curriculum of scienti c and teaching activity of ...abernardi/encv.pdf · november 2005{november...

Alessandra Bernardi’s CV

Curriculum of Scientific and Teachingactivity of Alessandra Bernardi

1 Essential Data

• Born June 27, 1977 in Porretta Terme, Bologna, Italy

• Nazionality Italian

• Actual Position, December 2013 – December 2016: Researcher RTD-b)

• Belonging to: Universita di Bologna, Dipartimento di Matematica

– Office Mailing Address:

Alessandra BernardiUniversita di BolognaDipartimento di MatematicaPiazza di Porta San Donato 5I-40126 BolognaItaly

– Office Phone Number: 0039 051 209 4459

– E.mail: [email protected]

– Web Page: http://www.dm.unibo.it/∼abernardi/

• Habilitations:

– Qualification to Maıtre de Conference in the section 25 (Pure Mathematics) in the Frenchuniversities. Obtained in February 2012.

– Qualification to Professeur in the section 25 (Pure Mathematics) in the French universities.Obtained in February 2012.

– Abilitazione to Professore Associato (Associate Professor) in Mathematics in the Italian uni-versities. Obtained in December 2013 (valid until December 30, 2019).

– Abilitazione to Professore Associato (Associate Professor) in Mathematics in the Italian uni-versities. Obtained in December 2014 (valid until December 30, 2020).

• Institutional and Organization charges:

– From April 2015 to April 2019. Segretario aggiunto of the UMI (Unione Matematica Italiana).

Bologna (Italy), October 30, 2015 1 Alessandra Bernardi

Alessandra Bernardi’s CV 1 ESSENTIAL DATA

– Form September 2015. Member of the UMI Working Group: “Gruppo Risorse Umane”.

– From September 2015. Member of the editorial committee of the electronic journal: “UMINewsletter”. (First Issue expected in January 2016).

– July 2015. Invited to join the FWO-Expertpanel (Fonds Wetenschappelijk Onderzoek Vlaan-deren) – (Flanders Research Foundation) for the evaluation of applications for fellowships andresearch projects.

• Leaves

– From January 13 to July 14, 2014. Maternity Leave.

• Guest at:

– Math. Department at Universita degli Studi di Trento, Italy.


Alessandra Bernardi’s CV CONTENTS

Contents

1 Essential Data 1

2 Education 5

3 Employment 5

4 Research Interests 64.1 Active research collaborations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

5 Research abroad 9

6 Talks and Conferences 126.1 Talks in Italian and international conferences . . . . . . . . . . . . . . . . . . . . . . . . . 126.2 Invited Talks in Italian and foreign Universities . . . . . . . . . . . . . . . . . . . . . . . . 136.3 Other presentations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146.4 Additional Conferences and Schools Attended . . . . . . . . . . . . . . . . . . . . . . . . . 15

7 Organization of Schools and Conferences 17

8 Coordination of Research Projects 178.1 Funded Research Projects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

8.1.1 International . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178.1.2 Italian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

8.2 Research projects that passed the first steps of the evaluation process . . . . . . . . . . . 188.3 Participation to other Research Projects . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

9 Awards 20

10 Teaching activity 2010.1 Teaching activity abroad (for PhD Students or higher) . . . . . . . . . . . . . . . . . . . . 2010.2 Teaching activity in Italy (for undergraduates) . . . . . . . . . . . . . . . . . . . . . . . . 21

10.2.1 Teaching professor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2110.2.2 Tutorials and Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

11 Scientific production 2111.1 Bibliometrics indicies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2111.2 Books . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2211.3 PhD Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2211.4 Published articles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2311.5 Preprints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

12 Reviewer and Referee Activities 3112.1 Referee . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3112.2 Reviewer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31


Alessandra Bernardi’s CV CONTENTS

13 Appendix 3213.1 Scientific Evaluation of the Marie Curie project by the European Community . . . . . . . 32


Alessandra Bernardi’s CV 3 EMPLOYMENT

2 Education

• June 1996. Graduated from the high school Liceo Scientifico of Polo Scolastico Maria Montessoriin Porretta Terme, Bologna, Italy, with 60/60.

• March 16, 2001 Laurea degree in Mathematics with full marks and honors (110/110 with praise) fromAlma Mater Studiorum Universita degli Studi di Bologna. Thesis title: “Schemi 0-dimensionalie forme canoniche di polinomi omogenei”, (i.e. “0-dimensional schemes and canonical forms ofhomogeneous polinomials”). Advisor: Prof. A. Gimigliano (University of Bologna).

In this thesis I firstly present the relations between already solved problems like “dimen-sions of secant varieties of Veronese varieties”, “postulations of fat points” and “BigWaring Problem”. Then I use Inverse Systems to compute the postulations of n-th fatpoints in some cases, and the dimension of some secant varieties of varieties parameter-izing forms of the type Ld−jF where L is a linear form in 3 variables and F is a form ofdegree j in 3 variables.

• 2001-2005. PhD in Mathematics, Universita degli Studi di Milano. Thesis title: “Varieties param-eterizing forms and their secant varieties”. Advisor: Prof. A. Gimigliano (University of Bologna).

In this thesis I study various problems related with varieties parameterizing forms ortensors:

– Secant varieties to osculating varieties to Veronese varieties (the dimensions are com-puted in many cases);

– Secant varieties to varieties that parameterize forms that can be written ad the productof forms in different degrees (the dimensions are computed in some cases);

– Varieties that parameterize forms in n+1-variables that can be written as the productof d linear forms (the dimension of their secant varieties are computed in many cases;moreover it is found a contraexample to a conjecture formulated by R. Ehrenborg in1999 that states that the secant varieties to the Grassmannian G(n − 1, n + d − 1)is the same of the one of secant varieties of those varieties parameterizing forms inn+ 1-variables that can be written as the product of d linear forms);

– Secant varieties of Segre varieties (I relate two different approaches for studying thosevarieties: the one of Inverse System and a new one in Representation Theory).

Some parts of this thesis where produced during missions abroad (see Section “5 Research abroad”items 1. and 2 of this Curriculum).

3 Employment

• 2001–2005 PhD in Mathematics, Universita degli Studi di Milano, Italy.

• September 2005–January 2006, Research Assistant, Texas A&M University, College Station,Texas, USA.

• June 28–September 27, 2006, Investigador extranjero en la UCM (Universidad Complutense deMadrid, Spagna), financed by GRUPO SANTANDER.


Alessandra Bernardi’s CV 4 RESEARCH INTERESTS

• November 2005–November 2009, Assegnista di ricerca; Alma Mater Studiorum Universita deglistudi Bologna, Italy.

• July 2008, Teaching Assistant, MSRI - Mathematical Sciences Research Institute - (Berkeley,California - USA).

• November 2, 2009 – November 1, 2010: Post Doc, CIRM (Centro Internazionale per la RicercaMatematica) - Fondazione Bruno Kessler (Trento - Italy).

• November 8, 2010 – November 7, 2012: Individual Marie Curie Fellow (Post Doc) IEF (In-ternational European Fellowship), INRIA (Institut National de Recherche en Informatique et enAutomatique) Sophia Antipolis - Mediterranee (Francia).

• January 17 – February 26, 2011: Visitor, Mittag-Leffler Intitut (The Royal Swedish academy ofsciences) invited by A. Dickenstein, S. Di Rocco, R. Piene, K. Ranestad and B. Sturmfels for theSpring Semester 2011 “Algebraic geometry with a view towards applications”.

• November 2012–December 2013, Researcher RTD a), University of Torino, Department of Math-ematics “Giuseppe Peano”, Italy.

• December 2013–December 2016, Researcher RTD b), University of Bologna, Department ofMathematics, Italy.

