066 13001 92787 66111 95909 21642 01989 38095 25720 10654 85863 27886 59361 53381 82796 82303 01952 03530 18529 68995 77362 25994 13891 24972 17752 83479 13151 55748 57242 45415 06959 50829 53311 68617 27855 88907 50983 81754 63746 49393 19255 06040 09277 01671 13900 98488 24012 85836 16035 63707 66010 47101 81942 95559 61989 46767 83744 94482 55379 77472 68471 04047 53464 62080 46684 25906 94912 93313 67702 89891 52104 75216 20569 66024 05803 81501 93511 25338 24300 35587 64024 74964 73263 91419 92726 04269 92279 67823 54781 63600 93417 21641 21992 45863 15030 28618 29745 55706 74983 85054 94588 58692 69956 90927 21079 75093 02955 32116 53449 87202 75596 02364 80665 49911 98818 34797 75356 63698 07426 54252 78625 51818 41757 46728 90977 77279 38000 81647 06001 61452 49192 17321 72147 72350 14144 19735 68548 16136 11573 52552 13347 57418 49468 43852 33239 07394 14333 45477 62416 86251 89835 69485 56209 92192 22184 27255 02542 56887 67179 04946 01653 46680 49886 27232 79178 60857 84383 82796 79766 81454 10095 38837 86360 95068 00642 25125 20511 73929 84896 08412 84886 26945 60424 19652 85022 21066 11863 06744 27862 20391 94945 04712 37137 86960 95636 43719 17287 46776 46575 73962 41389 08658 32645 99581 33904 78027 59009 94657 64078 95126 94683 98352 59570 98258 22620 52248 94077 26719 47826 84826 01476 99090 26401 36394 43745 53050 68203 49625 24517 49399 65143 14298 09190 65925 09372 21696 46151 57098 58387 41059 78859 59772 97549 89301 61753 92846 81382 68683 86894 27741 55991 85592 52459 53959 43104 99725 24680 84598 72736 44695 84865 38367 36222 62609 91246 08051 24388 43904 51244 13654 97627 80797 71569 14359 97700 12961 60894 41694 86855 58484 06353 42207 22258 28488 64815 84560 28506 01684 27394 52267 46767 88952 52138 52254 99546 66727 82398 64565 96116 35488 62305 77456 49803 55936 34568 17432 41125 15076 06947 94510 96596 09402 52288 79710 89314 56691 36867 22874 89405 60101 50330 86179 28680 92087 47609 17824 93858 90097 14909 67598 52613 65549 78189 31297 84821 68299 89487 22658 80485 75640 14270 47755 51323 79641 45152 37462 34364 54285 84447 95265 86782 10511 41354 73573 95231 13427 16610 21359 69536 23144 29524 84937 18711 01457 65403 59027 99344 03742 00731 05785 39062 19838 74478 08478 48968 33214 45713 86875 19435 06430 21845 31910 48481 00537 06146 80674 91927 81911 97939 95206 14196 63428 75444 06437 45123 71819 21799 98391 01591 95618 14675 14269 12397 48940 90718 64942 31961 56794 52080 95146 55022 52316 03881 93014 20937 62137 85595 66389 37787 08303 90697 92077 34672 21825 62599 66150 14215 03068 03844 77345 49202 60541 46659 25201 49744 28507 32518 66600 21324 34088 19071 04863 31734 64965 14539 05796 26856 10055 08106 65879 69981 63574 73638 40525 71459 10289 70641 40110 97120 62804 39039 75951 56771 57700 42033 78699 36007 23055 87631 76359 42187 31251 47120 53292 81918 26186 12586 73215 79198 41484 88291 64470 60957 52706 95722 09175 67116 72291 09816 90915 28017 35067 12748 58322 28718 35209 35396 57251 21083 57915 13698 82091 44421 00675 10334 67110 31412 67111 36990 86585 16398 31501 97016 51511 68517 14376 57618 35155 65088 49099 89859 98238 73455 28331 63550 76479 18535 89322 61854 89632 13293 30898 57064 20467 52590 70915 48141 65498 59461 63718 02709 81994 30992 44889 57571 28289 05923 23326 09729 97120 84433 57326 54893 82391 19325 97463 66730 58360 41428 13883 03203 82490 37589 85243 74417 02913 27656 18093 77344 40307 07469 21120 19130 20330 38019 76211 01100 44929 32151 60842 44485 96376 69838 95228 68478 31235 52658 21314 49576 85726 24334 41893 03968 64262 43410 77322 69780 28073 18915 44110 10446 82325 27162 01052 65227 21116 60396 66557 30925 47110 55785 37634 66820 65310 98965 26918 62056 47693 12570 58635 66201 85581 00729 36065 98764 86117 91045 33488 50346 11365 76867 53249 44166 80396 26579 78771 85560 84552 96541 26654 08530 61434 44318 58676 97514 56614 06800 70023 78776 59134 40171 27494 70420 56223 05389 94561 31407 11270 00407 85473 32699 39081 45466 46458 80797 27082 66830 63432 85878 56983 05235 80893 30657 57406 79545 71637 75254 20211 49557 61581 40025 01262 28594 13021 64715 50979 25923 09907 96547 37612 55176 56751 35751 78296 66454 77917 45011 29961 48903 04639 94713 29621 07340 43751 89573 59614 58901 93897 13111 79042 97828 56475 03203 19869 15140 28708 08599 04801 09412 14722 13179 47647 77262 24142 54854 54033 21571 85306 14228 81375 85043 06332 17518 29798 66223 71721 59160 77166 92547 48738 98665 49494 50114 65406 28433 66393 79003 97692 65672 14638 53067 36096 57120 91807 63832 71664 16274 88880 07869 25602 90228 47210 40317 21186 08204 19000 42296 61711 96377 92133 75751 14959 50156 60496 31862 94726 54736 42523 08177 03675 15906 73502 35072 83540 56704 03867 43513 62222 47715 89150 49530 98444 89333 09634 08780 76932 59939 78054 19341 44737 74418 42631 29860 80998 88687 41326 04721 56951 62396 58645 73021 63159 81931 95167 35381 29741 67729 47867 24229 24654 36680 09806 76928 23828 06899 64004 82435 40370 14163 14965 89794 09243 23789 69070 69779 42236 25082 21688 95738 37986 23001 59377 64716 51228 93578 60158 81617 55782 97352 33446 04281 51262 72037 34314 65319 77774 16031 99066 55418 76397 92933 44195 21541 34189 94854 44734 56738 31624 99341 91318 14809 27777 10386 38773 43177 20754 56545 32207 77092 12019 05166 09628 04909 26360 19759 88281 61332 31666 36528 61932 66863 36062 73567 63035 44776 28035 04507 77235 54710 58595 48702 79081 43562 40145 17180 62464 36267 94561 27531 81340 78330 33625 42327 83944 97538 24372 05835 31147 71199 26063 81334 67768 79695 97030 98339 13077 10987 04085 91337 46414 42822 77263 46594 70474 58784 77872 01927 71528 07317 67907 70715 72134 44730 60570 07334 92436 93113 83504 93163 12840 42512 19256 51798 06941 13528 01314 70130 47816 43788 51852 90928 54520 11658 39341 96562 13491 43415 95625 86586 55705 52690 49652 09858 03385 07224 26482 93972 85847 83163 05777 75606 88876 44624 82468 57926 03953 52773 48030 48029 00587 60758 25104 74709 16439 61362 67604 49256 27420 42083 20856 61190 62545 43372 13153 59584 50687 72460 29016 18766 79524 06163 42522 57719 54291 62991 93064 55377 99140 37340 43287 52628 88963 99587 94757 29174 64263 57455 25407 90914 51357 11136 94109 11939 32519 10760 20825 20261 87985 31887 70584 29725 91677 81314 96990 09019 21169 71737 27847 68472 68608 49003 37702 42429 16513 00500 51683 23364 35038 95170 29893 92233 45172 20138 12806 96501 17844 08745 19601 21228 59937 16231 30171 14448 46409 03890 64495 44400 61986 90754 85160 26327 50529 83491 87407 86680 88183 38510 22833 45085 04860 82503 93021 33219 71551 84306 35455 00766 82829 49304 13776 55279 39751 75461 39539 84683 39363 83047 46119 96653 85815 38420 56853 38621 86725 23340 28308 71123 28278 92125 07712 62946 32295 63989 89893 58211 67456 27010 21835 64622 01349 67151 88190 97303 81198 00497 34072 39610 36854 06643 19395 09790 19069 96395 52453 00545 05806 85501 95673 02292 19139 33918 56803 44903 98205 95510 02263 53536 19204 19947 45538 59381 02343 95544 95977 83779 02374 21617 27111 72364 34354 39478 22181 85286 24085 14006 66044 33258 88569 86705 43154 70696 57474 58550 33232 33421 07301 54594 05165 53790 68662 73337 99585 11562 57843 22988 27372 31989 87571 41595 78111 96358 33005 94087 30681 21602 87649 62867 44604 77464 91599 50549 73742 56269 01049 03778 19868 35938 14657 41268 04925 64879 85561 45372 34786 73303 90468 83834 36346 55379 49864 19270 56387 29317 48723 32083 76011 23029 91136 79386 27089 43879 93620 16295 15413 37142 48928 30722 01269 01475 46684 76535 76164 77379 46752 00490 75715 55278 19653

Mathematics @ IISER Pune

2015

Chitrabhanu Chaudhuri Debangana Mukherjee Debargha Banerjee Diganta Borah Dipramit Majumdar Girish Kulkarni Gunja Sachdeva Hitesh Raundal Jatin Majithia Jyotirmoy Ganguly K Hariram Kalpesh Pednekar Kaneenika Sinha Krishna Kaipa Makarand Sarnobat Manidipa Pal

A Raghuram Advait Phanse Akash Krishna Aman Jhinga Amit Hogadi Anindya Goswami Anisa Chorwadwala Anup Biswas Anupam Singh Ayan Mahalanobis Ayesha Fatima Baskar Balasubramanyam Bhagyalaxmi Bhakti Bhushan Manna Chaitanya Ambi Chandrasheel Bhagwat

Milan Kumar Das Mousumi Bhakta Neha prabhu Nishad Mandlik Prabhat Kushwaha Pralhad Shinde Pranay Goel Preeti Rabeya Basu Rama Mishra Rashmi Kulkarni Reshma Chandrasekharan Rohit Joshi Ronnie Sebastian Sanket Nandan Shirish Kulhari

Shiva Chidambaram Soumen Maity Steven Spallone Sudhir Pujahari Supriya Pisolkar Sushil Bhunia Suvarna Gharat Tathagata Mandal Tejas Kalelkar Uday Jagadale Uttara Naik-Nimbalkar Vivek Mallick Yasmeen Akhtar

People in Math@IISER Pune

Compiling, Editing and Design: Anisa Chorwadwala and Shanti Kalipatnapu Photo Courtesy: Makarand Sarnobat, VS Rao, Anisa Chorwadwala, Stefan Friedl, and other contributors from IISER Pune Cover Page: Pi value up to 10,000 digits taken from http://www.math.utah.edu/~pa/math/pi.html

I am now into my fourth year as Coordinator for Mathematics at IISER Pune, and life here, as always, is full of new beginnings. Starting this semester, all the mathematics personnel are now comfortably ensconced in the top floor of the Main Building at IISER Pune. Such beginnings invariably give a new energy and there is this feeling that in front of us is evolving a path that we were born to take… a path full of beautiful theorems and pretty lemmas just waiting to be proved by the eager minds of IISER Pune!

The last year has seen us consolidate our strengths. We are now 22 regular faculty members, 1 INSPIRE fellow, and 1 visiting professor, 2 post-docs with possibly two more joining us later this year. Our PhD program is now going very well, and it is a pleasure to see some of our students blossoming into mathematicians. From this coming fall semester we will be starting an integrated-PhD program. Our BS-MS students who graduated in 2014 got selected into top-quality programs around the world such as University of Michigan, USA; University of Washington at Seattle, USA; Essen University, Germany; INSEAD, France etc.

We have continued with our tradition of hosting high-profile events at IISER Pune. In June 2014, there was an international workshop on “p-adic Aspects of Modular Forms” followed by the “29th Annual Conference of the Ramanujan Mathematical Society.” The “Young Women and Mathematics” symposium in July capped off a very busy summer. And, later in December, we had “Advances in Mathematical Biology.” Events such as these go a long way in establishing IISER Pune as a vibrant center for Mathematics!

A Raghuram Professor and Coordinator Mathematics, IISER Pune

Academic & Administrative Support

Welcome Message

Algebraic Geometry

One can describe algebraic geometry as the study of varieties, which are spaces defined by vanishing of polynomial equations. I have been interested in moduli spaces which are special types of varieties which parametrize geometric objects. In the last couple of decades, people have succeeded in applying ideas from topology, especially homotopy theory, to the study of algebraic varieties. This interplay between homotopy theory and algebraic geometry has been one of my latest fascinations. Currently, I am working on problems which are sometimes clubbed under the title homotopical algebraic geometry and have applications to K-theory, motivic cohomology and also classical topics like Brauer groups. Selected Publications With Indranil Biswas. Fundamental group of quotient singularities. To appear in International

Mathematics Research Notices.

Esnault, H. and Hogadi, A. (2012). On the algebraic fundamental group of smooth varieties in

characteristic p>0. Transactions of the American Mathematical Society 364:2429-2442.

Hogadi, A. and Mehta, V. (2011). Birational invariance of the S-fundamental group scheme. Pure and

Applied Mathematical Quarterly 7(4):1361-1370.

Hogadi, A. and Pisolkar, P. (2011). On the cohomology of Witt vectors of p-adic integers and a

conjecture of Hesselholt. Journal of Number Theory 131(10):1797-1807.

Hogadi, A. and Xu, C. (2009). Degenerations of rationally connected varieties. Transactions of the

American Mathematical Society 361(7):3931-3394.

Amit Hogadi

Associate Professor amit@iiserpune.ac.in Amit Hogadi received PhD from Princeton University, USA in 2007. He was at Tata Institute of Fundamental Research (TIFR), Mumbai, India before joining IISER Pune in December 2013.

Stochastic Control – Game Theory, Math Finance, Queuing Networks, Renewal Processes

I am exploring various topics in Applied Probability. Those include generalization of Black-Sholes-Merton PDE for options in semi-Markov modulated market, Föllmer Schweizer decomposition of an unattainable contingent claim, equilibrium of non-cooperative semi-Markov game under ergodic cost, optimal control under risk sensitive cost, portfolio optimization, large deviation limit, fluid limit in queuing network, PDE techniques in stochastic control and differential games etc.

I use Markov models, filtering techniques, stochastic calculus, infinitesimal generator for semigroup of operators, mild solution technique for parabolic equations, viscosity solution method for HJB/HJI equations, stability analysis of numerical schemes for solving PDE or IE, convergence of value iteration schemes, marginalization technique in rare event simulation for hybrid processes, martingale formulation for Markov processes etc.

