mathematical conjectures

8/3/2019 mathematical conjectures

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INFOMATOktober 2008

Kjre leser!

Selv om vi fortsatt har litt

sol og gode varmegrader er

det ikke lenge til vinteren og

dermed tida for planleggeen tur til Rondane. Les mer

om Ski og Matematikk 2009 i

dette nummeret.

Hsten ser ut til vre de na-

sjonale fagmters tid, bde

algebra og topologi har nr

forestende mter p nasjo-

nalt plan.

Og til slutt er det p tide

minne fagmiljene p ten-

ke p ske om programmer

ved Institut Mittag-Lefer,

skndasfristen er rett over

nyttr.

hilsen Arne B.

INFOMAT kommer ut med 11 nummer i ret og gis ut av Norsk Matematisk Forening. Deadline for neste

utgave er alltid den 10. i neste mned. Stoff til INFOMAT sendes tilinfomat at math.ntnu.no

Foreningen har hjemmesidehttp://www.matematikkforeningen.no/INFOMATAnsvarlig redaktr er Arne B. Sletsje, Universitetet i Oslo.

SKI OG MATEMATIKKRondablikk, 3.-6. januar 2009

pent for pmelding p:

http://www.math.uio.no/~dnormann/skiogmatematikk2009.html


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ARRANGEMENTER

Matematisk kalender

2008

Oktober:

30.-31.Nasjonalt algebramte, Oslo.November:

27.-28.Nordisk topologimte, Trondheim.Desember:

8.-9. Onsager-forelesningen,Trondheim.2009

Januar:

3.-6. Ski og matematikk,Rondane.Juni:

1.-4. Abelsymposiet, Combinatorial aspects ofcommutative algebra and algebraic geometry,

Voss8.-11.Britisk-Nordisk Matematikerkonf., OsloOktober:

12.-17.An international Conference on StochasticAnalysis and Applications, Hammamet, Tunisia(CMA).

NASJONALT AL-

GEBRAMTE,

Oslo, 30.-31. oktober

2008

Torsdag 30. og fredag 31. oktober inviterer vi tildet 2. nasjonale algebramte i Oslo. Mtet er foralle som er interessert i algebra eller algebraiskgeometri ved universiteter og hgskoler i Norge.Hensikten med mtet er gi hverandre innsikti hva som foregr innen forskning i algebra ogalgebraisk geometri i Norge. Mtet vil bli holdt

p Blindern.

Send en epost til Arne B. Sletsje ([email protected]) dersom du er interessert i delta. Del-takere som nsker holde et faglig foredrag bes

gi beskjed om dette.

NORDISK TOPOLOGIMTE,

Trondheim, 27.-28. november

The Topology group at NTNU in Trondheim andthe project Topology in Norway have the great

pleasure to invite fellow topologist to the secondNordic Topology Meeting in Trondheim 27 - 28November 2008.The programme will start on Thursday 27th No-

vember at 10 am and end on Friday 28th No-vember at 5 pm.All participants are kindly asked to register byemail to Inger Seehus (inger.seehusmath.ntnu.no), informing about how many nights you re-quire a hotel room.Please register as soon as possible for hotel res-ervations, and no later than Friday 17th Octo-ber.

Nye doktorgrader:

Marte Godvik fors-varer 20. oktober sin

avhandling On a Traf-c Flow Modell. Hovedveileder har vrt frstea-manuensis Harald Hanche-Olsen, Institutt formatematiske fag, NTNU.

Gjester i oktober:

Shahaf Hahamaov gjester professor KristianSeip, Analysegruppen.Gordana Todorov er gjest hos professor IdunReiten, Algebragruppen.

SKI OG MATEMATIKK

Rondane, 3.-6. januar 2009

F o r m l e tmed Ski og

Matematikker bringes k i g l a d ematematikere fra Norge og utland sammen tilfaglig og sosialt samvr.