• November 2014–December 2014. Long-Term Participant at Simons Institute for Theory ofComputing (Berkeley, CA, USA), in the framework of the Fall Program 2014 “Algorithms andComplexity in Algebraic Geometry”, Invited by P. Burgisser, JM Landsberg, K. Mulmuley, B.Sturmfels.

4 Research Interests

My research interests are in the field of Algebraic Geometry, Algebra and their applications. In particular:

Secant varieties, their dimensions and ideals; 0-dimensional schemes and their postulations;Varieties parameterizing polynomials and/or tensors both in the complex case and in the realcase (Veronese variety, Segre variety, Grassmannians, Flag varieties, Homogeneous varieties);Rank of symmetric tensors and structured tensors; Uniqueness of the decomposition of a ten-sor; algebraic and numerical algorithms for the tensor decomposition both in the complex andreal case; Applications to telecommunications, complexity theory, data analysis, phylogeneticsand physics.

The main objective of my present research is the kick-off of an independent research line undermy own responsibility on the topics on which I have accumulated international experience in the firststages of my scientific career, namely the DECOMPOSITION OF STRUCTURED TENSORS and theCOMPUTATION OF THEIR STRUCTURED RANK.

The Tensor Decomposition (TD) problem from linear and multilinear algebra point of view consistsof writing a structured tensor as a minimal linear combination of r indecomposable tensors of the samestructure, r being the rank. In geometrical terms, dealing with rank 1 structured tensors, corresponds tostudying subvarieties of Segre varieties that parametrize rank 1 tensors of a certain structure.



One of the central problems in this field is the determination of ALGORITHMS to compute thestructured rank of a given tensor. Up to now, the only available ones are the classical Sylvester algorithmfor complex symmetric tensors in 2 variables and its modern generalization to partially symmetric tensors,developed during my stay at INRIA with Brachat, Comon and Mourrain. My scientific project is toproceed further investigating other cases, starting from skew-symmetric ones.

The main geometric tool to tackle these problems are SECANT VARIETIES that allow to naturallystudy a closely related concept of rank, the so called border rank. The most direct strategy to knowthe border rank of a structured tensor would be to test it in the equations of certain secant varieties.Despite the great interest that the mathematical community has dedicated to this area for decades, thedetermination of the equations of secant varieties is among the most significant open problems even from apure algebraic geometric point of view. So far, all available techniques to compute IDEALS OF SECANTVARIETIES of varieties parameterizing tensors (VPT) combine algebraic geometry and representationtheory in group theory. As varieties of this kind are homogeneous varieties for the action of some group,their ideal can be described in terms of irreducible Schur modules invariant for the action of the samegroup. I have learned those techniques during my visits at the Texas A&M University with Prof. JMLandsberg who has been one of the firsts that brought them into the field of TD. Moreover I have alreadyhad the opportunity of helping PhD students, both mathematicians and applied ones, in tackling TDopen problems during my TA for the PhD course at MSRI – Berkeley (2008).Another project that I have is to further exploit these techniques to obtain new results on specific secantvarieties.

Another problem that has stimulated important advances in this field is the one of the dimensions of se-cant varieties, which has led to the introduction of concepts such as APOLARITY and 0-DIMENSIONALHILBERT SCHEMES to this context. I plan to extend the concept of apolarity to more general classesof structured tensors starting from skew-symmetric ones. This will serve to extend the Alexander-Hirschowitz theorem and determine the dimension of secant varieties of various VPT, as well as to writealgorithms for computing the rank of the corresponding structured tensors. Apolarity and 0-dimensionalHilbert schemes naturally appear in generalized singular value decompositions based on Henkel matrices,which are the key tool of all existing TD algorithms.

The algorithmic part of my projects started firstly with pure algebraic methods for the decompositionof symmetric and partially symmetric tensors. Now, thanks to my international network, I am becominginterested also in the numerical side of this problem, in particular I am developing a numerical algorithmthat will allow to find the solution for TD with the software Bertini. I have built up this project togetherwith one of the developers of the software Bertini (in particular J. Hauenstein) and with B. Mourrain.This is an ambitious but very realistic project and we will involve PhD students and/or Post Doc’s thatwould be interested in it.

The invitation to participate at the workshop in Palo Alto during the summer 2008 (Section 5 item6 of this cv) gave me a more insite interest in the APPLICATIONS (multilinear techniques for dataanalysis in signal processing for telecommunication; algebraic statistics; geometric approaches for theP?=NP problem; hidden variables problems in phylogenetics and medical engineering; entanglement inquantum information theory).This interest has been its first realization in the writing and winning of my Marie Curie project at INRIA(Section ?? of this cv) in collaboration with B. Mourrain and P. Comon in the telecommunications field(the knowledge of the TD of a tensor allows to solve problems of Blind Identification and of Tensorpolyadic decomposition for Antenna Array Processing). I will pursue this direction by a long visit atGrenoble CNRS in the equipe directed by P. Comon.Another applied side that I intend to work on will be the one on the effective decomposition of noisy



tensors (namely tensors coming from concrete data analysis). I will work on this together with L. DeLathauwer (KU Leuven, Belgio) who has already written a package in MATLAB for the TD of noisytensors. I will also want to tackle the problem of identifiability of a noisy tensor together with N.Vannieuwenhoven (PhD student at KU Leuven, Belgio) who is already working on this from a morecomputational point of view and who has recently contacted me for an interesting collaboration.

4.1 Active research collaborations

In the following collaborations, the underlined ones are those which have already led to papers/preprints.

• Pure mathematical collaborations:

– SECANT VARIETIES AND THEIR DIMENSIONS, POSTULATIONS OF 0-DIMENSIONALSCHEMES:

H. Abo (Idaho Univ.), E. Ballico (Univ. Trento), E. Carlini (Monash Univ., Melbourne),MV Catalisano (Univ. Genova), A.V. Geramita (Queens Univ., Canada), A. Gimigliano(Univ. Bologna), M. Ida (Univ. Bologna).

– ALGORITHMS FOR TENSOR DECOMPOSITION:

E. Ballico (Univ. Trento), A. Gimigliano, M. Ida (Univ. Bologna), B. Mourrain (INRIA,Sophia Antipolis, France).

– IDENTIFIABILITY OF TENSORS:

E. Ballico (Univ. Trento), MV Catalisano (Univ. Genova), L. Chiantini (Univ. Siena), N.Vannieuwenhoven (KU Leuven, Belgium).

– STUDY OF SKEW-SYMMETRIC TENSORS:

E. Arrondo (Univ. Complutense, Madrid), B. Mourrain (INRIA, Sophia Antipolis, Francia),M. Michalek (MSRI, Berkeley), C. Raicu (Princeton Univ.).

– CACTUS RANK:

– J. Jelisiejew (Univ. Warsaw), P. M. Marques (Univ. Evora, Portugal), K. Ranestad (Univ. ofOslo).

– TENSOR DECOMPOSITION FOR REAL SYMMETRIC TENSORS:

G. Blekherman (Georgia Tech), G. Ottaviani (Univ. Firenze).

– REPRESENTATION THEORY FOR THE TENSOR DECOMPOSITION PROBLEM:

JM Landsberg (Texas A&M), M. Michalek (MSRI, Berkeley), C. Raicu (Princeton Univ.).

• Applied collaborations:

– ALGORITHMS FOR THE DECOMPOSITION OF PARTIALLY SYMMETRIC TENSORS(in telecommunication):

P. Comon (CNRS Grenoble), B. Mourrain (INIRA, Sophia Antipolis, France).

– OTTIMIZATION AND APPROXIMATION OF NOISY TENSORS (in mathematical engi-neering):

Lieven De Lathauwer, N. Vannieuwenhoven (KU Leuven, Belgium).