Selected Publications Goswami, A. and Saini, R.K. (2014). Volterra equation for pricing and hedging in a regime switching

market. Cogent Economics & Finance 1(2):1-11. Atar, R., Goswami, A. and Shwartz, A. (2014). On the risk-sensitive cost for a Markovian multiclass

queue with priority. Electronic Communications in Probability 19(11):1-13. Atar, R., Goswami, A. and Shwartz, A. (2013). Risk-sensitive control for the parallel server model.

SIAM Journal on Control and Optimization 51:4363-4386. Basak, G.K., Ghosh, M.K. and Goswami, A. (2011). Risk minimizing option pricing for a class of exotic

options in a Markov modulated market. Stochastic Analysis and Applications 29:259-281. Ghosh, M.K., Goswami, A. and Kumar, S.K. (2010). Portfolio optimization in a Markov modulated

market: Chapter in Modern Trends In Controlled Stochastic Processes: Theory and Applications. Luniver Press, pp. 181-195.

Ghosh, M.K., Goswami, A. and Kumar, S.K. (2009). Portfolio optimization in a semi-Markov modulated market. Applied Mathematics & Optimization 60:275-296.

Ghosh, M.K. and Goswami, A. (2009). Risk minimizing option pricing in a semi-Markov modulated market. SIAM Journal on Control and Optimization 48:1519-1541.

Ghosh, M.K. and Goswami, A. (2008). Partially observable semi-Markov games with average payoff. Journal of Mathematical Analysis and Applications 345:26-39.

Anindya Goswami Assistant Professor anindya@iiserpune.ac.in

Anindya Goswami received his PhD from Indian Institute of Science (IISc), Bangalore, India in 2008. Following this, he held postdoctoral positions at the Universiteit Twente in Enschede, The Netherlands; INRIA in Rennes, France; and Technion in Haifa, Israel before joining IISER Pune in 2011.

Shape Optimization Problems

My research work falls mainly in the following two branches of Mathematics: Partial differential equations and Riemannian geometry. I work on shape optimization problems including isoperimetric problems. A typical shape optimization problem is to find a shape which is optimal in the sense that it minimizes a certain cost functional while satisfying given constraints. In many cases, the functional being minimized depends on the solution of a given partial differential equation defined on the variable domain.

We have solved some shape optimization problems for a class of doubly connected domains over Rank-one symmetric spaces of non-compact type. Among the Rank-one symmetric spaces of compact type, we dealt only with the case of Sn, the unit sphere in ℝn+1 with the induced metric. In fact, we gave a uniform proof for all the three space forms. Here, the functionals to be optimized were the energy functional and the principal frequency associated with the Dirichlet boundary value problem and the Dirichlet Eigenvalue problem respectively, for both linear as well non-linear operators, namely the Laplacian and the p-Laplacian.

Moving Plane Method for a punctured ball on the unit sphere

Selected Publications Anisa, M.H.C. and Mahadevan, R. A shape optimization problem for the p-Laplacian. Proceedings of

the Royal Society of Edinburgh (Accepted for Publication). Anisa, M.H.C., Mahadevan, R. and Toledo, F. (2015). On the Faber-Krahn inequality for the Dirichlet

p-Laplacian. ESAIM: Control, Optimisation and Calculus of Variations DOI: 10.1051/cocv/2014017

Anisa, M.H.C. and Vemuri, M.K. (2013). Two functionals connected to the Laplacian in a class of doubly connected domains on rank one symmetric spaces of non-compact type. Geometriae Dedicata 167(1):11-21.

Anisa M H Chorwadwala

Assistant Professor anisa@iiserpune.ac.in Anisa Chorwadwala received her PhD from University of Mumbai in 2007. Following this, she held postdoctoral positions at the Institute of Mathematical Sciences (IMSc), Chennai; Abdus Salam International Centre for Theoretical Physics (ICTP), Trieste, Italy; and Tata Institute of Fundamental Research (TIFR), Mumbai. She has been on the faculty of IISER Pune since April 2011.

Stochastic Controls and Queuing Theory

My broad research area falls under Applied Probability. I am mainly interested in stochastic controls, small noise diffusion, asymptotics of queuing networks and many other related models.

In the last couple of years, I have worked on problems from queuing theory that involves measure-valued process. Such processes have proven powerful in modeling queuing networks with general service and reneging distributions. Another important area of queuing theory is scheduling control where one looks for a policy that optimizes certain cost associated to the model. I also work on such control problems.

Selected Publications Arapostathis, A., Biswas, A. and Pang, G. Ergodic control of multi-class M/M/N+M queues in the

Halfin-Whitt regime. To appear in Annals of Applied Probability.

Atar, R., Biswas, A. and Kaspi, H. Fluid limits of G/G/ 1+G queues under non-preemptive Earliest-

Deadline-First discipline. To appear in Mathematics of Operation Research.

Biswas, A. (2014). Risk-sensitive control for the multiclass many-server queues in the moderate

deviation regime. Mathematics of Operation Research 39(3):908-929.

Atar, R. and Biswas, A. (2014). Control of the multiclass G/G/1 queue in the moderate deviation

regime. Annals of Applied Probability 24(5).

Anup Biswas

Assistant Professor anup@iiserpune.ac.in Anup Biswas received his PhD from TIFR-Centre for Applicable Mathematics, Bangalore, India in 2011. He held postdoctoral positions at Technion, Israel, and University of Texas, Austin, USA before joining IISER Pune.

Conjugacy Questions and Representation Theory of Groups

Conjugacy questions in group theory have been of interest for its connection with the representation theory and they have not been understood very well for Algebraic Groups over arbitrary field. Usually groups are difficult objects and one studies them via their representations to get better understanding.

Let G (e.g. GLn) be an algebraic group defined over a field k. We denote the k points of G by G(k) (e.g. GLn(k), SLn(k) etc.). An element t of G(k) is said to be real if it is conjugate to its own inverse in G(k). I have been concerned with finding real elements in algebraic groups. Very interestingly often it relates to finding strongly real elements (the elements which are product of two involutions in G(k)).

Apart from studying structure of real elements in Algebraic Groups over k, I also looked at many examples such as linear groups, orthogonal groups, symplectic groups and the groups of type G2 to get better understanding of the problem. Finding real elements helps in the understanding of real characters of the group which in turn give information about those complex representations of the group which are either orthogonal or symplectic.

Selected Publications Gates, Z., Singh, A. and Ryan Vinroot, C. Strongly real classes in finite Unitary groups of odd

characteristic. To appear in the Journal of Group Theory. Kulshrestha, A. and Singh, A. (2011). Real elements and Schur indices of a group. The Mathematics

Student 80:73-84. Gill, N. and Singh, A. (2011). Real and strongly real classes in PGLn(q) and quasi-simple covers of

PSLn(q). Journal of Group Theory 14:461-489. Gill, N. and Singh, A. (2011). Real and strongly real classes in SLn(q). Journal of Group Theory 14:437-459.

Anupam Kumar Singh

Assistant Professor anupam@iiserpune.ac.in After doing MSc (Mathematics) from Indian Institute of Technology (IIT) Kanpur, Anupam Singh worked for his doctorate at Harish Chandra Research Institute, Allahabad and Indian Statistical Institute (ISI), Bangalore, India and got PhD from ISI in 2007. He held postdoctoral positions at Tata Institute of Fundamental Research (TIFR), Mumbai and Institute of Mathematical Sciences (IMSc), Chennai, India before joining the faculty of IISER Pune in 2008.

Public Key Cryptography

I work at the intersection of pure mathematics (group theory) and public key cryptography. Cryptography, especially public key cryptography, is the backbone of a modern society. It serves us with the required tools for online transactions and trading, i.e., online commerce.

My research aims to find new cryptograhic primitives and to build secure protocols from that. We look for groups in which the discrete logarithm problem is secure. My recent work has shown that the group of non-singular circulant matrices over a finite field has some properties that make them attractive over the discrete logarithm problem on a finite field. This new finding has opened a new avenue in research of public key cryptography.

Selected Publications Mahalanobis, A. The ElGamal cryptosystem over circulant matrices (Submitted). Mahalanobis, A. and Shah, J. (2014). A new guess-and-determine attack on the A5/1 stream cipher.

Computer and Information Science 7(1):115-124. Mahalanobis, A. (2013). Are matrices useful in public-key cryptography? International Mathematical

Forum 8(39):1939-1953. Mahalanobis, A. The MOR cryptosystem and extra-special p-groups. Proceedings of WCC 2012,

Castro Urdiales, Spain July 9-13, 2012 & To appear in Journal of Discrete Mathematics and Cryptography.

Mahalanobis, A. (2013). The automorphism group of the group of unitriangular matrices over a field. International Journal of Algebra 7(15):723-733.

Mahalanobis, A. (2012). A simple generalization of the ElGamal cryptosystem to non-abelian groups II. Communications in Algebra 40:3583-3596.

Mahalanobis, A. (2010). The discrete logarithm problem in the group of non-singular circulant matrices. Groups Complexity Cryptology 2:83-89.

Ayan Mahalanobis

Assistant Professor ayanm@iiserpune.ac.in Ayan Mahalanobis obtained his PhD from Florida Atlantic University, Boca Raton, USA in 2005. He was a Visiting Assistant Professor at the Stevens Institute of Technology, New Jersey, USA for a few years before joining IISER Pune in 2009.

Modular Forms and Galois Representations

My research interests are in Number Theory. A modular form is essentially a function defined on the complex upper half-plane (everything above the real axis) that behaves in a good way under transformations of certain 2x2 matrices with integer entries. The expansion at infinity of such a function gives us a power series whose coefficients have interesting arithmetic properties. An important example of numbers that arise in such a way is the Ramanujan Tau function τ(n). In order to understand these coefficients, it is useful to consider an object attached to it called the L-function (these are generalizations of the Riemann zeta function).

A Galois group is a set of permutations of roots of an irreducible polynomial. For example, complex conjugation permutes the roots of x2+1. It is possible to represent such permutations by matrices. One of the problems in Number Theory is to try and understand the Galois group by studying its representations. One can also attach L-functions to Galois representations and in some cases modular forms and Galois representations are related through their L-functions.

Selected Publications Balasubramanyam, B., Ghate, E. and Vatsal, V. (2013). On local Galois representations over totally

real fields. Manuscripta Mathematica 142:513-524. Balasubramanyam, B. and Longo, M. (2010). ∧-adic modular symbols over totally real fields.

Commenterii Mathematici Helvetici 86:841-865.

Balasubramanyam, B. and Raghuram, A. Special values of adjoint L-functions and congruences for

automorphic forms on GL(n) over a number field (Submitted)

Baskar Balasubramanyam

Assistant Professor baskar@iiserpune.ac.in Baskar Balasubramanyam completed his PhD from Brandeis University, USA in 2007. In 2007-08, he was a postdoctoral fellow at the Center for Advanced Study in Mathematics at the Ben-Gurion University of the Negev in Israel. Following this, he was a Bateman Instructor at California Institute of Technology, USA during 2008-10. He has been with IISER Pune since September 2010.

Representation Theory, Analysis & Geometry of Locally Symmetric Spaces, Number Theory

The interplay between arithmetic, spectral theory and geometry was studied by mathematicians like Selberg, Maass, and Sunada among many others. From the last few years, I have been working on the study of arithmetic aspects of the spectral theory and geometry of symmetric spaces. My thesis work involved proving various analogues of the classical number theoretic results in the context of symmetric spaces. I am also interested in the study of analytic properties of the Zeta functions associated to a rank one locally symmetric space, which encode a lot of spectral and geometric data. They can be considered as the spectral counterparts of the Dedekind zeta functions associated to number fields. I would like to look at some of the `inverse problems’ on locally symmetric spaces with the aid of the Zeta functions mentioned above.

In a joint work with Prof CS Rajan and Dr Supriya Pisolkar, we have established some results which relate the notions of weak commensurability (introduced by Prasad and Rapinchuk) and representation equivalence of arithmetic lattices in Lie groups. These notions are in turn related to the geometry and spectral theory of the locally symmetric spaces defined by them. I am currently working (jointly with Dr Supriya Pisolkar) on some of the related problems on discrete subgroups of Lie groups.

My joint work with Prof Raghuram establishes period relations for the tensor product of motives which together with the celebrated Deligne’s conjecture; predict the results of a similar nature about the special values of Rankin - Selberg L-functions and Dirichlet L-series. I am interested in working on some related problems about special values for automorphic L-functions associated to representations of algebraic groups; using techniques like Cohomology of sheaves and Langlands constant term theory.

Selected Publications Bhagwat, C. (2015). On Deligne's periods for tensor product motives. Comptes rendus –

Mathématique 353:191-195. Bhagwat, C., and Raghuram, A. (2013). Ratios of periods for tensor product motives. Mathematical

Research Letters 20(4):615-628. Bhagwat, C., Pisolkar, S., and Rajan, C.S. (2013). Commensurability and representation equivalent

arithmetic lattices. International Mathematics Research Notices (IMRN) doi:10.1093/imrn/rns282. Bhagwat, C. and Rajan, C.S. (2011). On a multiplicity one property for the length spectra of even

dimensional compact hyperbolic spaces. Journal of Number Theory doi:10.1016/j.jnt.2011.05.009.

Bhagwat, C. and Rajan, C.S. (2010). On a spectral analogue of the strong multiplicity one theorem. International Mathematics Research Notices doi:10.1093/imrn/rnq243.

Chandrasheel Bhagwat

Assistant Professor cbhagwat@iiserpune.ac.in Chandrasheel Bhagwat obtained Bachelor of Science in Mathematics from Fergusson College, Pune in 2003 followed by Master of Mathematics at Indian Statistical Institute, Bangalore in 2005. He completed PhD in Mathematics from Tata Institute of Fundamental Research (TIFR) Mumbai, India in 2011 and spent a few months as a postdoctoral fellow at IISER Pune. He has received the DST-INSPIRE faculty award and research grant in 2011 and has joined IISER Pune as INSPIRE Faculty Fellow in March 2012. From December 1, 2014, he has been working as an Assistant Professor at IISER Pune.

Automorphic Forms and Arithmetic Geometry

In arithmetic geometry, we study the integral solutions of polynomial equations. In arithmetic geometry we usually work over non-algebraically closed fields (like rational numbers), and often in fields of non-zero characteristic (like finite fields), and we may even restrict ourselves even to rings that are not a field (like integers). We use the rich theory of modular forms (more generally, automorphic representations) to find these solutions.

Modular forms/ automorphic forms are generalizations of the periodic functions like sine or cosine. The theory of modular forms made major contributions in several important discoveries in modern mathematics, including the uniform boundedness of torsion point of elliptic curves.

I am interested in understanding objects in geometry called “motives” and objects in analysis called automorphic representations. The overarching bridge/conjecture of Langlands connects these two fairly faraway worlds. I am interested in understanding the integral and $p$-adic bridges that connect these two beautiful universes.

In the automorphic universe, I wish to focus on modular symbols and special values of L-functions (one of the main objects of study in the Langlands' program). Motives can be described by different cohomology theories. I wish to understand and use different cohomology theories using modular symbols, which in turn give insights into special values of L-functions.

In another work, I developed the theory of differential modular forms for Shimura curves over totally real fields. The differential modular forms were invented by Buium and his collaborators. These work open the p-adic bridge of certain automorpic forms.