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INSTITUT MITTAG-LEFFLER

POST DOCTORAL FELLOWSHIP

GRANTS FOR 2009/2010

Institut Mittag-Lefer announces a number of

grants for the academic year 2009/2010. Thegrants, intended for recent PhDs and advancedgraduate students, consist of:*a stipend amounting to 10,000 - 13,000 SEK

per month,(For PhDs living in the Stockholmarea an extra rent allowance will be paid)*travel expenses to and from Stockholm,*accommodation free of charge and ofce space

Preference will be given to applications for long-er stays, preferably for a semester.The subject areas for the years two programsare:Mathematical Logice: Set theory and model the-

CALL FOR PROPOSALS

FOR 2011 - 2012

The board of Institut Mittag-Lefer invites pro-gram proposals for the academic year 2011-2012.The Institute runs research programs in specializedareas of mathematics to which leading scientists areinvited. Post-docs and advanced graduate studentsare offered fellowships to participate in a concur-rent junior visiting program.Here is a summary of information about the pro-grams: The programs can run for the whole year, or

be of semester length (Sept 1 - Dec 15 and Jan 15 -June 15, respectively). Around 25-28 visitors arein residence at any given time. Participation in theresearch programs is by invitation only. The mini-

mum length of stay is one month. It is expected thattwo or three leading mathematicians will stay for atleast a semester each. Seminars are conducted oneor two afternoons per week. There is an emphasison free time for research and interaction. Lecture

series or informal seminars specically for the jun-ior participants are encouraged. Normally no work-shops are organized at the Institute in connectionwith the scientic programs.

The Institute is housed in a patrician 19th centuryvilla in a suburb of Stockholm. Visitors are housedon the premises. Lists of past, present and future

programs can be found at www.mittag-lefer.se.

Each scientic program is led by an organizing co-mittee, usually consisting of 2-4 well-established

mathematicians. This committee is expected tosuggest invitees to the board work closely with thedirector in planning the program take responsibilityfor scientic, educational and social issues during

the period of the program make sure that at least

one member of the committee is present at alltimes during the program have at least one mem-

ber from a Scandinavian country.

The selection criteria for proposals are scienticstrength and timeliness, and the degree to whichthe program would benet mathematical research

and post-graduate training in Scandinavia.Proposals should contain:*a description of the intended area of speciali-zation motivation why the proposed program islikely to move this area forward plans, if any, forthe training of junior participants,*a list of suggested invitees, most of whom shouldhave indicated an interest in the program and awillingness to participate for at least one montha description of the Scandinavian connection themembers of the proposed organizing committeeone member of the organizing committee desig-nated to serve as contact person.The deadline for applications is January 15,2009.

For further information, consult the Institutehome page www.mittag-lefer.se or contact the

director, Professor Anders Bjrner bjorner@mit-

tag-lefer.se


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NYTT FRA IMU

H. Clemens, Chair of the

DCSG:

A year ago two lecturerswere sought to participatein the beautifulproject ofthe French organizationCIMPA (Centre Interna-tional deMathmatiques

Pures et Appliques) tohelp rebuild the mathematics infrastructure inCambodia. The context of this work was de-scribed to potential volunteers as follows:We seek lecturers for intensive 3-4 week courses

at universities in the developing world, at the ad-

vanced undergraduate level. The lecturer would

be assisted by a local mathematics professor who

prepares the students beforehand, assists when

necessary during the course, and takes care of

any necessary follow-up. These courses shouldhave a student audience of 20 or more, be con-

trolled, with examinations, and be part of a reg-

ular degree program at the university at which

they are offered.

Past experience in the developing world is desir-

able but not necessary. However what is required

is tolerance for working in circumstances of mod-

est resources, unexplained inefciencies, and lim-

ited physical comforts.