Alessandra Bernardi’s CV 5 RESEARCH ABROAD

– NUMERICAL ALGORITHMS FOR THE DECOMPOSITION OF STRUCTURED TEN-SORS (development of numerical softwares):

N. Daleo (Worchester State Univ., Massachusetts) J. Hauenstein (Univ. Notre Dame, Indiana).

– ENTANGLEMENT (in quantum physics):

I. Carusotto (INO-CNR-BEC, Trento).

5 Research abroad

In this section only the long stays abroad and the most significant international events for my career arehighlighted.

1. September 17 – December 17, 2004, [Long Stay] at Queen’s University (Kingston, Ontario,Canada), invited by Prof. A.V. Geramita.

During this visit the research area was:

• “Secant Varieties of Osculating Varieties of Veronese Varieties” with Prof. A.V.Geramita;

• Representation Theory techniques to study the problem of generation of the ideals of“Secant varieties to Segre varieties” with Prof. M. Roth and I. Dimitrov.

The results obtained during this visit were posted in my PhD thesis.

2. January 9 – March 1, 2005, [Long Stay] at Universidad Complutense de Madrid (Madrid, Spain),invited by Prof. E. Arrondo.

During this visit the research area was the study of secant varieties of varieties parameter-izing forms that can be written as product of linear forms. We produced a contraexamle tothe conjecture of Ehrenborg (1999) that stated that the dimension of certain secant vari-eties to Grassmanians was the same of certain secant varieties to varieties parameterizingforms splitting as a product of linear forms. The results obtained during this visit wereposted in my PhD thesis. We formulate a conjecture that turned out to be very interestingfor the community that nowadays si working in proving it (in particular H. Abo is veryactive in this attempt).

3. First semester 2005–2006, [Long Stay] at Texas A&M University (College Station, Texas, USA),Researcher Assistant for the PhD course “MATH 689-computational complexity geometry” for Prof.J.M. Landsberg.

During this visit, beside the above research assistant activity, I started the study of thedimensions of the first secant varieties to adjoint varieties (homogeneous varieties asso-ciated to Lie Algebras) with Prof. JM Landsberg.

4. June 28 – September 27, 2006, [Long Stay] at Universidad Complutense de Madrid (Madrid,Spain), invited by Prof. E. Arrondo in the framework “Programa de visitantes distinguidos einvestigadores extranjeros en la UCM” financed by “GRUPO SANTANDER”.

During this visit, I studied in collaboration of Prof. E. Arrondo the intersection locusbetween Grassmannians and



• Veronese varieties,

• Secant varieties to Veronese varieties,

• Tangential varieties and Veronese varieties,

• Osculating varieties to Veronese varieties,

• Varieties parameterizing forms that are decomposable as product of linear forms.

5. July 7 – 20, 2008, [Long Stay] at MSRI (Mathematical Sciences Research Institute), Berkeley(California - USA) invited as Teaching Assistant for the Graduate Workshop “Geometry and rep-resentation theory of tensors for computer science, statistics and other areas”.

This workshop was organized by JM Landsberg (Texas A&M - Texas - USA), L.-H. Lim(UC Berkeley - California - USA) and J. Morton (UC Berkeley - California - USA) withthe goal of introducing PhD students to relevant topics in Geometry and RepresentationTheory. Computational complexity, statistical learning theory, signal processing, scien-tific data analysis, were recently formulated in geometric terms via representation theory.Specifically the problem studied was the one of “matrix multiplication”. During the sec-ond week of the workshop it was possible to work on open problems and I supported thestudents in their work. Now, some of those students are established researchers.

6. July 21 – 27, 2008, at AIM (American Institute of Mathematics) of Palo Alto (California - USA)for the Workshop “Geometry and representation theory of tensors for computer science, statisticsand other areas”.

This workshop was organized by JM Landsberg (Texas A&M - Texas - USA), L.-H. Lim(UC Berkeley - California - USA), J. Morton (UC Berkeley - California - USA) and J.Weyman (Northeastern University - Boston - MA - USA).It was devoted to the study of problems in quantum computing, complexity theory, statis-tical learning theory, signal processing, and data analysis, problems in algebraic geometryand representation theory. In all these areas there are varieties in tensor spaces that areinvariant by change of coordinates.Our mathematical work in this workshop was to translate problems from the applied worldinto mathematical language and solve them where possible. This workshop opened manynew research areas and techniques.

7. November 2010 – November 2012, [Long Stay] at INRIA (Sophia Antipolis, France) as Marie Curiefellow (Post Doc). Proget: FP7-PEOPLE-2009-IEF - 252367 - DECONSTRUCT: “Decompositionof Structured Tensors, Algorithms and Characterization”.

SUMMARY OF THE PROJECT: Tensors play a wide role in numerous application areasas Signal Processing for Telecommunications, Arithmetic Complexity or Data Analysis.In some applications tensors may be completely symmetric, or symmetric only in somemodes, or may not be symmetric. In most of these applications, the decomposition ofa tensor into a sum of rank-1 terms is relevant, since tensors of interest have a re-duced rank. Most of them are structured i.e. they are either symmetric or enjoy someindex-invariance. Lastly, they are often real, which raises open problems concerning theexistence and calculation of the decompositions. These issues build the basic bricks of theresearch program we propose. The classes of tensors described above have a geometric



translations in terms of classical algebraic varieties: Segre, Veronese, Segre-Veronese va-rieties and Grassmannians and their secant varieties. A complete description of equationsfor those secant varieties and their dimensions is still not known (only dimensions of se-cant varieties to Veronsean are classified), although they have been studied by algebraicand differential geometers and algebraists for a long period up to now. The aim of thisresearch project is:

• to attack both the description of the ideal of those secant varieties and their dimen-sions, starting from low dimensions and low degrees,

• to propose algorithms able to compute the rank of structured tensors.

Workshops in Palo Alto (CA-USA, 2008) and in Nice (FR, 2009) showed that Italyand France are among the most active in Europe in the field of tensor decompositions.Both the coordinator of this project and the hosting organization have already obtainedresults in this field regarding equations and algorithms. Hence this program is crucialfor the development of those research areas in the European Community, along with thenumerous international collaborations already existing. The impact of this project will bevisible in both academic and industrial worlds.

8. January, 17 – February 26, 2011, [Long Stay] at Mittag-Leffler Institut (The Royal Swedishacademy of sciences) invited as Visitor by A. Dickenstein, S. Di Rocco, R. Piene, K. Ranestadand B. Sturmfels to participate at the Spring Semester 2011 nell’ambito “Algebraic geometry witha view towards applications”.

I was invited by the organizers of the semester as an expert on secant varieties, rank oftensors and applications of the same. I started collaborations with K. Ranestad (see mypublication 17), J. D. Hauenstein on an effective numerical algorithm for the computationof the rank of any polynomial, E. S. Allman, J. A. Rhodes on a problem in phylogeneticwhere tensor rank is needed.

9. September 1–7, 2013, Lukecin, Polonia. Invited by J. Buczynski, E. Carlini, J. Jelisiejew and M.Korascome as one of the three speakers of the 36th autumn school of polish Algebraic Geometry.

Together with Prof. G. Ottaviani (Univ. Firenze) I gave the main lectures of the school,while Prof. K. Ranestad (Uio Oslo) was in charge of the exercise session. The level ofthe school was advanced, from PhD level on.

10. November 2014–December 2014, [Long Stay] Long-Term Participant at the Simons Institute forTheory of Computing (Berkeley, CA, USA), in the framework of the fall program 2014 “Algo-rithms and Complexity in Algebraic Geometry”, Invited by Prof. P. Burgisser, JM Landsberg, K.Mulmuley, B. Sturmfels.