Selected Publications Banerjee, D. (2014). A note on the Eisenstein elements of prime square level. Proceedings of the

American Mathematical Society 142:3675-3686. Banerjee, D. (2014). Differential modular forms on Shimura curves over totally real fields. Journal of

Number Theory 135:353-373. Banerjee, D. and Ghate, E. (2013). Adjoint lifts and modular endomorphism algebras. Israel Journal of

Mathematics 195(2):507-543. Banerjee, D. and Ghate, E. (2011). Crossed product algebras attached to weight one forms.

Mathematical Research Letters 18(1):139-149. Banerjee, D., Ghate, E. and Kumar, N. (2010). ∧-adic forms and the Iwasawa main conjecture.

Iwasawa Theory of totally real Fields (Proceedings of a Workshop held at IIT Guwahati, published by Ramanujan Mathematical Society) 2010, No. 12. pp.15-47.

Banerjee, D. and Krishnamoorthy, S. The Eisenstein elements inside the space of modular symbols (Submitted).

Banerjee, D. and A. Raghuram, p-adic L-functions for GLn (preprint, expository article)

Debargha Banerjee

Assistant Professor debargha@iiserpune.ac.in Debargha Banerjee received his PhD degree from Tata Institute of Fundamental Research, Mumbai. He earned his Master’s degree in Mathematics from Indian Statistical Institute and BSc from St Xavier’s College, Kolkata. He got the Australian Research council Discovery postdoctoral fellowship for 2 years at the Australian National University, Canberra, Australia. He was a visiting scientist at the IMSC, Chennai, India and later a guest scientist at the Max Planck institute of Mathematics, Bonn, Germany before joining IISER Pune in November 2013.

Several Complex Variables

My research interests are in Several Complex Variables, Potential Theory and in Differential Geometry. In the past, I studied various properties of a Kahler metric, known as the Robin metric defined on bounded pseudoconvex domains in Cn, n>1. This metric was constructed by N. Levenberg and H. Yamaguchi using the Robin function that arises from the Green function associated to the standard Laplacian in C^n. Currently, I am studying various questions related to the motion of critical points and the differential geometry of level lines of the Green function of a bounded multiply connected domain in the complex plane. I am also investigating properties of the metric induced by the capacity function on such domains. Selected Publications Remarks on the metric induced by the Robin function III (Submitted). Borah, D. (2013). Remarks on the metric Induced by the Robin Function II. Michigan Mathematical

Journal 62(3):581-630. Borah, D. and Verma, K. (2011). Remarks on the metric induced by the Robin function. Indiana

University Mathematics Journal 60:751-802.

Diganta Borah

Assistant Professor dborah@iiserpune.ac.in Diganta Borah received his PhD from the Indian Institute of Science (IISc), Bangalore, India in 2010 and was a Research Associate there until 2011. He joined IISER Pune in January 2012.

Analytic Number Theory, Harmonic Analysis and Arithmetic Geometry

My primary research work is concerned with extremal functions in Fourier analysis, equidistribution of Fourier coefficients of modular cusp forms, Eichler-Selberg trace formula and arithmetic of modular curves. Modular forms play an extremely important role in number theory and their Fourier coefficients carry fundamental information about points of elliptic curves over finite fields, values of the partition function, class numbers and representations of integers by quadratic forms. They are essential tools in addressing many fundamental problems in Mathematics, like Fermat's Last Theorem. Modular forms are a special case of automorphic representations and lead to the Langlands program, a theme that drives much of the twenty first century research in number theory and representation theory. My research program focuses on the behavior of the Fourier coefficients of normalized Hecke eigenforms and their connections with Jacobian varieties of modular curves.

My research program in number theory heavily draws ideas and techniques from various mathematical areas, like harmonic analysis and arithmetic geometry. The problems pursued by me are posed in the language of algebra and geometry, where as the techniques used in resolving them come from harmonic analysis. Moreover, a comprehensive understanding of these questions necessitates approaching them from a representation-theoretic point of view.

Selected Publications Bucur, A., David, C., Feigon, B., Lalín, M. and Sinha, K. (2012). Distribution of zeta zeroes of Artin-

Schreier covers. Mathematical Research Letters.

Lalín, M. and Sinha, K. (2011). Higher Mahler measure for cyclotomic polynomials and Lehmer's

question. The Ramanujan Journal 26:257-294.

Ram Murty, M. and Sinha, K. (2010). Factoring newparts of Jacobians of certain modular curves.

Proceedings of the American Mathematical Society 138:3481-3494.

Ram Murty, M. and Sinha, K. (2009). Effective equidistribution of eigenvalues of Hecke operators.

Journal of Number Theory 129:681-714.

Kaneenika Sinha

Assistant Professor kaneenika@iiserpune.ac.in Kaneenika Sinha completed her PhD from Queen's University, Canada in 2006. She has held postdoctoral fellowships at University of Toronto, University of Alberta and Mathematical Sciences Research Institute, Berkeley. She was an assistant professor in IISER Kolkata before joining IISER Pune in December 2012.

Algebraic Geometric Coding Theory

My recent work is about studying Error Correcting Codes from the viewpoint of projective geometry over finite fields.

To give a flavour of the kind of questions I am working on currently, consider k by n matrices over a finite field with q elements (say q is odd) such that all k by k minors of this matrix are nonzero. Let us call such a matrix MDS.

Question: What can we say about 3 by q+1 MDS matrices? Segre showed that any such matrix is row equivalent to a matrix whose columns lie on the conic y^2 = xz. Question: Do there exist k by q+2 MDS matrices when k <q? The negative answer to this question is the main conjecture about MDS matrices/codes. Selected Publications Kaipa, K. (2014). An asymptotic formula in q for the number of [n,k] q-ary MDS codes. IEEE

Transactions on Information Theory 60(11):7047-7057. With Harish Pillai (2013). Weight spectrum of codes associated with the Grassmannian G(3,7), IEEE

Transactions on Information Theory 59(2):986-993. With Sudhir Ghorpade (2013). Automorphism groups of Grassmann codes, Finite fields and its

Applications 23:80-102. With Peter Grinevich (2009). Multiscale limit for finite-gap Sine-Gordon Solutions and Calculation of

Topological Charge using Theta-functional Formulae. Proceedings of Steklov Mathematical Institute 266(1):49-58.

Krishna Kaipa

Assistant Professor kaipa@iiserpune.ac.in Krishna Kaipa obtained a BTech from IIT Bombay and an MS degree from University of Maryland College Park, both in Mechanical Engineering. He then pursued a PhD in Mathematics from University of Maryland, College Park. He held assistant professor positions at IIT Bombay and IISER Bhopal before moving to IISER Pune in 2014.

Elliptic Partial Differential Equations

My research interest includes semilinear and quasilinear elliptic partial differential equations arising from geometry and physics. I study existence/nonexistence of positive/sign-changing solutions, qualitative properties of solutions, regularity properties etc using the techniques from nonlinear analysis.

One of my main research areas is studying the second order and fourth order semilinear and quasilinear elliptic equations with singularity. Such second order equations for example, Hardy-Sobolev type equations arise in astrophysics. Fourth order equations, for example, equations with biharmonic operator arise in continuum mechanics, bio-physics, geometry. In particular, in the modeling of thin elastic plates, clamped plates and in the study of the Paneitz-Branson equation etc.

The other area of my research is studying the semilinear elliptic equations with measure data, generalized boundary trace and generalized boundary value problems.

Selected Publications Bhakta, M. A note on semilinear elliptic equation with biharmonic operator and multiple critical

nonlinearities. To appear in Advanced Nonlinear Studies.

Bhakta, M. (2015). Entire solutions for a class of elliptic equations involving p-biharmonic operator

and Rellich potentials. Journal of Math Analysis and Applications 423(2).

Bhakta, M and Marcus, M. (2014). Semilinear elliptic equations admitting similarity transformations.

Journal of Functional Analysis 267(10).

Bhakta, M. and Marcus, M.(2014). Reduced limit for semilinear boundary value problems with

measure data. Journal of Differential Equations 256(8).

Bhakta, M, and Musina, R. (2012). Entire solutions for a class of variational problems involving the

biharmonic operators and Rellich potentials. Nonlinear Analysis 75(9).

Bhakta, M. and Sandeep, K. (2012). Poincar’e-Sobolev equations in the hyperbolic space. Calculus of

Variations and Partial Differential Equations 44(1-2).

Bhakta, M, and Biswas, A. (2011). Hardy-Sobolev type equations for p-Laplacian, 1<p<2, in bounded

domain. Differential and Integral Equations 24(1-2).

Bhakta, M. and Sandeep, K. (2009). Hardy-Sobolev-Mazy’a type equations in bounded domains,

Journal of Differential Equations 247(1).

Mousomi Bhakta

Assistant Professor mousomi@iiserpune.ac.in Mousomi Bhakta received her PhD from TIFR-Centre for Applicable Mathematics, Bangalore, India in August, 2011. After that she held visiting scientist position in ICTP, Trieste, Italy for two months. Next, she had postdoctoral positions at Technion, Israel for two years and University of New England, NSW, Australia for one year before joining IISER Pune in August 2014.

Dynamical Systems Modeling of Multiscale Phenomena in Biology

Dynamical processes in biology naturally span several systems and multiple scales, both in space and in time. We are interested in studying the dynamical behavior of biological processes through mathematical modeling to complement experimental understanding. My research focuses primarily on theoretical neuroscience, cardiac dynamics and diabetes. Each of these areas is rich with issues that arise from a fundamental need to develop theoretical frameworks, and to handle multiscale dynamics within those.

Our understanding of glucose-stimulated insulin secretion from the pancreatic endocrine tissue, the islets of Langerhans, has developed considerably over the last three decades. Much of my recent work has been related to analyzing some newly proposed models of islet voltage oscillations (called “bursting”) that implicate both ionic as well as metabolic activity as being jointly responsible for function. Simultaneously, we are also interested in modeling and analysis of data collected from patients diagnosed with Type 2 diabetes. This is joint work with researchers at the University of Pune and K. E. M. Hospital, Pune.

Although we are a dry lab, since such research is highly interdisciplinary in nature, we collaborate extensively with experimentalists.

Selected Publications Goel, P. and Sherman, A. (2009). The geometry of bursting in the dual oscillator model of pancreatic

beta-cells. SIAM Journal on Applied Dynamical Systems (SIADS) 8:1664-1693.

Goel, P., Sherman, A. and Friedman, A. (2009). Multiscale modeling of electrical and intracellular

activity in the pancreas: The islet Tridomain equations. SIAM Multiscale Modeling and Simulation

7:1609-1642.

Zhang, M., Fendler, B. Peercy, B., Goel, P., Bertram, R., Sherman, A., Satin, L. (2008). Long lasting

synchronization of calcium oscillations by cholinergic stimulation in isolated pancreatic islets.

Biophysical Journal 95:4676-4688.

Higgins, E.R., Goel, P., Puglisi, J.L., Bers, D.M., Cannell, M. and Sneyd, J. (2007). Modeling calcium

microdomains using homogenization. Journal of Theoretical Biology 247:623-644.

Goel, P., Sneyd, J. and Friedman, A. (2006). Homogenization of the cell cytoplasm: The calcium

bidomain equations. SIAM Multiscale Modeling and Simulation 5:1045-1062.

Pranay Goel

Assistant Professor pgoel@iiserpune.ac.in Pranay Goel received his PhD in Physics at the University of Pittsburgh, USA. His postdoctoral work was carried out at the Mathematical Biosciences Institute, The Ohio State University, and at the Laboratory of Biological Modeling, NIDDK, National Institutes of Health, USA. He joined the Mathematics and Biology faculty at IISER Pune in 2009.

Classical Algebraic K-theory

My work is based on problems in classical K-theory which are related to Serre’s problem on projective modules, widedly known as Quillen-Suslin theorem.

One of such problem is Quillen-Suslin’s local-global principle. This was one of the main ingredient for the proof of Serre’s problem. I work on the matrix version of this theorem introduced by A. Suslin to give a simpler proof of the theorem. There are many generalizations and variations of this local-global technique for different types of classical groups. I have worked for general quadratic and general Hermitian groups.

Another type of problems is stabilization of K1 functor and the structure of unstable K1 Groups. These problems are also studied for different types of classical groups. Recently, I have studied the solvability property of the unstable K1 group for the general Hermitian group.

Our method of proof can be used uniformly for many other classical groups. In my PhD thesis we have given the uniform treatment for general linear, symplectic and orthogonal groups. We have also deduced a module theoretic version of local-global principle which is useful to generalize results from the free case to the module case. At present I am working on this local-global principle for the transvection subgroup of the general quadratic module.

Selected Publications Basu, R. Local-global principle for the general quadratic and the general Hermitian groups and the

nilpotence of KH1 (Submitted).

Basu, R. (2013). On elementary subgroup of GLn over rings. Ramanujan Mathematical Society

Newsletter 24(3).

Basu, R. (2011). Absence of torsion for NK1(R) over associative rings. Journal of Algebra and its

Applications 10:793-799.

Basu, R. and Rao, R.A. (2010). Injective stability for K1of regular rings. Journal of Algebra 323:367-

377.

Bak, A., Basu, R. and Rao, R.A. (2010). Local-global principle for Transvection groups. Proceedings

of the American Mathematical Society 138:1191-1204.

Basu, R. and Sridharan, R. (2007). An expository article: On Forster's conjecture and related results.

Punjab University Research Journal.

Rabeya Basu

Assistant Professor rbasu@iiserpune.ac.in Rabeya Basu received her PhD from Tata Institute of Fundamental Research (TIFR), Mumbai, India in 2007. She then undertook postdoctoral work initially at Harish Chandra Research Institute, Allahabad and later as an NBHM Fellow at the Indian Statistical Institute, Kolkata, India. She was in IISER Kolkata as an assistant professor before joining IISER Pune in 2010.

Low Dimensional Topology

For a reasonably long period of time my research focused around the Polynomial representation of long knots. It was motivated by the issue of settling a long lasting conjecture of Abhayankar. We established the equivalence between polynomial isotopic classes of long knots with the ambient isotopic classes of classical knots. Thus the entire knot theory can be done over polynomial knot category. I am trying to compute some numerical knot invariants such as unknotting number through polynomial knot theory. Quantum topology is one of the emerging research areas. Many knot invariants naturally arise through nice matrix algebra representation of interesting quantum groups. They have been related to several models in statistical mechanics. I would like to explore some models that are related to Singular knot theory.

I am also interested in classical knot invariants and their application in mathematics and biological sciences. My joint work with Prof Louis Kauffman on nodal parity invariants of knotted rigid vertex graphs discusses the application of this invariant on protein folding classification.

Selected Publications Mishra, R. (2014). Polynomial unknotting and singularity index. Kyungpook Mathematical Journal

54(2):271-292.

Kauffman, L. and Mishra, R. (2013). Nodal parity invariants for knotted rigid vertex graphs. Journal of

Knot Theory and its Ramifications 22(4):1340002.