Funds for all expenses, including travel, will beprovided; however, we request that the mathema-

ticians home institution offer leave with pay dur-

ing his/her 3-4 week absence. We believe that a

strong case can be made that cooperation with

this program will not only bring personal and pro-

fessional benet to the lecturer, but will also redound

to the credit of the lecturers institution.

40 volunteers immediately responded! Such an out-pouring of interest in contributing to the formationof students of mathematics in the developing worldcould not be ignored! The Developing CountriesStrategy Group of the International MathematicalUnion, in cooperation with CIMPA and the U.S.

National Committee for Mathematics, have builton that nucleus of 40 volunteers to launch the Vol-unteer Lecturer Program (VLP), whose goal is to

provide mathematician volunteers to give intensivemonth-long courses at universities in the develop-

ing world. The program is quite modest in size dueto the limited nancial resources of the sponsoring

organizations. But mathematicians interested inparticipating in the VLP, universities in the devel-oping world interested in hosting lecturers to teachin the context described above, and, as importantly,donors desiring to provide the E.3000 necessaryto support a VLP lecturer, should contact: SharonBerry Laurenti, Administrative Secretary, Develop-ing Countries Strategy Group of the International

Mathematical Union, e-mail: [email protected]

ory, fall 2009Dynamics and PDE:s, spring 2010In order to be considered for one of these grants

you must fulll the following conditions:*your research interest must fall within the areaof the program,*you must be either an advanced graduate stu-dent or a recent PhD (degree obtained in 2005orlater),Applications should be sent no later than Janu-ary 20, 2009.

Inquiries may be directed to the Institute direc-tor, Prof. Anders Bjrner bjorner@mittag-lefer.

se or, for practical matters, to Ms. Marie-LouiseKoskull [email protected]

EMMY NOETHER LECTURER:

FOR ICM 2010 IN HYDERABAD

Emmy Noether was one of the great mathemati-cians of her time, someone who worked and strug-gled for what she loved and believed in. Her life andwork remain a tremendous inspiration. The 2010Emmy Noether Lecture will be presented as a ple-

nary lecture at the International Congress of Math-ematicians in August 2010 in Hyderabad, to honourwomen who have made fundamental and sustainedcontributions to the mathematical sciences.There have been Emmy Noether Lectures at four

previous ICMs, and this will be the second timethat the selection of the Emmy Noether Lecturerhas been made formally by the IMU. The IMU Ex-ecutive Committee has established a committee ofve, chaired by Cheryl Praeger (Australia), to select

the 2010 Emmy Noether Lecturer. The committeewill conduct their work over the next 6-9 months,and suggestions for consideration by the committeemay be sent to Cheryl Praeger at [email protected]


5/8

PRESSEKLIPP

MATHEMATICIANS ILLUMINATE

DEEP CONNECTION BETWEEN

CLASSICAL AND QUANTUM

PHYSICS

Science Daily(Oct. 17, 2008)

In a seminar co-organized by Stanford Univer-sity and the American Institute of Mathematics,Soundararajan announced that he and RomanHolowinsky have proven a signicant version

of the quantum unique ergodicity (QUE) conjec-ture.This is one of the best theorems of the year, said

Peter Sarnak, a mathematician from Princetonwho along with Zeev Rudnick from the Univer-sity of Tel Aviv formulated the conjecture fteen

years ago in an effort to understand the connec-tions between classical and quantum physics.

I was aware that Soundararajan and Holowinsky

were both attacking QUE using different tech-

niques and was astounded to nd that their meth-

ods miraculously combined to completely solve

the problem, said Sarnak. Both approaches come

from number theory, an area of pure mathematicswhich recently has been found to have surprisingconnections to physics.The motivation behind the problem is to under-stand how waves are inuenced by the geometry

of their enclosure. Imagine sound waves in a con-cert hall. In a well-designed concert hall you canhear every note from every seat. The sound wavesspread out uniformly and evenly. At the oppositeextreme are whispering galleries where sound

concentrates in a small area.The mathematical world is populated by all kindsof shapes, some of which are easy to picture, likespheres and donuts, and others which are con-structed from abstract mathematics. All of theseshapes have waves associated with them. Sound-ararajan and Holowinsky showed that for certainshapes that come from number theory, the wavesalways spread out evenly. For these shapes thereare no whispering galleries.The quantum unique ergodicity conjecture