I was invited to participate to the whole semester, but for family reasons (maternityleave) I participated only to one month. It has been the most important event of 2014for what concerns the study of tensors both from a theoretical point of view and froma more applied one. During my stay I had the opportunity to get in touch with manyalgebraists, geometers, computer scientists and applied researchers of various kind (fromthe world of Google to the one of quantum physicists for the tensor network) and I hadthe chance of starting new collaborations. Moreover I had the possibility of reinforcing the


Alessandra Bernardi’s CV 6 TALKS AND CONFERENCES

already existing collaborations and in particular I concluded two already begun projects:one on a numerical algorithm for the decomposition of structured tensors together withJ. Hauenstein that will be implemented on Bertini, and one on the decomposition of realsymmetric tensors with G. Blekherman and G. Ottaviani.

6 Talks and Conferences

6.1 Talks in Italian and international conferences

1. “Osculating varieties of Veronesean and their higher secant varieties”, December 10, 2004 - CMS2004 Winter Meeting, Montreal (Quebec, Canada).

2. “Varieta delle secanti a varieta che parametrizzano forme ottenute come prodotto di forme lineari”,May 29, 2006, Giornate di Geometria Algebrica e argomenti correlati VIII, Univ. Trieste.

3. [Invited] “Secant Varieties and Ideals of varieties parameterizing certain symmetric tensors”, July17, 2008, MSRI (Mathematical Sciences Research Institute) (Berkeley, California, USA).

4. “Sylvester’s Algorithm”, June 10, 2009, Workshop on tensors and interpolation, Nice, France.

5. “From the Waring problem to tensor rank through secant varieties”, March 18, 2010, SAGA WinterSchool, Auron, Nice, France.

6. [Invited] “Decomposition of Homogeneous Polynomials”, September 15, 2010, Workshop on TensorDecompositions and Applications (TDA 2010). September 13–17 2010. Monopoli, Bari, Italy.

7. [Invited] “Applicazioni recenti di risultati classici su varieta delle secanti a varieta che parametriz-zano tensori. Dal problema di Waring al rango di tensori”, November 22, 2010, Progressi Recentiin Geometria Reale e Complessa, October 17–22, 2010, Levico Terme (Trento, Italy).

8. “Secant varieties and Rank of tensors”, February 1, 2011, Mittag-Leffler Institute, Spring Semester:“Algebraic Geometry with a view towards applications” 17 January – 15 June 2011.

9. [Invited] “Ranks of Tensors, related varieties and applications”, November 18, 2011, Genova-Torino-Milano Seminar: some topics in Commutative Algebra and Algebraic Geometry, November17–18, 2011, Milano (Italy).

10. [Invited] “Algebraic Geometry in Signal processing, Phylogenetic and Quantum Physics”, Collo-quium Politecnico di Torino, May 30, 2013, Politecnico di Torino, Italy.

11. [Invited] “Tensor Ranks”, 2013 SIAM Conference on Applied Algebraic Geometry. August 1, 2013,Fort Collins (Colorado, USA).

12. [Invited] Main Speaker at the 36th Autumn School in Algebraic Geometry on “Power sumdecomposition and apolarity, a geometric approach”. September 1-7, 2013, Lukecin, Poland.

13. [Invited], [Declined for family reasons (maternity leave)] Invited Speaker to the “Tensors andOptimization” Conference, May 19–22, 2014 for the SIAM Optimization Meeting, San Diego (CA,USA).



14. [Invited], [Declined for family reasons (maternity leave)] Invited Speaker for ComputationalNonlinear Algebra, for the ICERM Conference, June 2–6, 2014, Brown University (Providence,USA).

15. [Invited] “Cactus Varieties of Cubic Forms: Apolar Local Artinian Gorenstein Rings”, November13, 2014, inside the Workshop Tensors in Computer Science and Geometry in the framework of thefall program 2014 ”Algorithms and Complexity in Algebraic Geometry“, Invited by P. Burgisser,JM Landsberg, K. Mulmuley, B. Sturmfels.

16. “On the cactus variety of cubic forms”. AMS-EMS-SPM Joint meeting (Porto), June 10-13, 2015.

17. [Invited] Invited Speaker at MEGA Effective Methods in Algebraic Geometry, “Tensor decom-position and homotopy continuation”. Trento, 15–19 June, 2015.

18. “A geometric view of the splitting type for plane rational curves”. September 8, 2015, ConvegnoUMI, September 7–12, 2015, Siena, Italy.

19. [Planned], [Invited] Invited Speaker al MAG2015, December 2–4, 2015, Barcellona, Spain.

6.2 Invited Talks in Italian and foreign Universities

20. “Secant varieties to osculating varieties of Veronesean” , February 18, 2005 - Departamento deAlgebra, Universidad Complutense de Madrid. (Madrid, Spain).

21. “Secant varieties and Big Waring Problem”, October 7, 2005, Mathematical Department, TexasA&M University (College Station,Texas, USA).

22. “Secant varieties to osculating varieties of Veronese Varieties”, September 4, 2008 - Departamentode Algebra, Universidad Complutense de Madrid, (Madrid, Spain).

23. “Rappresentazione di varieta algebriche”, October 28, 2008, Univ. Bologna (Italy).

24. “Varieta che parametrizzano polinomi completamente decomponibili”, March 13, 2009, Univ. Firenze(Italy).

25. “Sylvester’s Algorithm”, June 10, 2009 - Workshop on tensors and interpolation, Nice (France).

26. “Dal problema di Waring alle telecomunicazioni”, December 10, 2009, Univ. Trento (Italy).

27. “Dal problema di Waring alle telecomunicazioni”, April 20, 2010, Univ. Ancona (Italy).

28. “Un assaggio di scienza nell’iconografia russa”, June 17, 2010, Univ.Trento (Italy).

29. “Varieta delle secanti a varieta che parametrizzano tensori: attualita del problema di Waring,aspetti geometrici correlati ed applicazioni”, October 7, 2010. Univ. Trieste (Italy).

30. “Polynomial and Tensor Decompositions”, March 22, 2011, GALAAD–INRIA, Sophia AntipolisMediterranee, France.

31. “Decomposition of Structured Tensors, Algorithms and Characterization”, May 9, 2011, MultimediaGeometry Seminars, Univ. Trento (Italy).



32. “Varieta delle secanti: dimensioni, ideali e rango di tensori”, May 23, 2011, Poltiecnico di Torino(Italy).

33. “Tensor decompositions: achievements and developments”, October 26, 2011, Univ. Trento (Italy).

34. “Ranghi di Tensori”, November 16, 2011, Univ. Torino (Italy).

35. “Decomposition of partially symmetric tensors”, December 2, 2011, Univ. Firenze (Italy).

36. “Tensor Decomposition: a link between Algebraic Geometry and Applications”, April 4, 2012, Univ.Bologna (Italy).

37. “Various approaches for polynomial decomposition”, October 23, 2012, Univ. Pau (France).

38. “A generalization of Sylvester Algorithm”, December 4, 2012, Universidad Complutense de Madrid(Spain).

39. “On the local cactus rank of generic cubic forms”, December 4, 2014, Simons Institute for Theory ofComputing (Berkeley, CA, USA), seminar in the framework of the fall program 2014 “Algorithmsand Complexity in Algebraic Geometry”.

6.3 Other presentations

40. “Sulle funzioni convesse”, February 27, 2002, Univ. Trieste (Italy).

41. “Dimostrazione del teorema di Darboux”, September 27, 2002, Univ. Trieste (Italy).

42. “Programma di Sarkisov in dimensione 2 per la classificazione degli Spazi Fibrati di Mori secondola Teoria di Mori”, July 18, 2002, Univ. Milano (Italy).

43. “Esposizione dell’articolo di G. Canuto Curve associate e Formule di Pluker nelle Grassmaniane,apparso su “Inventiones Mathematicae”, 53, 77-90 (1979)”, January 15, 2003, Univ. Milano (Italy).

44. “How one’s can calculate all the differential invariants of Seg(Pn × Pn) ∩H, where H is a generichyperplane. Understand this as a homogeneous variety of Sln+1C”, February 13, 2003, Univ.Trieste (Italy).