Mishra, R. and Bhushan, S. (2012). Knot theory in understanding proteins. Journal of Mathematical

Biology 65:1187-1213.

Prabhakar, M. and Mishra, R. (2009). Minimal degree sequence for torus knots of type (p,q). Journal

of Knot Theory and its Ramifications 18:485-491.

Prabhakar, M. and Mishra, R. (2009). Polynomial representation for long knots. International Journal

of Mathematical Analysis 3:325-337.

Mishra, R. (2006). Polynomial representations of strongly invertible knots and strongly negative

amphicheiral knots. Osaka Journal of Mathematics 43:625-639.

Prabhakar, M. and Mishra, R. (2006). Minimal degree sequence of 2–bridge knots. Fundamenta

Mathematicae 3:190.

Rama Mishra

Associate Professor r.mishra@iiserpune.ac.in Rama Mishra has obtained her PhD from Indian Institute of Technology (IIT) Bombay, India in 1994. She spent a few years with Harish Chandra Research Institute, Allahabad and Indian Statistical Institute, Delhi as a postdoctoral fellow and then served as a faculty at IIT Kharagpur and IIT Delhi for several years. She worked as a JSPS fellow at Osaka City University, Japan for one year and as a visiting faculty at Boise State University, USA before joining IISER Pune.

Number Theory, Representation Theory and Automorphic Forms

My group is currently studying the arithmetic properties of special values of automorphic L-functions.

The earliest prototype of a special value of an L-function is the classical formula by Euler which says that the sum ∑ 1/n^2 of reciprocals of squares of all positive integers is π^2/6. More generally, suppose M = {a_n} is a sequence of numbers coming from some interesting data, for example, a_p can be the number of solutions of an equation modulo a prime p, then a guiding principle in modern number theory says that to study the sequence M one should study the L-function L(s, M) = ∑ a_n/n^s. One can glean much information about the sequence M by studying first the analytic properties, and second the arithmetic properties of L(s,M).

The Langlands program, considered by many as a grand unifying principle in modern mathematics, bridges different areas of mathematics, like geometry (elliptic curves), number theory (Galois representations) and representation theory (automorphic forms). The central theme making these bridges possible is the notion of an L-function.

Our work uses the results and techniques of the Langlands program to prove theorems about special values of various L-functions. These values encode within them a lot of arithmetic and geometric information of the objects to which the L-functions are attached. In earlier work stemming from my thesis, we have also studied the representation theory and harmonic analysis of p-adic groups.

Selected Publications and Editorial Work Critical values for Rankin-Selberg L-functions for GL(n) x GL(n-1) and the symmetric cube L-functions

for GL(2). To appear in Forum Mathematicum. The Bloch – Kato Conjecture for the Riemann Zeta Function, Editors: John Coates, A. Raghuram,

Anupam Saikia and R. Sujatha. pp. 312 To be published by Cambridge University Press. With Harald Grobner. On the arithmetic of Shalika models and the critical values of L-functions for

GL(2n). With an appendix by Wee Teck Gan. American Journal of Mathematics 136 (2014) 675-728.

With Chandrasheel Bhagwat. Ratios of periods of tensor product motives. Mathematical Research Letters 20 (2013) No. 4, 615-628.

With Wee Teck Gan. Arithmeticity for periods of automorphic forms. To appear in the Proceedings of the International Colloquium on “Automorphic representations and L-functions,” held in TIFR Mumbai, January 2012.

With Günter Harder. Eisenstein cohomology and ratios of critical values of Rankin-Selberg L-functions. C. R. Acad. Sci. Paris, Ser. I 349 (2011) 719-724.

With Naomi Tanabe. Notes on the arithmetic of Hilbert modular forms. Journal of the Ramanujan Mathematical Society 26(3) (2011) 261-319.

On the special values of certain Rankin-Selberg L-functions and applications to odd symmetric power L-functions. International Mathematical Research Notices (2010) No. 2, 334-372.

A Raghuram

Professor and Coordinator raghuram@iiserpune.ac.in After getting a BTech in Computer Science and Engineering from Indian Institute of Technology (IIT) Kanpur, Raghuram moved to Mathematics and got a PhD in Mathematics in 2001 from the Tata Institute of Fundamental Research (TIFR), Mumbai, India. He had postdoctoral positions at University of Toronto, Canada and TIFR, Mumbai, India and visiting assistant professorships at Purdue University and University of Iowa, USA. He joined Oklahoma State University, USA in 2006 as a tenure-track assistant professor and was promoted to associate professor with tenure in 2011.Raghuram joined IISER Pune in December 2011 as a Professor and the Coordinator of Mathematics. His research has been partially funded by the National Science Foundation, USA, and the Alexander von Humboldt Foundation, Germany.

Algebraic Geometry

My research so far has dealt with questions in algebraic geometry. More specifically, with problems related to cycles on abelian varieties and problems related to moduli of vector bundles on curves and surfaces. In cycles I have been interested in a conjecture of Voevodsky which says that smash equivalence is the same as numerical equivalence. This conjecture has some very nice consequences, for instance, it implies that numerical and homological equivalence coincide, which is suggested by the standard conjectures of Grothendieck. My work on moduli of vector bundles has focused on proving Torelli theorems and theorems on rationality of vector bundles. I am currently focusing on expanding my research to number theory.

Selected Publications Sebastian, R. (2013). Smash nilpotent cycles on varieties dominated by products of curves.

Compositio Mathematica 149(9):1511-1518.

Biswas, I. and Sebastian, R. (2013). On rationality of moduli spaces of vector bundles on real

Hirzebruch surfaces. Proceedings of the Indian Academy of Sciences Mathematical Sciences

123(2):213-223.

Ronnie Sebastian

INSPIRE Faculty Fellow ronnie@iiserpune.ac.in After a Masters’ in Mathematics and Scientific Computing from Indian Institute of Technology (IIT) Kanpur, Ronnie Sebastian did a PhD with V Srinivas and Indranil Biswas at Tata Institute of Fundamental Research (TIFR), Mumbai. He then pursued postdoctoral research at the Institute of Mathematical Sciences, Chennai; Humboldt University, Berlin as an IMU Berlin Einstein Foundation Fellow; and at the Indian Statistical Institute, Bangalore before joining IISER Pune in May 2013.

Combinatorics − covering arrays, and cryptography

I am mostly interested in combinatorial problems. More specifically, I have been working on covering arrays on hypergraphs, and construction of cryptographically important Boolean functions. Covering Arrays on Hypergraphs: Covering arrays are combinatorial structures which extend the notion of orthogonal arrays and have applications in the realm of software and circuit testing. A covering array of strength three is an array with the property that any three rows are qualitatively independent. A covering array is optimal if it has the minimum number of columns among covering arrays with the same number of rows. We work on upper and lower bounds on the size of covering arrays on hypergraphs based on hypergraph homomorphism. Cryptography: Boolean functions are used as nonlinear combining functions in LFSR based stream ciphers. A Boolean function is said to be resilient if its output leaks no information about its input values. My research in this area presents some strategies to modify the bent functions, by toggling some of its outputs, in getting a large class of 1-resilient functions with very good nonlinearity and autocorrelation. Selected Publications Akhtar, Y, Maity, S. and Chandrasekharan, R.C. Covering arrays of strength four and software

testing. To appear in Springer Proceedings in Mathematics and Statistics.

Maity, S., Arackaparambil, C. and Meyase, K. (2013). A new construction of resilient Boolean

functions with high nonlinearity. Ars Combinatoria 109:171-192.

Maity, S. (2012). 3-Way software testing with budget constraints. IEICE Trans. Information & Systems

E95-D (9): 2227-2231.

Akhtar, Y. and Maity, S. (2012). Mixed covering arrays on hypergraphs. Communications in Computer

and Information Science 305:327-338.

Soumen Maity

Associate Professor soumen@iiserpune.ac.in Soumen Maity received a PhD from the Theoretical Statistics & Mathematics Unit at Indian Statistical Institute, Kolkata, India in 2002. He has postdoctoral experience from Lund University Sweden; Indian Institute of Management (IIM) Kolkata, India; and University of Ottawa, Canada. Prior to joining IISER Pune in 2009, he was at Indian Institute of Technology (IIT) Guwahati and Indian Institute of Technology (IIT) Kharagpur, India.

Representation Theory and Canonical Forms

A basic theme in representation theory for a topological group is the duality between the geometry of the group and its spectral theory. In one project, I study arithmetically interesting representations called “discrete series” using this duality. I attempt to write their multiplicities in terms of measures over conjugacy classes of p-adic groups.

In another project, I study representations of isometry groups of quadratic forms, notably those induced from a stabilizer P of a nondegenerate subspace. I show that relationships between such representations are illuminated by first decomposing P into two subgroups M and N, and then by finding canonical forms for the conjugation action of M on N.

To introduce another project, consider square matrices, with entries modulo a cubefree integer. I study the question of when two such matrices are conjugate. I have also written some papers regarding when two germs of dynamical systems fixing a point are conjugate, in the p-adic setting.

Selected Publications Spallone, S. (2012). Stable trace formulas and discrete series representations. Pacific Math Journal

256:435-488.

Jenkins, A. and Spallone, S. (2012). Local analytic conjugacy of semi-hyperbolic mappings in two

variables, in the non-archimedean setting. International Journal of Mathematics 23:1250059.

Shahidi, F. and Spallone, S. (2010). Residues of intertwining operators for SO(6) as character

identities. Compositio Mathematica 146:772-794.

Spallone, S. (2008). Residues of intertwining operators for classical groups. International Mathematics

Research Notices 056:37.

Margalit, D. and Spallone, S. (2007). A homological recipe for pseudo-Anosovs. Mathematical

Research Letters 14:853-863.

Steven Spallone

Associate Professor sspallone@iiserpune.ac.in Steven Spallone received his PhD from the University of Chicago, USA in 2004. Afterwards he did postdoctoral work at the Max-Planck Institute in Bonn, at Purdue University, and at the University of Oklahoma, USA. He also visited the Tata Institute of Fundamental Research (TIFR) Mumbai, India. He joined the faculty of IISER Pune in July 2012.

Number Theory, Galois Cohomology, Arithmetic Aspects of Symmetric Spaces

Broadly speaking, my area of research is number theory and I have been working on problems mostly related to local fields. My thesis deals with questions having a common theme of understanding behavior of norm maps in Galois extensions of local fields. As an application, I computed the Chow group of Zero-cycles of degree zero on Châtelet surfaces over local fields. This work relies on the work of Bloch, Swinnerton-Dyer, Colliot-Téllène, Sansuc.

In joint work with Dr A Hogadi, we proved a conjecture of Hesselholt which predicts the vanishing of the cohomology group H1(G(L/K),W(OL)) for a Galois extension of local fields L/K. This can be seen as an analogue of Hilbert theorem-90. In the future, I would like to work on generalizations of this result.

Over the last couple of years I have also been fascinated by arithmetic aspects of locally symmetric spaces which are special type of manifolds. The theory of locally symmetric spaces is a beautiful amalgamation of theory of Lie groups, algebraic groups, analysis, differential geometry, representation theory. In a joint work with Prof CS Rajan and Dr C Bhagwat we have studied questions related to commensurability type problems of these spaces.

Currently, I am interested in understanding the work of Gopal Prasad and Rapinchuk which establishes a connection between arithmetic and geometric aspects of these spaces, giving rise to series of questions in this area.

Selected Publications Bhagwat, C., Pisolkar, S. and Rajan, C.S. (2013). Commensurability and representation equivalent

arithmetic lattices. International Mathematical Research Notices doi: 10.1093/imrn/rns282.

Hogadi, A. and Pisolkar, S. (2013). An equicharacteristic analogue of Hesselholt’s conjecture on

cohomology of Witt vectors. Acta Arithmetica 158(2):165-171.

Hogadi, A. and Pisolkar, S. (2011). On the cohomology of Witt vectors of p-adic integers and a

conjecture of Hesselholt. Journal of Number Theory 131(10):1797-1807.

Pisolkar, S. (2008). The Chow group of zero-cycles on certain Châtelet surfaces over local fields.

Indagationes Mathematicae 19(3):427-439.

Supriya Pisolkar

Assistant Professor supriya@iiserpune.ac.in Supriya Pisolkar obtained her PhD degree from Harish Chandra Research Institute, Allahabad, India in 2010. She was a postdoctoral fellow at Tata Institute of Fundamental Research, Mumbai for about three years before joining IISER Pune in December 2013.

Low Dimensional Topology

My area of research is low-dimensional topology. This is a very active area of research with several longstanding conjectures proved fairly recently, like Thurston’s Geometrization conjecture (which implies the Poincare conjecture) and the Virtual Fibering conjecture. Within low-dimensional topology I focus mainly on foliations, triangulations and Heegaard splittings of 3-dimensional manifolds.

A closed book looks like a solid 3-dimensional object, but on closer analysis is observed to consist of 2-dimensional pages stacked tightly together. Similarly, every 3-manifold can be built by stacking 2-dimensional surfaces tightly together into what is called a foliation. I am studying a special class of foliations called taut foliations which tell us useful topological properties of the 3-manifold.

On cutting open a 3-manifold along a special embedded surface, called the Heegaard-splitting surface, we end up with two simple pieces called handlebodies. Every closed 3-manifold has such a splitting surface which may not be unique. I am currently working on a structure for these splitting surfaces when a 3-manifold has infinitely many of them.

Every 3-manifold can be built by suitably sticking tetraheda together. Normal surfaces are surfaces embedded particularly `nicely' with respect to such a triangulation. I have proved several results using normal surfaces, such as a weak converse of Haken’s well-known result about normality of incompressible surfaces with respect to every triangulation of the 3-manifold.

Selected Publications Kalelkar, T. and Roberts, R. Taut foliations in surface bundles with multiple punctures.

arXiv:1211.3637, Pacific Journal of Mathematics 273:257-275.

Gadgil, S. and Kalelkar, T. (2013). A Chain complex and Quadrilaterals for normal surfaces. Rocky

Mountain Journal of Mathematics, 43(2):479-487.

Kalelkar, T. (2009). Incompressibility and normal minimal surfaces. Geometriae Dedicata 142(1):61-

70.

Kalelkar, T. (2008). Euler characteristic and quadrilaterals of normal surfaces. Proceedings of the

Indian Academy of Sciences Mathematical Sciences 118(2):227-233.

Tejas Kalelkar

Assistant Professor tejas@iiserpune.ac.in After completing his MSc from Indian Institute of Technology, Bombay, Tejas Kalelkar got his PhD from Indian Statistical Institute, Bangalore in 2010. He was then a postdoctoral fellow at Institute of Mathematical Sciences, Chennai and a Chauvenet Postdoctoral Fellow at the Washington University in St Louis, USA. He joined IISER Pune in December 2013.

Statistics

My research interests are in the areas of inference in stochastic processes, survival analysis reliability theory and statistics in finance. Currently I am working on two problems.

(i) Modeling and analysis of statistical dependence: for example, in load sharing systems the failure of a component may reduce (increase) the lifetimes of the surviving components resulting in dependence between their lifetimes. (ii) Hypothesis testing problems in competing risks with missing causes of failure: the failure of a unit is caused by one of the several risks acting on it. It is of interest to know whether some risk dominates the others but sometimes the actual cause of failure for some units is missing.