(QUE) comes from the area of physics known asquantum chaos. The goal of quantum chaos isto understand the relationship between classical

physics--the rules that govern the motion of mac-

roscopic objects like people and planets when theirmotion is chaotic, with quantum physics-the rulesthat govern the microscopic world.

The work of Holowinsky and Soundararajan isbrilliant, said physicist Jens Marklof of BristolUniversity, and tells us about the behaviour of a

particle trapped on the modular surface in a strong

magnetic eld.The problems of quantum chaos can be understoodin terms of billiards. On a standard rectangular bil-liard table the motion of the balls is predictableand easy to describe. Things get more interesting ifthe table has curved edges, known as a stadium.Then it turns out most paths are chaotic and overtime ll out the billiard table, a result proven by the

mathematical physicist Leonid Bunimovich.In their QUE conjecture, Rudnick and Sarnak hy-

pothesized that for a large class of systems, unlikethe stadium there are no scars or bouncing ballstates and in fact all states become evenly distrib-uted. Holowinsky and Soundararajans work showsthat the conjecture is true in the number theoreticsetting.The conjecture of Rudnick and Sarnak deals with

certain kinds of shapes called manifolds, or moretechnically, manifolds of negative curvature, someof which come from problems in higher arithmetic.

Fundamental domains and zeros of cusp forms. This pic-

ture shows the zeros of a weight 500 Hecke eigenform in a

particular fundamental domain for SL(2,Z). Zeev Rudnick

proved that QUE implies that the zeros of the associatedcusp forms also are equidistributed in the (hyperbolic) up-

per half-plane. So, this picture is an illustration of the result

of Holowinsky and Soundararajan. (Credit: Image courtesy

of Fredrik Stromberg)


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ONSAGER-FORELESNINGEN 2008

TERENCE TAO ER LARS ONSAG-

ER FORELESER 2008 VED NTNU

Hvert r avholdes det en

Lars Onsager forelesningved NTNU, oppkalt et-ter Lars Onsager (1903-1976; sivilingenir NTH1925, Nobelprisen i kje-mi i 1968). Foreleserener en fremragende for-sker innen feltene kjemi,fysikk eller matematikk.Mer informasjon ns p

websiden www.math.ntnu.no/onsager.rets foreleser er Terence Tao fra UCLA (http://www.math.ucla.edu/~tao/). Hans mange utmer-kelser skulle vre velkjente for INFOMATs le-sere, s la oss nye ossmed si at han tok PhDved Princeton da han var20 r gammel, ble full

professor ved UCLAsom 24-ring, og mottokFields-medaljen i 2006.Han arbeider innen ereomrder av matema-tikken - fra tallteori tildifferensialligninger.

Tao skal gi to forelesninger ved NTNU. Mandagden 8. desember kl. 11:15-12:00 i R2, Glshau-gen, holder han den ofsielle Onsager-forelesnin-gen: Structure and randomness in the prime num-bers}Abstract: God may not play dice with the universe,but something strange is going on with the prime

numbers (Paul Erds) The prime numbers are afascinating blend of both structure (for instance,almost all primes are odd) and randomness. It iswidely believed that beyond the obvious struc-tures in the primes, the primes otherwise behaveas if they were distributed randomly; this pseu-dorandomness then underlies our belief in many

unsolved conjectures about the primes, from thetwin prime conjecture to the Riemann hypothesis.This pseudorandomness has been frustratinglyelusive to actually prove rigorously, but recentlythere has been progress in capturing enough of this

pseudorandomness to establish new results aboutthe primes, such as the fact that they contain arbi-trarily long progressions. We survey some of thesedevelopments in this talk.Tirsdag den 9. desember kl. 11:15-12:00 i EL2,