45. “Un’introduzione al problema dello studio della Postulazione dei Punti Grassi”, March 19, 2003,Univ. Milano (Italy).

46. “Un’introduzione al problema dello studio della Postulazione dei Punti Grassi e recenti appli-cazioni”, May 23, 2003, Univ. Pavia (Italy).

47. “Waring type problems and Auxiliary varieties Associated to Veronese varieties”, October 6, 2004,Queen’s University (Kingston, Ontario, Canada).

48. “Secant varieties to the Osculating varieties of the Veronesean”, October 13, 2004, Queen’s Univer-sity (Kingston, Ontario, Canada).

49. “Varieta delle secanti alle Veronese e applicazioni algebriche”, January 26, 2005, Departamento deAlgebra Universidad Complutense de Madrid (Madrid, Spain).



50. “Varieta delle secanti alle varieta tangenziali ed osculanti a varieta di Veronese”, February 2, 2005,Departamento de Algebra, Universidad Complutense de Madrid (Madrid, Spain). (Madrid, Spain).

51. “Construction of Cominuscule Varieties”, October 6, 2005, Texas A&M University (College Station,Texas, USA).

52. “An introduction to Representation Theory”, November 2, 2005, Texas A&M University (CollegeStation, Texas, USA).

53. “An introduction to de Rham Cohomology I, II, III”, November 17, 18, 22, 2005, Texas A&MUniversity (College Station, Texas, USA).

54. “On Alexander-Hirshowitz theorem via Lemma d’Horace”, December 1, 2005, Texas A&M Univer-sity (College Station, Texas, USA).

55. “Lemma d’Horace differentielle”, December 5, 2005, Texas A&M University (College Station, Texas,USA).

56. “Dall’Algebra Lineare a questioni irrisolte”, May 15, 2008, Talk inside the “Corso di Laurea AlgebraSuperiore”, Dipartimento di Matematica, Univ. Bologna (Italy).

57. “Ideale delle varieta di Segre-Veronese”, June 12, 2008, Univ. Genova (Italy).

58. “Rango e rango simmetrico di tensori simmetrici.”, March 3, 2009 , Univ. Bologna (Italy).

59. “Algorithms for computing the rank of a tensor”, February 11, 2011, Mittag-Leffler Institute, SpringSemester: “Algebraic Geometry with a view towards applications” 17 Janaury – 15 June 2011(Sweeden).

60. “Tenseurs”, March 8, 2011, GALAAD–INRIA, Sophia Antipolis Mediterranee (France).

6.4 Additional Conferences and Schools Attended

• “Summer School Perugia”, Perugia (Italy), July 29 – September 1, 2001.

• “Pragmatic 2003”, Catania (Italy), June 9 – 28, 2003.

• “Interpolation problem and Projective embeddings”, Torino (Italy), September 15 – 20, 2003;

• “Workshop on Algebraic curves, monodromy and related topics”, Milano (Italy), April 1-2, 2004.

• “International school on Projective Geometry”, Anacapri (Italy), June 1–5, 2004.

• “Projective Varieties with unexpected geometric properties”, Siena (Italy), June 8–12, 2004.

• “School/Workshop on Computational Algebra for Algebraic Geometry and statistics”, Torino (Italy),September 6 – 11, 2004.

• “Rt. 81 conference in honor of Graham Evans and Workshop on Resolution (for young researchers)”,Cornell University of Ithaca, New York, USA, October 1–3, 2004.

• “AGaFE, Geometry of Algebraic Varieties”, Ferrara (Italy), June 22–25, 2005.



• “Texas Geometry and Topology conference”, Austin, Texas (USA), September 30 – October 2,2005.

• “Geometric and Probabilistic Methods in group theory and dynamical systems”, November 4–6,2005, Texas A&M University, College Station, Texas (USA).

• “Harvey/Polking conference, Singularities in Analysis, Geometry and Topology”, November 11–13,2005, Rice University, Houstin, Texas (USA).

• “INDAM workshop: Geometry of projective varieties” (Roma), September 30 – October 4, 2008.

• “Conference on Classical and recent aspects in the study of projective varieties. In honor of LucianBadescu on the occasion of his 65th birthday”, Genova (Italy), January 21–22, 2010.

• “INdAM Conference “Complex Geometry””, Levico Terme, Trento (Italy), May 31 – June 4, 2010.

• “Summer school: Geometry of tensors and applications”, Sophus Lie Conference Center, Nord-fjordeid (Norway), June 14 – 18, 2010.

• “School (and Workshop) on The Minimal Model Program and Shukurov’s ACC Conjecture”, Povo(Trento), June 5 – 10, 2010.

• “International Conference on Perspectives on Algebraic Varieties”, Levico Terme, Trento (Italy),September 5–10, 2010.

• “Algebraic Geometry in the sciences”, Oslo (Norway), January 10–14, 2011.

• “CIAM workshop: An afternoon of biology and mathematics”, KTH, Stockholm (Sweden), Febru-ary 4, 2011.

• “Solving polynomial equations”, KTH, Stockholm (Sweden), February 21–25, 2011.

• “MEGA 2011: Effective Methods in Algebraic Geometry” , Stockholm University (Stockholm,Sweden), May 30–June 3, 2011.

• “Genova, Torino, Milano Seminar: Some Topics in Commutative Algebra and Algebraic Geometry”,June 28–29, 2012, Torino (Italy).

• “Groebner Bases, Curves, Codes and Cryptography”, July 30 – August 10, 2012, Trento (Italy).

• “School (and Workshop) on Invariant Theory and Projective Geometry”, September 17 – 22, 2012,Trento (Italy).

• “3rd SAGA Workshop”, October, 9–11, 2012, Trento (Italy).

• “Genova-Torino-Milano Seminar: Some Topics in Commutative Algebra and Algebraic Geometry”,January 28–29, 2014 (Politecnico di Milano, Italy).

• “Vector Bundles Days II, Pau-Trieste Workshop on Vector Bundles and Related Topics. On theoccasion of Emilia Mezzetti’s 60th birthday”, January 29–31, 2014 (Trieste, Italy).


Alessandra Bernardi’s CV 8 COORDINATION OF RESEARCH PROJECTS

7 Organization of Schools and Conferences

• Summer School: “An Interdisciplinary Approach To Tensor Decomposition”At: University of Trento / Fondazione Bruno Kessler-IRST, Italy.Period: July, 13–18, 2014.Organizing Committee:

– A. Bernardi,

– A. Boralevi,

– E. Postinghel.

Main Speakers:

– JM Landsberg (Texas A&M University, College Station, TX),

– B. Mourrain (GALAAD, INRIA Mediterranee, Sophia Antipolis, Cedex France),

– K. Ranestad (Matematisk institutt, Universitetet i Oslo, Norway).

Young Speakers:

– C. Bocci (Univ. Siena, Italy),

– E. Carlini (Monash Univ. Australia),

– M.C. Brambilla (Univ. Politecnica delle Marche, Italy)

Financied by: FBK–CIRM, Compositio Mathematica, Dipartimento di Matematica “GiuseppePeano” Univ. Torino, GNSAGA.

• Workshop on “Symbolic and Numerical Methods for Tensors and Representation The-ory”,At: Simons Institute (Berkeley, CA, USA).Period: November 18–21, 2014.Organizing Committee: A. Bernardi, A. Leykin, C. Raicu, C. Vinzant.Webpage: http://simons.berkeley.edu/workshops/algebraicgeometry2014-4

Financed by: Simons Institute, MSRI (Berkeley).

8 Coordination of Research Projects

8.1 Funded Research Projects

8.1.1 International

• Title of the project: “Programa de visitantes distinguidos e investigadores extranjeros en laUCM”.Financed by: GRUPO SANTANDER.Duration: 3 months; period: June 28 – September 27, 2006.Host: Prof. E. Arrondo (Universidad Complutense de Madrid - Spain).