Selected Publications Sutar, S.S. and Naik-Nimbalkar, U.V. (2014). Accelerated failure time models for loadsharing

systems. IEEE Transactions on Reliability 63(3):706-714.

Deshpande, J.V., Dewan, I. and Naik-Nimbalkar, U.V. (2010). A family of distributions to model load

sharing systems. Journal of Statistical Planning and Inference 140(6):1441-1451.

Lam, K.F., Deshpande, J.V., Lau, E.H., Naik-Nimbalkar, U.V., Yip, P.S. and Xu, Y. (2009). A test for

constant fatality rate of an emerging epidemic, with applications to the SARS syndrome in Hong

Kong and Beijing. Biometrics 64(3):869-876.

Abegaz, F. and Naik-Nimbalkar, U.V (2008). Modeling statistical dependence of markov chains via

copula models. Journal of Statistical Planning and Inference 138(4):1131-1146.

Uttara Naik-Nimbalkar

Visiting Faculty uvnaik@iiserpune.ac.in Uttara Naik-Nimbalkar joined IISER in February 2015. She has about thirty years of teaching and research experience at the University of Pune with visiting positions at the Michigan State University, the University of Edinburgh and University of Waterloo.

Algebraic Geometry

My research can be divided into three categories: intersection theory, derived categories, and T-varieties.

Intersection theory In intersection theory, one defines invariants of algebraically defined geometric spaces in terms of how the spaces lying on the given space intersect each other. One can study those invariants to determine deep geometric properties of the space.

Derived category Given a variety (a type of algebraically define geometric space), one can define another algebraic object called derived category. It is known that a lot of the geometric properties of the space translate to algebraic properties of the derived category.

T-variety While studying an object one many times first determine its group of symmetries. The same holds for varieties. When the group of symmetries contain a torus, one can, with some additional hypothesis describe a variety purely in terms of some combinatorial data. Currently I am working on such varieties.

Selected Publications Dubey, U.V. and Mallick, V.M. (2012). Reconstruction of a superscheme from its derived category.

Journal of the Ramanujan Mathematical Society 27(4). Dubey, U.V., Mallick, V.M. (2012). Spectrum of some triangulated categories. Journal of Algebra

364:90-118. Mallick, V.M. (2009). Roitman's theorem for singular projective varieties in arbitrary characteristic.

Journal of K-Theory 3:501-531.

Vivek Mohan Mallick

Assistant Professor vmallick@iiserpune.ac.in After completing BStat (1999) and MStat (2001) from Indian Statistical Institute, Vivek Mallick got his PhD from Tata Institute of Fundamental Research (TIFR) Mumbai, India in 2008. He has joined IISER Pune in 2012 after completing his postdoctoral research at the Institute of Mathematical Sciences in Chennai and Centre de Recerca Matematica in Barcelona, Spain.

SA Katre Professor & Head Department of Mathematics University of Pune, Pune E-mail: sakatre@math.unipune.ac.in sakatre@gmail.com

SA Katre received Masters degree in Mathematics from University of Pune and PhD from Panjab University, Chandigarh, India. He began his academic career from SP College of Pune and moved to University of Pune in 1988 as a faculty member and has been there since. Prof Katre’s work is in the area of Algebra and Number Theory, in particular, cyclotomy, number of points on curves over finite fields, Waring's problem for matrices, coding theory, and group theory. His pedagogical interests include contributing to mathematics olympiads, open source mathematical software, and e-learning in mathematics. Prof Katre had served as the editor of pedagological journal Bona Mathematica and has organized the NBHM sponsored ATM Schools in Mathematics during 2004-2012.

Sujatha Ramdorai

Canada Research Chair, Department of Mathematics University of British Columbia, Canada Sujatha Ramdorai obtained her PhD in TIFR/Bombay University in 1992 and was with TIFR till January 2012. She currently holds a Canada Research Chair at the Department of Mathematics, University of British Columbia. Her research interests include Iwasawa theory and the theory of motives. Prof Ramdorai is a recipient of the Shanti Swarup Bhatnagar Award and the ICTP Ramanujan Award. She was a Member of the National Knowledge Commission and is a Member of the Scientific Advisory Council to the Prime Minister, and also the National Innovation Council. She is also interested in broader educational issues and in policy matters related to Higher Education and Research.

Adjunct Faculty Members

Amlan Barua Postdoctoral Research Associate (till January 2015) Amlan’s research work focuses primarily on the numerical solution of partial differential equations that are encountered in different fields of applications. Earlier, he had worked on problems of Materials Science where his task was to find effective solvers for boundary integral equations. More lately, he has developed an interest in the field Bio-Mathematics. With Dr Pranay Goel at IISER Pune, Amlan was working on several research projects ranging from clinical biology to numerical simulation of partial differential equations that emerge from the modeling of Islets of Langerhans. Apart from applied mathematics, he is also interested in functional analysis and theoretical partial differential equations. Amlan is presently working as a Development Engineer with Comsol Multiphysics in Bangalore. Barua, A., Li, S., Feng, H. and Li, X. (2013). An efficient rescaling algorithm for simulating the evolution of multiple elastic precipitates.

Communications in Computational Physics 14(4):940-959. Feng, H., Barua, A., Li, S. and Li, X. (2013). A parallel adaptive treecode algorithm for evolution of elastically stressed solids. Communications in

Computational Physics 15(2):365-387.

Bhakti Bhushan Manna Postdoctoral Research Associate Bhakti did his PhD from TIFR-CAM Bangalore. His area of research is partial differential equation. He has completed the degree on December 2014 under the guidance of Prof PN Srikanth. He has joined IISER Pune as a Post doctoral Research Associate (PRA) on March 1, 2015. His thesis work involved mainly two classes of problems: First one concerning concentrating solutions and the other on the so-called problem of resonance. Singularly perturbed elliptic equations have been a great interest in PDE for last two decades. And his focus has been on finding solutions with higher dimensional concentrations. He is also interested in finding the existence results for the classical resonance problem which has been partly answered in one of their recent works. Manna, B.B. and Srikanth, P.N. (2015). On a problem of resonance with exponential nonlinearity. Journal of Mathematical Analysis and

Applications 421(2):1603-1615. Manna, B.B. and Srikanth, P.N. (2014). On the solutions of a singular elliptic equation concentrating on a circle. Advances in Nonlinear Analysis

3(3):141-155. Manna, B.B. and Srikanth, P.N. (2014). On the solutions of a singular elliptic equation concentrating on two orthogonal spheres. Nonlinear

Differential Equations Applications NoDEA 21(6):915-927. Manna, B.B. and Santra, S. On a superlinear Ambrosetti Prodi problem: Interior concentration on geodesics (preprint).

Chitrabhanu Chaudhuri Postdoctoral Research Associate Chitrabhanu did his PhD in Mathematics from Northwestern University 2007-2013 and was a postdoctoral fellow at Max Plank Institute for Mathematics (2013-2014) before joining IISER Pune. His research revolves around the topology and geometry of the Moduli of Curves over Complex numbers. The Moduli Space of Curves parameterize algebraic curves or Riemann surfaces, up to isomorphisms. It has been a central topic in mathematical research for several decades and brings various fields of mathematics together, for example Algebraic Geometry, Geometric Group theory and Teichmüller theory. It has important connections with physics as well. There are mainly two directions of research that Chitrabhanu has pursued: one roughly concerns finding some bounds on the topological complexity of certain partial compactifications on the Moduli of genus g curves. This involves computing certain cohomology groups; and the other line of research is about certain geometrically relevant subrings of the cohomology ring of the Moduli space known as the Tautological ring. The Cohomological Excess of Certain Moduli Spaces of Curves of Genus g. International Mathematical Research Notices IMRN (2013). Topological Bounds on Certain open Subvarieties of the Compactified Moduli space of Curves; PhD thesis, Northwestern University 2013. Equivariant Polynomial of certain Moduli of Weighted Pointed Rational Curves (In preparation)

Postdoctoral Fellows

Dipramit Majumdar Postdoctoral Research Associate Dipramit Majumdar obtained his PhD from Brandeis University, USA in 2013. He was a visiting scientist in ISI Bangalore from 2013-2014 before joining IISER Pune in 2014. Dipramit's research interest lies in number theory. Even though he is sometimes intrigued by elementary number theoretic problems such as Class Groups and Diophantine equations, his main research interest lies in p-adic families of modular forms. Modular forms are certain functions on the complex upper half planes with a lot of symmetries. To a modular form one can associate certain object called the L-function. One of the most promising ways to understand classical modular forms and their associated L-function is via study of their p-adic analogue. Study of p-adic modular forms was initiated by Serre, later Hida and then Coleman-Mazur constructed p-adic familes of 'nice' modular forms, called Hida family and eigencurve respectively. These objects plays crucial role in understanding and solving many problems in number theory, for example, key step in Mazur-Wiles proof of Iwasawa main conjecture for rational numbers is understanding geometry of the eigencurve at certain points. Majumdar, D. Geometry of the eigencurve at critical Eisenstein series of weight 2. To appear in Journal de Théorie des Nombres de Bordeaux. Majumdar, D. Endoscopic transfer between eigenvarieties of definite unitary groups (Submitted) Kulkarni, M., Majumdar, D. and Balasubramanian, S. l-Class groups of cyclic extensions of prime degree l (Submitted)

Postdoctoral Fellows

Advait Phanse Graduate Student Advait has completed MSc from Sir Parshurambhau College in July 2014 and joined IISER Pune in August 2014. Presently he is doing PhD program related course work.

Girish Kulkarni Graduate Student Girish completed MSc Mathematics from IIT Madras in 2010 and MSc from University of Western Ontario, Canada in 2012. Girish joined IISER Pune in 2013. In December 2014 he attended Advanced Instructional School on Schemes and Cohomology and has done minor thesis under the guidance of Prof Tejas Kalelkar. He is working toward PhD with the guidance of Dr Amit Hogadi. Girish’s expository article has appeared recently (Representation Theory and Particle Physics, Forays-14 Souvenir 55-56).

Ayesha Fatima Graduate Student Ayesha completed her BS-MS from IISER Pune in 2012 before joining the PhD program in August 2013. She has since completed her course work and is currently reading about Lie Algebras with Dr Bhagwat. Her interest lies in Number Theory and Representation Theory.

Gunja Sachdeva Graduate Student Gunja completed MPhil in Mathematics from Dayalbagh Educational Institute, Deemed University, Agra in December 2011 and joined IISER Pune in August 2012. She is currently working toward PhD under the guidance of Prof A Raghuram in the area of Number Theory.

Chaitanya Ambi Graduate Student Chaitanya completed his MSc from IIT Kharagpur in 2009. He joined IISER Pune in August 2013 as a Project Fellow. He is a PhD student now and is completing the course work.

Hitesh Raundal Graduate Student Hitesh obtained MSc in Applied Mathematics from the University of Hyderabad and joined IISER Pune in January 2011. He is a graduate student with Dr Rama Mishra in the area of knot theory. He has been working on the minimal polynomial representations of knots and their super bridge indices, and trying to build relation between various numerical knot invariants particularly polynomial degree, edge number and super bridge index of knots.

Debangana Mukherjee Graduate Student Debangana has completed her MSc from Mount Carmel College (under Bangalore University) in 2013 and joined IISER Pune soon after as a graduate student and has completed a one year coursework as a part of the Mathematics PhD program. She is currently reading in the area of elliptic partial differential equations under the guidance of Dr Mousomi Bhakta.

Jyotirmoy Ganguly Graduate Student Jyotirmoy completed MSc in Mathematics from University of Hyderabad in 2013 and joined IISER Pune soon after. He has completed a one year course work as a part of the Mathematics PhD program at IISER Pune. His research interest is in Representation Theory of Lie groups.

Graduate Students, BS MS Project Students & Teaching Assistants

Makarand Sarnobat Graduate Student Makarand completed MSc in Mathematics from Sir Parshurambhau College, Pune in 2012 and joined IISER Pune immediately after that. He is working with Prof Raghuram toward PhD in the area of algebraic number theory and representations theory. Makarand has been a teaching assistant for these courses: Introduction to Proofs; Linear Algebra; Multivariable Calculus; and Complex Analysis. He has attended a conference on Lie Groups and Lie Algebras in IIT Bombay in July 2014.

Prabhat Kushwaha Graduate Student Prabhat completed MSc from the Department of Mathematics, Banaras Hindu University, Varanasi and joined IISER Pune in January 2012. He has successfully completed all the requirements by the Institute viz. course work, comprehensive exams and minor-thesis. Prabhat is currently working with Dr Ayan Mahalanobis his broad area of research is public key cryptography.

Manidipa Pal Graduate Student Manidipa joined IISER Pune in January 2012. She has completed course work, comprehensive exams and minor thesis, which are in partial fulfillment of PhD program. Her minor thesis was carried out with guidance from Chandrasheel Bhagwat. Manidipa’s is now working with Dr Baskar Balasubramanyam in the area of algebraic number theory.

Pralhad Shinde Graduate Student Pralhad completed Masters in Mathematics in 2011 from University of Pune, Pune and joined IISER Pune in January 2012. He is working with Dr Ayan Mahalanobis and Dr Anupam Singh in the areas of cryptography and computational group theory.

Milan Kumar Das Graduate Student Milan completed MSc from Vidyasagar University, West Bengal in 2012. He joined IISER Pune in August 2013.

Rashmi Kulkarni Graduate Student Rashmi obtained MSc in Microbiology from MS University, Baroda and an MTech from the Centre for Modeling and Simulation, University of Pune, Pune. She joined IISER Pune in August 2010 and is working with Dr Pranay Goel toward her PhD. Her research involves quantitating oxidative stress in the development of insulin resistance.

Neha Prabhu Graduate Student Neha completed her MSc in Mathematics from IIT Bombay and joined IISER Pune in August 2012. She is currently working toward PhD under the guidance of Dr Kaneenika Sinha. Her interests lie in number theory and representation theory.

Rohit Joshi Graduate Student Rohit has a Masters degree from IIT Kanpur. He has completed course work and cleared comprehensive exams toward IISER Pune’s PhD program in Mathematics and is currently working with Dr Steven Spallone. He was the winner of silver medal in International Mathematics Olympiad in 2004 while in his 12th standard and was chosen as the IISER Pune Mathematics Student of the Year in 2013.

Sudhir Pujahari Graduate Student Sudhir obtained MSc in Mathematics from Utkal University, Orissa. He joined IISER Kolkata in January 2011 as a CSIR JRF and shifted to IISER Pune in December 2012. He is working with Dr Kaneenika Sinha in the area of Analytic Number Theory. Some of his work has been accepted for publication (with Meher, J. and Shankhadhar, K.D.; Sign changes of coefficients of certain Dirichlet series Functiones Et Approximatio Commentarii Mathematici).

Akash Krishna BS MS Student Akash is currently working on his BS MS thesis with Dr Anindya Goswami. His thesis studies option pricing problem in a market model where semi-Markov switching of the parameters is considered in a Levy process dynamics.