Glshaugen, holder han flgende forelesning:Compressed sensingAbstract: Suppose one wants to recover an un-known signal x in Rn from a given vectorAx=Bin Rm of linear measurements of the signal x. Ifthe number of measurements m is less than the de-grees of freedom n of the signal, then the prob-lem is underdetermined and the solution x is notunique. However, if we also know thatx issparseorcompressible with respect to some basis, then itis a remarkable fact that (given some assumptionson the measurement matrixA) we can reconstruct

x from the measurements b with high accuracy, andin some cases with perfect accuracy. Furthermore,the algorithm for performing the reconstructionis computationally feasible. This observation un-derlies the newly developing eld ofcompressed

sensing. In this talk we will discuss some of themathematical foundations of this eld.

Helge Holden

(leder av Onsager-komiten ved NTNU)

The corresponding waves are analogous to highlyexcited states in quantum mechanics.Soundararajan and Holowinsky each developednew techniques to solve a particular case of QUE.The waves in this setting are known as holo-morphic Hecke eigenforms. The approaches of

both researchers work individually most of thetime and miraculously when combined they com-

pletely solve the problem. Their work is a lovelyblend of the ideas of physics and abstract mathe-

matics, said Brian Conrey, Director of the Ameri-can Institute of Mathematics.According to Lev Kaplan, a physicist at TulaneUniversity, This is a good example of mathemati-

cal work inspired by an interesting physical prob-lem, and it has relevance to our understanding of

quantum behavior in classically chaotic dynami-

cal systems.


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SKI OG MATEMATIKK

SKI OG MATEMATIKK (2009)

Sted: Rondablikk hyfjellshotell.Tid: 03.01.2009 -06.01.2009 med ankomst tillunsj 3/1 og avreise etter frokost 6/1.Merk at dette ret vil arrangementet g fra lrd-ag til tirsdag.Formlet med Ski og Matematikk er bringeskiglade matematikere fra Norge og utlandsammen til faglig og sosialt samvr. Poten-sielle deltagere som nsker presentere sinefaglige interesser eller et tema de nner allment

interessant for kolleger, inviteres til melde innforedrag. Det endelige programmet vil bli sattsammen ut fra hvilke forslag som kommer inn

og ut fra hvem som melder seg p.

PriserPr. deltager/dobbeltrom NOK 2.150Pr. samboer/ektefelle NOK 1.660Pr. person/enkeltrom NOK 2.450.Barn under 15 r i ekstraseng, NOK 250 prdgn.Hotellet kan formidle transport fra og til Vin-stra stasjon. Prisen p transporten vil avhenge

av hvor mange som benytter seg av de enkeltetilbud.

Bekreftede foredragsholdere pr dd.Magnus B. LandstadArild Stubhaug

Lrdag 3/1:15.15 - 16.00: TBA16.00 - 16.30: Kaffepause16.30 - 17.15: TBA17.25 - 18.10: TBA

Sndag 4/1:15.15 - 16.00 TBA

16.00 - 16.30: Kaffepause16.30 - 17.15: TBA17.25 - 18.10: TBA

Mandag 7/1:15.15 - 16.00: TBA16.00 - 16.30: Kaffepause16.30 - 17.15: TBA17.25 - 18.10: TBA

PmeldingDag Normann e-post [email protected]

Pmeldingsfrist: 15.12.2008.Deltagere som melder seg p alene, vil bli plas-

sert p enkeltrom dersom de ikke ber om noe an-net. Deltagere som melder seg p sammen vil bli

plassert p dobbeltrom dersom de ikke ber om noeannet.


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SKI OG MATEMATIKK

Noen bilder fra Rondane.Foreningen nsker allevelkommen til Ski ogMatematikk 2009.

mathematical conjectures

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