• Title of the project: “Decomposition of Structured Tensors, Algorithms and Characterization”.Financed by: European Community in the framework of the program FP7-PEOPLE-2009-IEF -252367, Individual Marie Curie Fellow.Duration: 2 years, period: November 2010 – November 2012.Supervisor: Prof. B. Mourrain (INRIA Sophia Antipolis - Mediterranee - Nice -France)

8.1.2 Italian

• Title of the project: “Dimensione e ideali di varieta delle secanti di varieta che parametrizzanoforme e/o tensori. Generazione di algoritmi per il computo del rango strutturato dei loro elementi.”Financed by: CIRM – FBK (Trento).Duration: 1 year; period: November 2009 – November 2010.Supervisor: Prof. E. Ballico (Universita degli Studi di Trento).

• Title of the project: “Algebra e Geometria Algebrica”.Financed by: University of Torino, Department of Mathematics, in the framework of Local Foundsfor young researchers.Duration: 2 years; period: December 2013 – December 2015.Coordinator: Alessandra Bernardi.

8.2 Research projects that passed the first steps of the evaluation process

• Title of the project: “Geometry of varieties parameterizing tensors and applications to theirdecomposition”.In the framework of : FIRB 2013.Principal Investigator: Alessandra Bernardi.Mark at the national Pre-selection: 9.33/10.Mark at the national First selection: 13/15 (admitted to the second phase only the projectswith 14/15).

8.3 Participation to other Research Projects

• Title of the project: “Questioni di Geometria, Topologia e Algebra”.Financed by: Universita degli Studi di Milano, Dipartimento di Matematica “Federigo Enriques”.Duration: 1 year; period: 2002.Responsible: Prof. Antonio Lanteri (Universita degli Studi di Milano).

• Title of the project “Questioni di Geometria, Topologia e Algebra”.Financed by: Universita degli Studi di Milano, Dipartimento di Matematica “Federigo Enriques”.Duration: 1 year; period: 2003.Responsible: Prof. Antonio Lanteri (Universita degli Studi di Milano).




• Title of the project: “Geometria sulle varieta algebriche”.Financed by: MIUR (Ministry of Education and Research of the Italian Government) and Uni-versita degli Studi di Milano.Duration: 2 years; period: 2002-2004.Responsible: Prof. Antonio Lanteri (Universita degli studi di Milano), Prof. Alessandro Verra(Universita di Roma III).


• Title of the project: “Geometria sulle varieta algebriche”.Financed by: MIUR (Ministry of Education and Research of the Italian Government) e Universitadegli Studi di Milano.Duration: 2 years; period: 2005-2006.Responsible: Prof. Lambertus Van Geemen (Univerisita degli Studi di Milano), Prof. AlessandroVerra (Universita di Roma III).

• Title of the project: “Project PRIN 2004 (Progetti di rilevante interesse nazionale)”.Financed by: National government funds.Duration: 2 years; period: 2004-2005.Responsible: Prof. Angelo Vistoli (Universita degli Studi di Bologna).

• Title of the project: “RFO 2006 funds (Ricerca Fondamentale Orientata).”Financed by: Universita degli studi di Bologna.Duration: 1 year; period: 2006.Responsible: Prof. Mirella Manaresi (Universita degli Studi di Bologna).

• Title of the project: “Project PRIN 2006 (Progetti di rilevante interesse nazionale)”.Financed by: National government funds.Duration: 2 years; period: 2006-2007.Responsible: Prof. Mirella Manaresi (Universita degli Studi di Bologna).





Alessandra Bernardi’s CV 10 TEACHING ACTIVITY

• Title of the project: “Project PRIN 2008 (Progetti di rilevante interesse nazionale)”.Financed by: National government funds.Duration: 2 years; period: 2008-2009.Responsible: Prof. Mirella Manaresi (Universita degli Studi di Bologna).

• Title of the project: “RFO 2013 funds (Ricerca Fondamentale Orientata).”Financed by: Univ. di Bologna.Duration: 1 year; period: 2013.Responsible: Prof. Mirella Manaresi (Univ. Bologna).

• Title of the project: “Project PRIN 2013 (Progetti di rilevante interesse nazionale)”.Financed by: National government funds.Duration: 2 years; period: 2013-2016.Responsible: Prof. M. Mella (Univ. Ferrara).

9 Awards

1. “Borsa di studio ENAM per studenti universitari meritevoli”.Academic Years: 1996–1997, 1997–1998, 1998–1999, 1999–2000.

2. Selected among the 100 best students of the Italian high schools by University Orientation Coursefor at Cortona (Italy).SCUOLA NORMALE SUPERIORE DI PISA.Summer 1995.

3. Scholarship: “Best student of the Scientific Liceo, Polo Scolastico Maria Montessori” (PorrettaTerme, Bologna, Italy).Financed by Lions Club of Granaglione Alto Reno, December 1996.

4. Awards for the best student of the Scientific Liceo, Polo Scolastico Maria Montessori (PorrettaTerme, Bologna, Italy). Financed by City Council of Gaggio Montano (Bologna, Italy).Years: 1991–1992, 1992–1993, 1993–1994, 1994–1995, 1995–1996.

5. Award “VI Latinus Ludus”.Financed by Lions Club Cattolica, Maggio 1992.

6. Award for the best student of the Scuola Media Salvo D’Acquisto (Gaggio Montano, Bologna) .Year 1991–1992.

10 Teaching activity

10.1 Teaching activity abroad (for PhD Students or higher)

• Research Assistant for the American PhD course in Math.: MATH 689-computational complex-ity geometry, I Semester A.A. 2005-2006, Texas A&M University, College Station (Texas, USA);Teaching Professor: JM Landsberg (College Station, Texas, USA).


Alessandra Bernardi’s CV 11 SCIENTIFIC PRODUCTION

• Teaching Assistant for JM Landsberg (Texas A&M, Texas, USA), L.-H. Lim (UC Berkeley, Cali-fornia, USA) and J. Morton (UC Berkeley, California, USA) during the Graduate Workshop “Ge-ometry and representation theory of tensors for computer science, statistics and other areas”, atMSRI (Mathematical Sciences Research Institute), Berkeley (California - USA). July 2008.

• Main Speaker at “36th Autumn School in Algebraic Geometry: Power sum decomposition andapolarity, a geometric approach”. Advanced school for PhD students and higher. Lukecin, Poland,September 1-7, 2013.

10.2 Teaching activity in Italy (for undergraduates)

10.2.1 Teaching professor

1. Algebra 2, II year course of Mathematics, Univ. Torino, 2012–2013.

2. Geometria 1, I year course of Mathematics, Univ. Torino, 2012–2013.

3. Geometria, I year course of Engineering and architecture, Univ. Bologna, 2014–2016.

4. Linear Algebra (in english, agreement with Univ. of Glasgow) I year course of Statistical Sciences,Univ. Bologna, 2015–2016.

10.2.2 Tutorials and Exercises

1. Geometria e Algebra I, I year course of Mathematical and Physical Engineering, Politecnico diMilano, 2002–2003, teaching professor G. Bolondi.

2. Elementi di Analisi Matematica, Algebra e Geometria. I year course of Mechanical Engi-neering, Politecnico di Milano, 2003–2004, teaching professor F. Colombo.

3. Geometria e Algebra Lineare, (allievi A-K and L-Z). I year course of Management Engi-neering, Univ. Bologna, 2003–2004, 2006–2008 teaching professor A. Gimigliano.

4. Analisi Matematica B (allievi Ingegneri Civili). I year course of Ingegneria Civile, MilanoLeonardo Politecnico (Italy), 2004–2005, teaching professor G. Verzini.