Sushil Bhunia Graduate Student Sushil completed MSc (Mathematics) in 2010 from Jadavpur University, Kolkata, India. He joined IISER Pune in January 2012 and completed course work along with comprehensive examinations that are part of the graduate program. Sushil is presently working with Dr Anupam Singh on algebraic groups.

K Hariram BS MS Student Hariram is doing his fifth year project with Dr Ayan Mahalanobis. He is studying how to solve the discrete log problem using Function field sieve for index calculus-in particular, a new method to improve the sieving step called pinpointing which reduces the computation time significantly. He is also investigating whether this improvement can be adopted for other similar problems like integer factorization.

Tathagata Mandal Graduate Student Tathagata completed his MSc in Mathematics from Visva-Bharati University, Santiniketan, India in 2012. He joined IISER Pune in August 2013. He is presently doing coursework as a part of the Mathematics PhD program at IISER Pune and is interested in Number Theory and Algebraic Geometry.

Nishad Mandlik BS MS Student Nishad is working on his fifth year thesis project with Dr Rabeya Basu. The topic of his project is 'K-Theory: Completion of Unimodular Rows.' He is using the software 'Singular' to replicate a result on the completion of unimodular rows of length 3. Nishad is also interested in math and science education.

Yasmeen Akhtar Graduate Student Yasmeen completed MSc in Mathematics from University of Pune and joined IISER Pune in January 2011. She is working toward her PhD with Dr Soumen Maity in the area of combinatorics and graph theory. Recent Publications: Akhtar, Y., Maity, S. and Chandrasekharan, R.C. Covering Arrays of Strength four with budget constraints. Mathematical and Computational Sciences 106-114, Narosa Publishing; Akhtar, Y., Maity, S. and Chandrasekharan, R.C. Covering arrays of strength four and software testing. Springer Proceedings in Mathematics and Statistics (To appear).

Preeti BS MS Student Preeti is currently working on her BS MS fifth year project with Dr Ayan Mahalanobis on Secret sharing schemes and its various applications. This topic uses Lagrange interpolation in finite fields and has many applications in real life. Notable ones are e-voting and secure multiparty computations.

Reshma Chandrasekharan BS MS Student Reshma is working toward her BS MS fifth year project with Dr Soumen Maity on the topic "Construction of covering arrays". She likes programming and is interested in developing tools for solving mathematical problems. Publications: Chandrasekharan, R.C. and Maity, S. Covering Arrays of Strength Two and Pair wise Software Testing, Mathematical and Computational Sciences, Narosa, 2015, 115-121; Akthar, Y., Maity, S. and Chandrasekharan, R.C. Covering Arrays of Strength Four and Software Testing, Springer Proceedings in Mathematics and Statistics (To appear).

Aman Jhinga Teaching Assistant Aman graduated with BSc (Hons)-Maths and Computing degree in June 2010 and MSc (Mathematics) degree in June 2012 from Panjab University, Chandigarh. She has assisted Dr Amit Hogadi in conducting Single Variable Calculus course, Dr Steven Spallone for Introduction to Proofs and Dr Baskar Balasubramanyam for Linear Algebra for fall semester 2014. Aman is currently assisting Dr Soumen Maity in conducting Probability & Statistics course, Dr Debargha Banerjee for Multivariable Calculus and Dr Collins Assisi in conducting Introduction to Computation course for Spring semester 2015. She is also doing a reading project with Dr Steven Spallone on p-adic numbers.

Sanket Nandan BS MS Student Sanket is doing his project on Statistical inference of semi-Markov process and application in finance with Dr Anindya Goswami.

Jatin Majithia Teaching Assistant Jatin has an MSc in Mathematics degree from University of Pune and is presently assisting with teaching at IISER Pune.

Shirish Kulhari BS MS Student Shirish is working with Dr Anindya Goswami toward his BS MS fifth year project. The title of his research project is “Implied Volatility in a Regime Switching Market: Theory and Computation”.

Uday Jagadale Teaching Assistant Uday has completed MSc from the Department of Mathematics, University of Pune in 2014 and joined IISER Pune as a Teaching Assistant. He has assisted Dr Amit Hogadi and Dr Steven Spallone for courses on Calculus of One Variable and Introduction to Proofs respectively. Currently he is a teaching assistant for these courses: Calculus of multivariable (taught by Dr Debargha Banerjee); and Probability and Statistics (taught by Dr Soumen Maity).

Shiva Chidambaram BS MS Student Shiva is currently working on his fifth year project with Prof A Raghuram on Cohomology of GL(2). The goal of this project is to understand, in the language of automorphic forms of GL(2,F) for a number field F, the sheaf cohomology of a sheaf of vector spaces defined on a locally symmetric space attached to GL(2,F) from a highest weight irreducible representation of it. A specific goal is to understand the inner cohomology. He is also a Teaching Assistant for the course Multivariable Calculus taught by Dr Debargha Banerjee and Dr Anup Biswas.

Kalpesh Pednekar Office Assistant Kalpesh Pednekar completed his Bachelor Degree in Commerce from University of Mumbai. He joined IISER Pune in March 2013 and is presently assisting Mathematics group in various administrative responsibilities in addition to assisting the Physics Group at IISER Pune.

R Bhagyalaxmi Office Assistant Bhagyalaxmi completed her BSc from Osmania University, Hyderabad. Microbiology, Chemistry and Computer Applications were the subjects of her study in BSc. She also completed her MSc in Computer Science from Annamalai University, Tamilnadu. She joined IISER Pune in December 2014 and is providing administrative support to the Mathematics group.

Suvarna Gharat Office Assistant Suvarna completed her BSc in Physics from Fergusson College and her post-graduation from Modern College, Pune. She joined IISER Pune in July 2011 and is presently assisting the Mathematics group in various administrative responsibilities.

Support Staff

2015 Akhtar, Y., Chandrasekharan, R.C. and Maity, S.- Covering Arrays of Strength Four and Software

Testing. Springer Proceedings in Mathematics & Statistics (Accepted) Akhtar, Y., Chandrasekharan, R.C. and Maity, S.- Covering Arrays of Strength four with budget

constraints. Mathematical and Computational Sciences 106-114, Narosa Publishing House, 2015. Banerjee, D. and Raghuram, A. - p-adic L-functions for GL_n (Submitted) Banerjee, D. and Krishnamoorthy, S.- The Eisenstein elements inside the modular symbols for product of

two distinct primes (Submitted) Barua, A.; Goel, P. - The lattice origin of small-world networks in pancreatic tissues. (Submitted) Bhakta, M. - Entire solutions for a class of elliptic equations involving p-biharmonic operator and Rellich

potentials. Journal of Mathematical Analysis and Applications 423 (2015), no. 2, 1570-1579. Bhunia, S., Mahalanobis, A. and Singh, A.- Gaussian Elimination in Symplectic and Split Orthogonal

groups (Submitted) Chandrasekharan, R.C. and Maity, S.- Covering Arrays of Strength Two and Pairwise Software Testing.

Mathematical and Computational Sciences 115-121, Narosa Publishing House, 2015. Chaudhuri, C.- The Cohomological Excess of Certain Moduli Spaces of Curves of Genus g. International

Mathematics Research Notices 4 (2015) 1056-1074. Goswami, A., Patel, J. and Sevgaonkar P.- The optimal hedging in a semi-Markov modulated market

(Submitted) Kalelkar, T. Roberts, R.- Taut foliations in surface bundles with multiple boundary components. Pacific

Journal of Mathematics Vol No. 273 (2015) 257-275. Mahalanobis, A., Singh, A.- The MOR cryptosystem and unitary group in odd characteristic. (Submitted) Kulkarni, M., Majumdar, D. and Sury, B.- l-class groups of cyclic extensions of prime degree l. The

Journal of the Ramanujan Mathematical Society (Accepted) Mishra, R. and Raundel, H. - Spaces of polynomial knots in low degree (Submitted)

2014 Balasubramanyam, B. and Majumdar, D.- Ordinary families over definite unitary groups (Submitted) Balasubramanyam, B. and Raghuram, A.- Special values of adjoint L-functions and congruences for

automorphic forms on GL(n) over a number field (Submitted) Banerjee, D.- A note on the Eisenstein elements for prime square level. Proceedings of the American

Mathematical Society 142 (2014), 3675-3686. Banerjee, D. - Differential modular forms on the Shimura curves over totally real fields. Journal of

Number Theory 135 (2014), 353-373. Basu, R.- Local-global principle for quadratic and Hermitian groups and the nilpotence of KH1 (Submitted) Bhagwat, C.- On Deligne's periods for tensor product motives. Comptes rendus - Mathématique DOI:

10.1016/j.crma.2014.11.016. Bhakta, M.- Infinitely many sign changing solutions of an elliptic problem involving critical Sobolev and

Hardy-Sobolev exponent (Submitted) Bhakta, M.- Caffarelli-Kohn-Nirenberg type equations of fourth order with the critical exponent and Rellich

potential (Submitted) Bhakta, M.- Semilinear elliptic equation with biharmonic operator and multiple critical nonlinearities.

Advanced Nonlinear Studies (Accepted) Bhakta, M. and Marcus, M. - Semilinear elliptic equations admitting similarity transformations. Journal of

Functional Analysis Vol 267 (2014), no. 10, 3894-3930. Bhakta, M. and Marcus, M.- Reduced limit for semilinear boundary value problems with measure data.

Journal of Differential Equations Vol 256 (2014), no. 8, 2691-2710.

Publications

Arapostathis, A., Biswas, A. and Pang, Guodong - Ergodic control of multi-class M/M/N+M queues in the Halfin-Whitt regime . Annals of Applied Probability (Accepted)

Atar, R., Biswas, A., Kaspi, H.- Fluid limits of G/G/1+G queues under non-preemptive Earliest-Deadline-First discipline . Mathematics of Operation Research (Accepted)

Biswas, A.- Risk-sensitive control for the multiclass many-server queues in the moderate deviation regime. Mathematics of Operation Research 39 (2014), no. 3, 908-929.

Atar, R. and Biswas, A.- Control of the multiclass G/G/1 queue in the moderate deviation regime. Annals of Applied Probability 24 (2014), no. 5, 2033-2069.

Chorwadwala, A. and Mahadevan, R.- A shape optimization problem for the $p$-Laplacian. Proceedings of the Royal Society of Edinburgh (Accepted)

Chorwadwala, A., Mahadevan, R. and Toledo, F. - On the Faber-Krahn Inequality for the Dirichlet $p$-Laplacian. ESAIM:Control, Optimization and Calculus of Variations; Cambridge Journal (2014) DOI:10.1051/cocv/2014017.

Deshpande, J., Lam, K.F., Naik-Nimbalkar, U.V. and Xu, Y.- Tests for comparing the progression of an epidemic in two groups. Journal of Indian Statistical Association (Accepted)

Dwivedi, A. (Sponsor: Goel, P.) - A Stochastic Version of the Pedersen-Sherman Insulin Secretion Model. SIAM Undergraduate Research Online (SIURO) Published electronically Vol. 7. (2014) http://dx.doi.org/10.1137/12S011994.

Goswami, A. and Saini, R.K. - Volterra equation for pricing and hedging in a regime switching market. Cogent Economics and Finance 2(2014), no.1, 1-11.

Atar, R., Shwartz, A. and Goswami, A.- On the risk-sensitive cost for a Markovian multiclass queue with priority. Electronic Communications in Probability 19 (2014), no. 11, 1-13.

Kaipa, K.- An asymptotic formula in q for the number of [n,k] q-ary MDS codes. IEEE Transactions on Information Theory Vol PP, Issue 99 (early access).

Kaipa, K.- An asymptotic formula in q for the number of [n,k] q-ary MDS codes. IEEE Transactions on Information Theory 60 (2014), no. 11, 7047-7057.

Majumdar, D.- Endoscopic transfer between eigenvarieties for definite unitary groups (Submitted) Majumdar, D.- Geometry of the eigencurve at critical Eisenstein series of weight 2. Journal de Théorie

des Nombres de Bordeaux (Accepted) Sebastian, R. - Examples of smash nilpotent cycles on rationally connected varieties (Submitted)

Colloquia

Speaker Date Title of the Talk

Prof Nitin Nitsure TIFR, Mumbai Mar 13, 2015 Euclidean Geometry and Physics

Dr Abhishek Banerjee IISc Bangalore Feb 27, 2015 Hecke operators on Line bundles over Modular curves

Dr Chitrabhanu Chaudhary IISER Pune Jan 23, 2015 Operads and Moduli of Curves

Prof L Mahadevan Harvard University Jan 09, 2015

Of flags and fishes

Prof Michel Waldschmidt Institut de Mathématiques de Jussieu, Paris VI

Dec 18, 2014 Continued fractions : Introduction and applications

Dr Manoj Kumar Yadav HRI, Allahabad Dec 05, 2014 Automorphisms of groups preserving conjugacy classes

Prof Siegfried Boecherer Universität Mannheim, Germany Oct 31, 2014 Siegel modular forms mod p

Dr Anupam Kumar Singh IISER Pune Oct 17, 2014 Word problem in finite classical Chevalley groups

Dr Tejas Kalelkar IISER Pune Sep 19, 2014

Incompressible surfaces and normality in 3-manifolds

Dr Joël Riou Université Paris-Sud, France Aug 22, 2014 Purity and duality in étale cohomology (after O. Gabber)

Dr Raghav Kulkarni Centre for Quantum Technologies Aug 04, 2014 Decision Trees, Evasiveness, Solvable Groups, and

Music of Primes

Prof Jeffrey Adler American University Jul 24, 2014 Representation Theory and p-adic Numbers: What and

Why

Dr Moira Chas Stonybrook University Jul 11, 2014 The Goldman Bracket on Surfaces

Prof Steven Weintraub Lehigh University Jul 07, 2014 The adjoint of differentiation

Prof Mahan Maharaj RKM Vivekananda University, Belur Math

Jun 06, 2014 3-manifolds and (quasi)projective varieties

Dr Shanta Laishram ISI Delhi May 02, 2014 Grimm's Conjecture and Smooth Numbers

Prof Uttara Naik-Nimbalkar University of Pune Apr 25, 2014 Statistical tests for comparing the fatality of an epidemic

in two groups

Prof CS Aravinda TIFR-CAM, Bangalore Apr 11, 2014 Dynamics of geodesic conjugacies

Colloquia & Seminars

Prof Parameswaran Sankaran IMSC-Chennai Apr 04, 2014 Twisted conjugacy in R. Thompson's groups

Prof Amitava Bhattacharya TIFR, Mumbai Mar 21, 2014 Existence problems in Set Systems

Dr Stefan Friedl University of Regensburg Mar 14, 2014 The profinite completion of knot groups

Prof MS Narasimhan IISc, Bangalore Mar 08, 2014 Mathematical Research in India after Independence:

The early years

Prof Ravi Ramakrishna Cornell University Mar 07, 2014 Galois Representations

Algebraic Geometry Seminars

Speaker Date Title of the Talk

Prof Kapil Hari Paranjape IISER, Mohali Mar 04, 2015 The work of Grothendieck: Some aspects of his work