5. Geometria e Algebra (Corso integrato, moduli di Algebra e Geometria), I year course ofScienza della Formazione Primaria, Univ. Bologna, 2007–2008, teaching professor A. Gimigliano.

6. Analisi Matematica I, Geometria e Algebra Lineare (Corso integrato, moduli di Ge-ometria e Algebra Lineare), (allievi A-K and L-Z). I year course of Management Engineering,Univ. Bologna, 2008–2010 teaching professor A. Gimigliano.

11 Scientific production

11.1 Bibliometrics indicies

(Last update September 24, 2015)



Number of published papers: **26**(22 in last 5 years)

Normalized number of papers ** 26**To be compared to ANVUR value **9** for the Median among all Italian Professori Ordinari (full pro-fessors) in Geometry and AlgebraANVUR computational method (CM) = (]papers) ∗ 10/(academic age + 1)

Normalized number of papers on last 5 years **36,67**ANVUR CM= (]papers of last 5 years) ∗ 10/(5 + 1)

My academic age = 2015− 2006 = 9

The following data are computed on Scopus values on September 24, 2015.

Total number of citations received **132** in 91 papersMax citations by a paper **52**Normalized number of citations **13,2**To be compared to ANVUR value **3.23** for the Median among all Italian Professori Ordinari in Ge-ometry and AlgebraANVUR CM= (sum of citations)/(1 + academic age)

Number of citations normalized to the last 5 years **18,7**ANVUR CM= (sum of citations last 5 years)/(1 + 5)

h-index **6**Contemporary h-index **4**To be compared to ANVUR value **3** for the Median among all Italian Professori Ordinari in Geom-etry and AlgebraANVUR CM for each citation= 4 ∗ (]citations of a given paper)/(1 + age of the paper)

11.2 Books

Algebra lineare e geometria analitica by A. Bernardi, A. Gimigliano. Citta studi. 2014.

11.3 PhD Thesis

Varieties parameterizing forms and their secant varieties.Alessandra Bernardi.Dip. of Math. “Federigo Enriques” dell’ Univ. Milano.February 13, 2006.Advisor: Prof.Alessandro Gimigliano (Univ. di Bologna).

The ABSTRACT is at Section 2 of this Curriculum.



11.4 Published articles

1. Some defective secant varieties to osculating varieties of Veronese surfaces.A. Bernardi, M.V. Catalisano.Collect. Math. 57 (2006), no. 1, pp. 43–68.URL: http://www.collectanea.ub.edu/index.php/Collectanea/article/view/4084DOI: not assigned.ISSN: 0010-0757.

We consider the k-osculating varieties Ok,d to the Veronese d−uple embeddings of P2. Bystudying the Hilbert function of certain zero-dimensional schemes Y ⊂ P2, we find thedimension of Os

k,d, the (s− 1)thsecant varieties of Ok,d, for 3 ≤ s ≤ 6 and s = 9, and wedetermine whether those secant varieties are defective or not.

2. Osculating varieties of Veronese Varieties and their higher secant varieties.A. Bernardi, M.V. Catalisano, A. Gimigliano, M. Ida.Canad. J. Math. Vol. 59 (3), 2007 pp. 488–502.URL: http://www.math.ca/cjm/v59/p488DOI: not assigned.ISSN: 0008-414X.

We consider the k-osculating varieties Ok,n.d to the (Veronese) d−uple embeddings of Pn.We study the dimension of their higher secant varieties via inverse systems (apolarity).By associating certain 0-dimensional schemes Y ⊂ Pn to Os

k,n,d and by studying theirHilbert function we are able, in several cases, to determine whether those secant varietiesare defective or not.

3. Ideals of varieties parameterized by certain symmetric tensors.A. Bernardi.J. Pure Appl. Algebra 212 (6), 2008 pp. 1542–1559.URL: http://www.sciencedirect.com/science/article/pii/S002240490700271XDOI: 10.1016/j.jpaa.2007.10.022.ISSN: 0022-4049.

The ideal of a Segre variety Pn1 × · · · × Pnt ↪→ P(n1+1)···(nt+1)−1 is generated by the 2-minors of a generic hypermatrix of indeterminates. We extend this result to the case ofSegre-Veronese varieties. The main tool is the concept of “weak generic hypermatrix”which allows us to treat also the case of projection of Veronese surfaces from a set of gen-eral points and of Veronese varieties from a Cohen-Macaulay subvariety of codimension2.

4. Secant varieties to osculating varieties of Veronese embeddings of Pn.A. Bernardi, M.V. Catalisano, A. Gimigliano e M. Ida.J. Algebra 321 (2009) pp. 982–1004.URL: http://www.sciencedirect.com/science/article/pii/S0021869308005486DOI: 10.1016/j.algebra.2008.10.020.ISSN: 0021-8693.



A well known theorem by Alexander-Hirschowitz states that all the higher secant varietiesof Vn,d (the d-uple embedding of Pn) have the expected dimension, with few known ex-ceptions. We study here the same problem for Tn,d, the tangential variety to Vn,d, andprove a conjecture, which is the analogous of Alexander-Hirschowitz theorem, for n ≤ 9.Moreover. we prove that it holds for any n, d if it holds for d = 3. Then we generalize tothe case of Ok,n,d, the k-osculating variety to Vn,d, proving, for n = 2, a conjecture thatrelates the defectivity of σs(Ok,n,d) to the Hilbert function of certain sets of fat points inPn.

5. On the variety parametrizing completely decomposable polynomials.E. Arrondo, A. Bernardi.J. Pure Appl. Algebra 215 (2011) pp. 201–220.URL: http://www.sciencedirect.com/science/article/pii/S0022404910000824DOI: 10.1016/j.jpaa.2010.04.008.ISSN: 0022-4049.

The purpose of this paper is to relate the variety parameterizing completely decomposablehomogeneous polynomials of degree d in n + 1 variables on an algebraically closed field,called Splitd(Pn), with the Grassmannian of n − 1 dimensional projective subspaces ofPn+d−1. We compute the dimension of some secant varieties to Splitd(Pn) and finda counterexample to a conjecture that wanted its dimension related to the one of thesecant variety to G(n − 1, n + d − 1). Moreover by using an invariant embedding of theVeronse variety into the Plucker space, then we are able to compute the intersection ofG(n− 1, n+ d− 1) with Splitd(Pn), some of its secant variety, the tangential variety andthe second osculating space to the Veronese variety.

6. Computing symmetric rank for symmetric tensors.A. Bernardi, A. Gimigliano, M. Ida.Journal of Symbolic Computation 46 (2011) pp. 34–53.URL: http://www.sciencedirect.com/science/article/pii/S0747717110001240DOI: 10.1016/j.jsc.2010.08.001.ISSN: 0747-7171.

We consider the problem of determining the symmetric tensor rank for symmetric tensorswith an algebraic geometry approach. We give algorithms for computing the symmetricrank for 2× · · · × 2 tensors and for tensors of small border rank. From a geometric pointof view, we describe the symmetric rank strata for some secant varieties of Veronesevarieties.

7. Higher secant varieties of Pn × Pm embedded in bi-degree (1, d).A. Bernardi, E. Carlini, M.V. Catalisano.J. Pure Appl. Algebra 215 (2011), pp. 2853–2858.URL: http://www.sciencedirect.com/science/article/pii/S002240491100096XDOI: 10.1016/j.jpaa.2011.04.005.ISSN: 0022-4049.



Let X(n,m)(1,d) denote the Segre-Veronese embedding of Pn×Pm via the sections of the sheaf

O(1, d). We study the dimensions of higher secant varieties of X(n,m)(1,d) and we prove

that there is no defective sth secant variety, except possibly for n values of s. Moreover

when(m+dd

)is multiple of (m+ n+ 1), the sth secant variety of X

(n,m)(1,d) has the expected

dimension for every s.