Prof Kapil Hari Paranjape IISER, Mohali Mar 03, 2015

Lindel's theorem: A Vector bundle on X x A^1 comes from X

Analysis Seminars

Speaker Date Title of the Talk

Dr M Ashok Kumar Indian Institute of Science, Bangalore Feb 25, 2015 Statistical inference based on a parametric family of

divergences

Dr Amogh Deshpande University of Liverpool,UK Jan 7, 2015 On the role of Follmer-Schweizer minimal martingale

measure in risk sensitive control asset management

Dr Ronnie Sebastian IISER Pune Nov 07, 2014 Bounded Hermitian Operators and Schur's lemma

Dr Ronnie Sebastian IISER Pune Oct 31, 2014 Bounded Hermitian Operators and Schur's lemma

Dr Anisa Chorwadwala IISER Pune Oct 24, 2014 Geometric overview of Symmetric Spaces

Dr Anisa Chorwadwala IISER Pune Oct 17, 2014 Geometric overview of Symmetric Spaces

Dr Rahul Garg, Technion Israel Institute of Technology Oct 14, 2014 The lattice point counting problem on the Heisenberg

groups

Dr Anisa Chorwadwala IISER Pune Oct 10, 2014 Geometric Overview of Symmetric Spaces

Dr Supriya Pisolkar IISER Pune Sept 26, 2014 Representation of SL2(R)

Dr Debdip Ganguly TIFR-CAM, Bangalore Sept 25, 2014 Partial Differentiation Equation on Hyperbolic Space

Dr Supriya Pisolkar IISER Pune Sept 19, 2014 Representation of SL2(R)

Dr Chandrasheel Bhagwat IISER Pune Sept 12, 2014 Representation of SL2(R)

Dr Chandrasheel Bhagwat IISER Pune Aug 29, 2014 Representation of SL2(R)

Dr Ronnie Sebastian IISER Pune Aug 20, 2014 Representation theory of topological groups, Peter-

Weyl Theorem for compact groups

Mr Souvik Roy TIFR-CAM, Bangalore Jun 05, 2014

A Vorticity-Velocity Formulation for Incompressible 2-D Euler Flows using Discontinuous Finite Element Methods

Dr Supriya Pisolkar IISER Pune Jun 04, 2014 Analysis Lecture Series on Representation Theory and

Linear Lie Groups (Lecture XV)

Dr Supriya Pisolkar IISER Pune Jun 03, 2014 Analysis Lecture Series on Representation Theory and

Linear Lie Groups (Lecture XIV)

Dr Supriya Pisolkar IISER Pune May 30, 2014 Analysis Lecture Series on Representation Theory and

Linear Lie Groups (Lecture XIII)

Dr Chandrasheel Bhagwat IISER Pune May 22, 2014 Analysis Lecture Series on Representation Theory and

Linear Lie Groups (Lecture XII)

Dr Anisa Chorwadwala IISER Pune May 20, 2014 Analysis Lecture Series on Representation Theory and

Linear Lie Groups (Lecture XI)

Dr Chandrasheel Bhagwat IISER Pune May 15, 2014 Analysis Lecture Series on Representation Theory and

Linear Lie Groups (Lecture X)

Ms Neha Prabhu IISER Pune May 13, 2014 Analysis Lecture Series on Representation Theory and

Linear Lie Groups (Lecture IX)

Dr Chandrasheel Bhagwat IISER Pune May 06, 2014 Analysis Lecture Series on Representation Theory and

Linear Lie Groups (Lecture VIII)

Dr Chandrasheel Bhagwat IISER Pune Apr 29, 2014 Analysis Lecture Series on Representation Theory and

Linear Lie Groups (Lecture VII)

Prof Raju George IIST Thiruvantapuram Apr 21, 2014 Controllability of Systems Described by Differential

Equations Using Tools of Functional Analysis

Dr Anisa Chorwadwala IISER Pune Apr 18, 2014 Analysis Lecture Series on Representation Theory and

Linear Lie Groups (Lecture VI)

Dr Anisa Chorwadwala IISER Pune Apr 16, 2014

Analysis Lecture Series on Representation Theory and Linear Lie Groups (Lecture V)

Dr Apala Majumdar University of Bath Apr 11, 2014

Biaxial defect cores in nematic equilibria: an asymptotic result

Prof CS Aravinda TIFR-CAM, Bangalore Apr 10, 2014

Homotopy type and volume of locally symmetric spaces

Dr Anisa Chorwadwala IISER Pune Apr 09, 2014

Analysis Lecture Series on Representation Theory and Linear Lie Groups (Lecture IV)

Dr Supriya Pisolkar IISER Pune Apr 02, 2014 Analysis Lecture Series on Representation Theory and

Linear Lie Groups (Lecture III)

Dr Supriya Pisolkar IISER Pune Mar 26, 2014

Analysis Lecture Series on Representation Theory and Linear Lie Groups (Lecture II)

Dr Praveen C TIFR-CAM, Bangalore Mar 25, 2014

Kinetic schemes for convection-diffusion and Navier-Stokes equations

Dr Supriya Pisolkar IISER Pune Mar 19, 2014

Analysis Lecture Series on Representation Theory and Linear Lie Groups (Lecture I)

Prof Gopal Basak ISI Kolkata Mar 07, 2014

Diffusion Approximation to Adaptive MCMC

Number Theory Seminars

Speaker Date Title of the Talk

Dr Jonathan Huang University of Maryland Mar 09, 2015 Higher Fitting ideals and the structure of ideal class

groups

Dr Debargha Banerjee IISER Pune Mar 02, 2015 Eisenstein ideals

Dr Steven Spallone IISER Pune Feb 20, 2015 Weyl's Law: Euclidean Case

Dr Debargha Banerjee IISER Pune Feb 16, 2015 Eisenstein ideals

Dr Steven Spallone IISER Pune Feb 13, 2015 Weyl's Law: Euclidean Case

Dr Chandrasheel Bhagwat IISER Pune

Feb 06, 2015 Trace formula and its applications in isospectrality problems

Dr Supriya Pisolkar IISER Pune Jan 30, 2015 Trace Formula

Dr Steven Spallone IISER Pune Jan 19, 2015 Trace Formula

Dr Florian Sprung Princeton Univerity Jan 15, 2015 Rational points of modular abelian varieties in towers of

number fields: How to bound the rank.

Dr Abhishek Saha University of Bristol Jan 12, 2015

Siegel modular forms of degree 2: Fourier coefficients, L-functions, and functoriality

Dr Dipramit Majumdar IISER Pune Jan 05, 2014

An introduction to Eigenvarieties

Prof Wintenberger Jean-Pierre University of Strasbourg, France Nov 06, 2014

Ramification and Iwasawa theory

Dr Debargha Banerjee IISER Pune Nov 03, 2014

Hecke Theory for GL2 and converse theorem

Dr Chandrasheel Bhagwat IISER Pune Oct 27, 2014

Tate's thesis and Hecke Theory for GL2

Dr Steven Spallone IISER Pune Oct 13, 2014

(g,K)-module

Dr Supriya Pisolkar IISER Pune Oct 10, 2014

Jacquet Functors

Dr Baskar Balasubramanyam IISER Pune Sept 15, 2014

Principal series representations, parabolic induction

Dr Debargha Banerjee IISER Pune Sept 08, 2014

Whittaker Functionals

Dr Debargha Banerjee IISER Pune Aug 25, 2014

Global representations of GL(2)

Dr Dipramit Majumdar IISER Pune Aug 20, 2014

Representations of GL(2) over non-archimedean places

Dr Steven Spallone IISER Pune Aug 11, 2014

Representations of GL(2) over archimedean places

Dr Ronnie Sebastian IISER Pune Aug 04, 2014 Automorphic forms as function of adele groups

Dr Supriya Pisolkar IISER Pune May 21, 2014

Witt vectors and Hasselholt's Conjecture

Dr Dipramit Majumdar IISER Pune Apr 30, 2014

Overconvergent modular symbols

Dr Baskar Balasubramanyam IISER Pune Apr 23, 2014 Exceptional zero conjecture

Dr Baskar Balasubramanyam IISER Pune Apr 16, 2014 Two variable p-adic L-functions

Dr Debargha Banerjee IISER Pune Mar 26, 2014 Explicit construction of the p-adic distribution attached

ordinary elliptic Hecke eigenform

Dr Debargha Banerjee IISER Pune Mar 19, 2014 p-adic L-functions attached to modular forms

Dr Chandrasheel Bhagwat IISER Pune Mar 12, 2014 Siegel modular forms and automorphic representations

Visitors’ Seminars

Speaker Date Title of the Talk

Dr Xavier Viennot Emeritus research director at CNRS Feb 17, 2015

Trees in various sciences

Dr Shilpa Gondhali University of Haifa Feb 03, 2015

Higher Toda brackets and Massey products

Dr Umesh Dubey IISc, Bangalore Jan 30, 2015

Twisted sheaves and twisted integral transforms

Dr Florian Sprung Princeton University Jan 15, 2015

Rational points of modular abelian varieties in towers of number fields: How to bound the rank

Dr Nikhil Savale Lumpkins Visiting Assistant Professor, University of Notre Dame

Jan 07, 2015

Asymptotics of the eta invariant

Dr Swarnava Mukhopadhyay University of Maryland Jan 06, 2015

Rank-Level duality and Conformal Blocks divisors

Dr Shibasish Dasgupta Department of Information Systems and Analytics - Miami University, Ohio

Jan 02, 2015

A Bayesian Predictive Approach to Design Studies for Comparing Biomarkers

Dr Pritam Rajan Acadia University, Canada Dec 23, 2014

Sequential design schemes for efficient estimation of pre-specified process features in computer experiments

Prof Siegfried Boecherer Institut für Mathematik - Universität Mannheim, Germany

Oct 29, 2014

Congruence primes for Siegel modular forms via twisted L-functions.

Dr R Venkatesh TIFR, Mumbai Oct 24, 2014

Unique Factorization of Tensor Products for finite dimensional simple Lie Algebras

Dr Arnab Mitra Ben-Gurion University of the Negev Sept 26, 2014

Norm correspondence for unipotent radicals in classical groups

Dr Anandam Bannerjee TIFR, Mumbai Aug 28, 2014

Tensor Structure on Smooth Motives

Dr Anandam Bannerjee TIFR, Mumbai Aug 26, 2014

Equivalence relations on algebraic cobordism

Dr Manoj Gopalkrishnan TIFR, Mumbai Aug 12, 2014

The Geometry of Reaction Networks

Prof Jeffrey Adler American University Jul 30, 2014

Lifting representations of finite reductive groups

Dr Asilata Bapat University of Chicago Jul 23, 2014

Morse theory and intersection cohomology

Prof Steven Weintraub Lehigh University Jul 09, 2014 A generalization of continued fractions

Prof R Parthasarathy Bharathiar University, Coimbatore May 22, 2014

On the modules $A_{(\mathfrak q, \lambda)}$

Dr Krishna Kaipa IISER Bhopal Apr 22, 2014

Linear Codes and Grassmannians

Dr Kashyap Rajeevsarathy IISER Bhopal Apr 07, 2014

Multicurves and primitivity in Mod(Sg)

Mini-courses by Visitors

Speaker Date Title of the Talk

Prof Siddhartha Bhattacharya TIFR, Mumbai

Nov 10-14, 2014

A brief introduction to ergodic theory (Mini course)

Prof Jose Ignacio Burgos Gil ICMAT, Madrid Spain

Nov 04-07, 2014

Arakelov geometry of toric varieties (series of 4 lectures)

Prof Ramanan CMI, Chennai

Mar 18 - Apr 01, 2014

Mini-course on Algebraic Geometry

Dr Stefan Friedl University of Regensburg

Mar 05 - 12, 2014

The geometrization theorem for 3-manifolds (series of 3 lectures)

Minor Thesis Seminars

Speaker Date Title of the Talk

Mr Hitesh Raundal Jul 11, 2014

Computing Hodge-Deligne Numbers of Hypersurfaces on Toric Varieties

Mr Sudhir Pujahari Jul 2, 2014 Graph Homomorphisms

Mr Prabhat Kumar Kushwaha Apr 24, 2014 Ito Calculus Without Probabilities

Ms Manidipa Pal Apr 14, 2014 Can one hear the shape of a drum?

Mr Pralhad Shinde Mar 23, 2014 Extremal first Dirichlet Eigenvalue for the Laplacian and Dihedral Symmetry

Mr Makarand Sarnobat Mar 12, 2014 A topological Proof of Grushko's Theorem

Ms Gunja Sachdeva Mar 10, 2014 Membership Problem in the Bitprobe Model

Student Seminars

Speaker Date Title of the Talk

Mr Makarand Sarnobat Mar 12, 2015 The Local Langlands Correspondence

Ms Neha Prabhu Mar 5, 2015 Quadratic Reciprocity: A proof using Algebraic Number Theory-Part 2

Ms Neha Prabhu Feb 26, 2015 Quadratic Reciprocity: A proof using Algebraic Number Theory-Part 1

Mr Prabhat Kushwaha Feb 12, 2015 What is Public Key Cryptography and why do we need it?

Mr Sushil Bhunia Jan 29, 2015 Clifford Algebras and Spin Groups

Ms Manidipa Pal Nov 19, 2014 Siegel modular forms

Ms Manidipa Pal Nov 12, 2014 Siegel modular forms

Ms Neha Prabhu Nov 5, 2014 Introduction to Classical Modular Forms

Ms Neha Prabhu Oct 22, 2014 Introduction to Classical Modular Forms

Mr Makarand Sarnobat Oct 22, 2014 Representation Theory of Finite groups

Mr Makarand Sarnobat Oct 8, 2014 Representation Theory of Finite groups

Ms Ayesha Fatima Sept 24, 2014 Representation Theory of Finite groups

Ms Ayesha Fatima Sept 17, 2014 Representation Theory of Finite groups

Symposium on Math-Finance March 5, 2015

Organizer Anindya Goswami

This half-day in-house symposium on Math-Finance was organized to give the students an overall knowledge of research works in Math-finance being done in the department. This was open to all from IISER Pune and required no prior registration.

There were three sessions with two short breaks. The sessions were chaired by Dr Anup Biswas, Prof Uttara Naik-Nimbalkar and Dr Anindya Goswami respectively. Four students (Sanket Nandan, Shirish Kulhari, Nimit Rana and Akash Krishna) presented their Master’s project work.

This was the first symposium organized by the department where students had an opportunity to present their ongoing research. The talks in the symposium were on advanced research topics; nevertheless, efforts were made to make basic ideas tangible. In particular, the mathematical formulation of a real world problem, the relevant mathematical and statistical techniques were clarified carefully. A good number of students from inside and outside IISER Pune attended the event.

Home page: https://sites.google.com/site/anindyagoswami/home/symp2015

ICTS Program on Advances in Mathematical Biology December 7-16, 2014

Organizers LS Shashidhara, Pranay Goel and Sujatha Ramdorai

In addition to ICTS and IISER Pune, this Program was also supported by the Pacific Institutes of Mathematical Sciences (PIMS), Canada. The Program brought together leading mathematical biology researchers from

Symposia, Conferences & Events

Canada together with Indian scientists to deliver a series of pedagogical lectures on contemporary topics of interest. The opening lectures by Pranay Goel on the first day were an introduction to some essential mathematical techniques that were useful to later topics. The rest of the time was divided between three themes:

1. Mark Lewis, Daniel Coombs and Pauline van den Driessche lectured on topics in Ecology, Epidemiology and Immunology. Milind Watve, Ram Rup Sarkar and Sutirth Dey participated in the Discussions sessions centred on these topics.

2. Subhash Lele, Anil Gore, Shailaja Deshmukh and Akanksha Kashikar delivered lectures on Statistical inference in biological systems.

3. Lectures on Collective behaviour in cellular and organismal biology were delivered by Sitabhra Sinha, Debashish Chowdhury, Somdatta Sinha and Madan Rao. Collins Assisi participated in the discussion session on the topic.

Over 65 participants attended the Program from both Pune and all over India. The participants were drawn from varied backgrounds, rooted in theoretical science in some form or another, be it physics or mathematical biology or bioinformatics and so on. The participants were mostly at the early PhD level although some faculty and younger students also attended.

The atmosphere was vibrant with a very active participation from students, which was well appreciated by the speakers. The participants as well as speakers gave excellent feedback. All seemed to welcome the breadth of lectures, the high quality of the Program, the organization itself, and were generally pleased to have participated in the meeting.

The Program’s success indicates just how attractive topics in mathematical biology are for students in the country at this time. It speaks

to a burgeoning development of the field, and the awareness and maturity of the participants begs for an even greater investment in the conduction of such Programs that will disseminate high quality instruction to a very willing audience.

Mathematics Research Advisory Council July 26-28, 2014

The MRAC consists of the following five mathematicians of eminence:

Professor Manindra Agarwal, Indian Institute of Technology, Kanpur Professor TR Ramadas, Chennai Mathematical Institute Professor Ram Murty, Queen's University, Kingston, Canada Professor Dinesh Thakur, University of Rochester, USA Professor SRS Varadhan, Courant Institute, New York, USA

The first four members visited IISER Pune campus from July 26-28, 2014. The campus visit started with the Coordinator of Mathematics giving a presentation on mathematics at IISER Pune. This was followed for the next three days with meetings with each individual faculty member lasting for about 30 minutes; a meeting with each of the two postdocs; a meeting with all the mathematics PhD students; and a meeting with BS-MS students including the 5th year project students. At the end of their campus visit, the MRAC met with all discipline Coordinators and the Director to give their feedback about the entire mathematics programme. Later, they sent in their feedback in writing with critical comments and recommendations.

"Overall, the mathematics department is doing very well and is on track for becoming a leading department in India in terms of both teaching and research. Its present research strengths include number theory, representation theory and algebraic geometry. These areas are not unrelated to some of the other research areas of the department such as coding theory, graph theory, algebra and analysis and so there is room for some collaborative seminars amongst some of the research groups. In addition, the fact that IISER Pune has been the venue for high level research conferences and workshops, is an indication that it is moving in the right direction. The idea for PhD students to do a minor thesis before they embark on their doctoral thesis enables students to have a broader view of mathematics. This is an excellent initiative that we have not seen at many other universities. Clearly, some new and strategic appointments are needed to buttress the existing strengths of the department. The mathematics department of IISER Pune has had substantial growth and now has an impressive group of young faculty. It is doing quite well under a very good leadership. It is already on the international map, at least in the area of number theory and representation theory, because of the well-chosen high level research conferences and workshops organized or hosted here, as well as the innovative outreach activities. It will be a leading mathematics department in India once the other mathematics areas are also strengthened."

Young Women and Mathematics July 25-27, 2014

Scientific Committee & Organizers Anisa Chorwadwala (Convener); Anita Naolekar; Jaya Iyer (Chair); Mousumi Mandal; Pooja Singla Thakur

The Symposium Young Women and Mathematics (YWM-2014) was a follow-up of the Indian Women and Mathematics (IWM) symposia held twice in the past. The first one was IWM-2012 held at Institute of Mathematical Sciences, Chennai during January 8-10, 2012 and the next was IWM-2013 held at IISER Pune during July 26-28, 2013. The earlier IWMs were modeled to facilitate interaction between women mathematicians who are established researchers, and college teachers, and for undergraduate and graduate students.

Keeping in mind the increasing number of young women researchers in India in the recent years, the current meet, the third in the series, was named as "Young Women and Mathematics (YWM) Symposium". With National Board for Higher Mathematics (NBHM) India offering support for this venture, over 70 young women mathematicians from all over the country participated in the symposium. There were a few participants who were of Indian origin, either working or pursuing their doctoral studies abroad.

The plan of the symposium was to have (i) a few mini-courses, in order to introduce advanced areas of mathematics, (ii) some plenary talks by prominent researchers and (iii) some contributory talks by participants from varied fields of mathematics. There were two mini courses, one on “Knots, Graphs and Applications” and the second one was on "Lie Algebras and Representations". There were 9 plenary talks delivered by young women researchers from reputed Indian Institutes and Universities. The range of subjects varied from Number Theory to Commutative algebra, and from Homotopy Theory to Partial Differential Equations and Harmonic Analysis. All these focused and motivational talks were received with great enthusiasm from an informed audience.

There were around 15 contributory talks by researchers and post doctoral students. These talks were held in three parallel sessions namely (1) Analysis, (2) Algebra and its Applications and (3) Miscellaneous. There was a talk on the impact of some results from algebraic geometry to arithmetic circuits. The contributory talk by Seemin Rubab, NIT Srinagar titled "STEM Career and Women: Situation in Kashmir Valley” was interesting.

There was an invited talk by Dr Neena Gupta (INSA Young Scientist Award Recipient this year) from ISI Kolkata on her celebrated work "On

Zariski's Cancellation Problem". We also heard about her inspiring journey (she being a young woman achiever).

There was also a poster presentation session by participants, which showcased some interesting areas in mathematics. There was also a panel discussion on a career in Mathematics in India in the current scenario. The discussion focused on the funds and opportunities available to women, present research/job opportunities in India etc. The young audience comprising of graduate/ undergraduate students benefited highly from this discussion.

The symposium concluded with a session on feedback from the participants. In this age of specialization, many voices aired requests for Group Discussions, to initiate collaboration among women working in related areas. There was a very good suggestion that under the IWM funding, a group of women mathematicians planning to have a collaborative research work should gather at some specific location for a reasonably sufficient period of time. They need not hold formal lectures during this meet. They should hold discussions leading to the proposed collaborative research work. Some participants also expressed that more women of Indian origin, pursuing a career abroad should be invited to share their expertise.

The Mathematics discipline of IISER Pune, its Coordinator Professor Raghuram and Professor KN Ganesh, the Director of IISER Pune gave their whole-hearted support to host the event.

Home page: https://sites.google.com/site/ywmiisc/home

Topology and Geometry of Surfaces Symposium at the 29th Annual Conference of Ramanujan Mathematical Society June 30-July 7, 2014

Symposium Organizers Ravi Kulkarni, Tejas Kalelkar Local Organizers A Raghuram (Convener), Anisa Chorwadwala, Chandrasheel Bhagwat, Kaneenika Sinha and SA Katre (Co-convener) Invited Speakers Moira Chas (Stonybrook University), Ara Basmajian (CUNY) This symposium was part of the 29th Annual Conference of the Ramanujan Mathematical Society held in the week after the conclusion of the main events. It consisted of a mini-course on ”Computer driven

theorems and questions in geometry” by Prof Moira Chas and a mini-course on ”Identities of Hyperbolic surfaces” by Prof Ara Basmajian. Apart from students of IISER Pune, we also had participants from IISER Mohali, Pune University, Fergusson College and from industry. Homepage 29ac.ramanujanmathsociety.org

The 29th Annual Conference of Ramanujan Mathematical Society June 23-27, 2014

Local Organizers A Raghuram (Convener), Anisa Chorwadwala, Chandrasheel Bhagwat Kaneenika Sinha, and SA Katre (Co-convener) Invited Speakers Hyman Bass, V Suresh, KB Athreya, S Weintraub, Dinesh Thakur, G Rangarajan, S Sane, K Shiohama, S Thangavelu and Amiya Mukherjee

The RMS meeting is an annual event organised by RMS to promote mathematical research in India. With an attendance of more than 300 people, including junior and senior researchers from a wide range of institutions and universities across India, this is possibly the biggest annual mathematical event in India. We were extremely delighted to host this important event at IISER Pune in 2014. Apart from plenary talks by highly accomplished researchers and educators from across the world like Hyman Bass (University of Michigan, USA), Amiya Mukherjee (ISI Kolkata), KB Athreya (Iowa State University, USA), Dinesh Thakur (University of Rochester, USA) and K Shiohama

(Fukuoka University, Japan), Weintraub (Lehigh University, USA), SS Sane (IIT Bombay), G Rangarajan (IISc, Bangalore) and S Thangavelu (IISc, Bangalore), there were parallel symposia in several exciting research areas like Number Theory, Partial Differential Equations, Harmonic Analysis, Riemannian and Finsler Geometry, Complex Function Theory, Finite Groups, Logic, Discrete Mathematics, Topology and Geometry of Surfaces. An entire day was devoted to talks by experts on many recent advances in Mathematics which originate from Ramanujan's work. There were also several opportunities for graduate students to present their research work to a wide audience during contributed talk sessions. This meeting is very special because we hosted it at our Lecture Hall Complex almost immediately after it was dedicated to the nation by the President of India. We were able to accommodate almost all the participants in our brand new hostel and guest house buildings. Organizing an event of this magnitude and hosting huge number of participants at a new institute like ours was a huge administrative challenge. This was accomplished seamlessly through coordination between the Mathematics group, technical team, finance section, hostel and guest house staff, canteen staff and transport managers. Participants from all over the world and RMS executive committee members were highly impressed with the academic facilities and technical equipment made available by the institute. In fact, thanks to the near perfect execution of this meeting, RMS formally requested IISER Pune to host a joint meeting of RMS and Indian Mathematical Society with the American Mathematical Society --an international event of far bigger proportions in 2016! Homepage 29ac.ramanujanmathsociety.org

Number Theory Symposium at the 29th Annual Conference of Ramanujan Mathematical Society June 23-27, 2014

Symposium Organizer Debargha Banerjee Local Organizers A Raghuram (Convener), Anisa Chorwadwala, Chandrasheel Bhagwat, Kaneenika Sinha and SA Katre (Co-convener) Invited Speakers M Manickam (KSOM), VG Narasimha Kumar (IIT, H), Supriya Pisolkar

(IISER Pune), Baskar Balasubramanyam (IISER Pune), B. Ramakrishnan (HRI), K Srinivas (IMSC), S Katre (UoP). The number theory symposium started this year as part of the annual Ramanujan Mathematical Society meeting. This conference was supported by NBHM. Homepage 29ac.ramanujanmathsociety.org

ICTS Program on p-adic Aspects of Modular Forms June 10-20, 2014

Organizers A Raghuram, Baskar Balasubramanyam, Haruzo Hida, Jacques Tilouine Invited Speakers (a) For the workshop: R. Sujatha, Jacques Tilouine, Baskar Balasubramanyam, David Geraghty, Mladen Dimitrov, Haruzo Hida, A. Raghuram and Debargha Banerjee (b) For the advanced discussion meeting: Jeanine van Order, Haruzo Hida, Baskar Balasubramanyam, Olivier Fouquet, Chandrakant Sharma, Giovanni Rosso, Riccardo Brasca, Denis Benois, Mahesh Kakde, David Geraghty, Ming-Lun Hsieh, Devika Sharma, Fabian Januszewski, Eknath Ghate, Tadashi Ochiai, Mladen Dimitrov, Sudhanshu Shekhar, Ashay Burungale, Jacques Tilouine The aim of this program was to focus on the p-adic aspects of modular forms and related topics. The program consisted of two components, an instructional workshop followed by a discussion meeting. There were seven mini-courses in the workshop that focused on two broad themes: on p-adic families of automorphic forms with some modularity lifting applications in mind and on the construction of p-adic L-functions in various situations and their applications.

The final part of the program was a three day discussion meeting in which the state of current research in these topics were discussed.

Homepage http://www.icts.res.in/program/PAMF2014

Pune-Mumbai Number Theory Seminar April 4-5, 2014

Organizers Debargha Banerjee, Eknath Ghate, Ravi Raghunathan, Invited Speakers Jyoti Sengupta (TIFR), Amiya Kumar Mondal (IIT,B), Debargha Banerjee (IISER,P), Steven Spallone (IISER,P), Ravi Raghunathan (IIT,H), CS Rajan (TIFR) The inaugural Pune-Mumbai number theory meeting was organized at the Department of Mathematics, IIT Bombay. The aim of this seminar was to increase collaboration and interaction among the number theorists at IISER Pune, IITB and TIFR. This event has provided an opportunity for young number theorists to interact and collaborate with established mathematicians and is planned to be organized regularly every year/semester. Homepage https://sites.google.com/site/punebombaynumbertheoryseminar/

Mathematics Day 2014 March 08

The 2014 Math day had several following fun events along with a colloquium by Prof MS Narasimhan.

• We tested our mental arithmetic with the Shakuntala Devi Competition!

• Players squared off against an opponent in the Room of Games, in which you'll clash over NIM and Hackenbush, and learn the math to step up your game.

• We returned to LHC 101 for three party-type math games in the "Math Carnival".

• There were two activities in the Room of Symmetries: For one, we learned to make, decorate, and manipulate our own Hexaflexagons. We also learned the secrets of the timeless 15 Puzzle of sliding tiles, and its exotic variations!

• At the "Bubbles as Minimal Surfaces" workshop, we formed manifold shape-optimizing surfaces with soap and wires.

• The Prime Number Bee began at noon, which proceeded as follows: Students lined up as in a spelling bee, and successive students recited the prime numbers 2,3,5, ... Any student who gave a composite number, skipped a prime, or took too long had to sit, and the last two standing received a cash prize. Chandrasheel taught us some prime number trivia along the way.

• Women in Math Poster Competition and Showcase was conducted by Anisa during which teams of students designed a poster and quick talks to compete for a cash prize. Afterwards we watched the beloved Math Day Skit, bringing Scotland Yard to Pune with the "Sherlock Holmes: Game of Chances"!

• Then we had our eminent guest MS Narasimhan deliver his lecture "Mathematical Research in India after Independence: The Early Years", followed by the Award Ceremony where we celebrated our winners.

• Hard-core mathletes returned at 11pm for the CRYPTEX finals: our "Mathematical Treasure Hunt".

At work…

Turning coffee into theorems…

At Amlan’s farewell party

A Glimpse of Life in Math@IISER Pune

With Mathematics Research Advisory Council (MRAC) Members

The W

AY

Rationality is Overrated

Indian Institute of Science Education and Research (IISER) Pune Dr Homi J Bhabha Road, Pashan, Pune – 411 008, Maharashtra, India Phone: +91 20 2590 8001 Fax: +91 20 2586 5086 Website: www.iiserpune.ac.in