8. Multihomogeneous Polynomial Decomposition using Moment Matrices.A. Bernardi, J. Brachart, P. Comon, B. Mourrain.A. Leykin editor, International Symposium of Symbolic and Algebraic Computation (ISSAC), pp.35–42, San Jose, CA, USA, June, 2011, ACM New York.URL: http://portal.acm.orgcitation.cfm?id=1993886.1993898&coll=DL&dl=ACM&CFID=30387648&CFTOKEN=71177337

DOI: 10.1145/1993886.1993898.ISBN: 978-1-4503-0675-1.

In the paper, we address the important problem of tensor decompositions which can be seenas a generalisation of Singular Value Decomposition for matrices. We consider generalmultilinear and multihomogeneous tensors. We show how to reduce the problem to atruncated moment matrix problem and give a new criterion for flat extension of Quasi-Hankel matrices. We connect this criterion to the commutation characterisation of borderbases. A new algorithm is described which applies for general multihomogeneous tensors,extending the approach of J.J. Sylvester on binary forms. An example illustrates thealgebraic operations involved in this approach and how the decomposition can be recoveredfrom eigenvector computation.

9. On the X-rank with respect to linear projections of projective varieties.E. Ballico, A. Bernardi.Mathematische Nachrichten. 284 No. 17–18, (2011), pp. 2133–2140.URL: http://onlinelibrary.wiley.com/doi/10.1002/mana.200910275/fullDOI: 10.1002/mana.200910275.ISSN: 1522-2616.

In this paper we improve the known bound for the X-rank RX(P ) of an element P ∈ PN

in the case in which X ⊂ Pn is a projective variety obtained as a linear projection froma general v-dimensional subspace V ⊂ Pn+v. Then, if X ⊂ Pn is a curve obtainedfrom a projection of a rational normal curve C ⊂ Pn+1 from a point O ⊂ Pn+1, weare able to describe the precise value of the X-rank for those points P ∈ Pn such thatRX(P ) ≤ RC(O)−1 and to improve the general result. Moreover we give a stratification,via the X-rank, of the osculating spaces to projective cuspidal projective curves X. Finallywe give a description and a new bound of the X-rank of subspaces both in the general caseand with respect to integral non-degenerate projective curves.

10. On the X-rank with respect to linearly normal curves.E. Ballico, A. Bernardi.Collectanea Mathematica: Volume 64, Issue 2 (2013), Page 141–154.URL: http://link.springer.com/article/10.1007/s13348-011-0058-4?null



DOI: 10.1007/s13348-011-0058-4.ISSN: 0010-0757.

In this paper we study the X-rank of points with respect to smooth linearly normal curvesX ⊂ Pn of genus g and degree n+ g.We prove that, for such a curve X, under certain circumstances, the X-rank of a generalpoint of X-border rank equal to s is less or equal than n+ 1− s.In the particular case of g = 2 we give a complete description of the X-rank if n = 3, 4;while if n ≥ 5 we study the X-rank of points belonging to the tangential variety of X.

11. Algebraic Geometry tools for the study of entanglement: an application to spin squeezed states.A. Bernardi, I. Carusotto.J. Phys. A: Math. Theor. 45 (2012) 105304 (13pp).URL: http://iopscience.iop.org/1751-8121/45/10/105304?fromSearchPage=trueDOI: 10.1088/1751-8113/45/10/105304.ISSN 1751-8121.

A short review of Algebraic Geometry tools for the decomposition of tensors and poly-nomials is given from the point of view of applications to quantum and atomic physics.Examples of application to assemblies of indistinguishable two-level bosonic atoms arediscussed using modern formulations of the classical Sylvester’s algorithm for the de-composition of homogeneous polynomials in two variables. In particular, the symmetricrank and symmetric border rank of spin squeezed states is calculated as well as theirSchrodinger-cat-like decomposition as the sum of macroscopically different coherent spinstates; Fock states provide an example of states for which the symmetric rank and thesymmetric border rank are different.

12. A partial stratification of secant varieties of Veronese varieties via curvilinear subschemes.E. Ballico, A. Bernardi.Sarajevo Journal of Mathematics. Vol. 8 (20), 33–52 (2012).URL: http://www.anubih.ba/Journals/vol.8,no-1,y12/05RevBallico-11.pdf

DOI: Not assigned.ISSN 2233-1964.

We give a partial “ quasi-stratification ” of the secant varieties of the order d Veronesevariety Xm,d of Pm. It covers the set σt(Xm,d)† of all points lying on the linear span ofcurvilinear subschemes of Xm,d, but two “ quasi-strata ” may overlap. For low borderrank two different “ quasi-strata ” are disjoint and we compute the symmetric rank oftheir elements. Our tool is the Hilbert schemes of curvilinear subschemes of Veronesevarieties. To get a stratification we attach to each P ∈ σt(Xm,d)† the minimal label of aquasi-stratum containing it.

13. Decomposition of homogeneous polynomials with low rank.E. Ballico, A. Bernardi.Math. Z. (2012) 271:1141–1149.URL: http://link.springer.com/article/10.1007/s00209-011-0907-6DOI : 10.1007/s00209-011-0907-6.ISSN: 0025-5874.



Let F be a homogeneous polynomial of degree d in m+ 1 variables defined over an alge-braically closed field of characteristic zero and suppose that F belongs to the s-th secant

varieties of the standard Veronese variety Xm,d ⊂ P(m+dd )−1 but that its minimal decom-

position as a sum of d-th powers of linear forms M1, . . . ,Mr is F = Md1 + · · ·+Md

r withr > s. We show that if s+ r ≤ 2d+ 1 then such a decomposition of F can be split in twoparts: one of them is made by linear forms that can be written using only two variables,the other part is uniquely determined once one has fixed the first part. We also obtain auniqueness theorem for the minimal decomposition of F if the rank is at most d and amild condition is satisfied.

14. Higher secant varieties of Pn × P1 embedded in bi-degree (a, b).E. Ballico, A. Bernardi, M. V. Catalisano.Communications in Algebra. 40:3822–3840 (2012).URL: http://www.tandfonline.com/doi/full/10.1080/00927872.2011.595748DOI: 10.1080./00927872.2011.595748.ISSN: 0092-7872.

In this paper we compute the dimension of all the higher secant varieties to the Segre-Veronese embedding of Pn × P1 via the section of the sheaf O(a, b) for any n, a, b ∈ Z+.We relate this result to the Grassmann Defectivity of Veronese varieties and we classifyall the Grassmann (1, s− 1)-defective Veronese varieties.

15. Symmetric tensor rank with a tangent vector: a generic uniqueness theorem.E. Ballico, A. Bernardi.URL: http://www.ams.org/journals/proc/2012-140-10/S0002-9939-2012-11191-8/DOI: 10.1090/S0002-9939-2012-11191-8.ISSN: 0002-9939.

Let Xm,d ⊂ PN , N :=(m+dm

)−1, be the order d Veronese embedding of Pm. Let τ(Xm,d) ⊂

PN , be the tangent developable of Xm,d. For each integer t ≥ 2 let τ(Xm,d, t) ⊆ PN , bethe join of τ(Xm,d) and t − 2 copies of Xm,d. Here we prove that if m ≥ 2, d ≥ 7

and t ≤ 1 + b(m+d−2

m

)/(m + 1)c, then for a general P ∈ τ(Xm,d, t) there are uniquely

determined P1, . . . , Pt−2 ∈ Xm,d and a unique tangent vector ν of Xm,d such that P is inthe linear span of ν ∪ {P1, . . . , Pt−2}, i.e. a degree d linear form f (a symmetric tensorT of order d) associated to P may be written as

f = Ld−1t−1Lt +

t−2∑i=1

Ldi , (T = v

⊗(d−1)t−1 vt +

t−2∑i=1

v⊗di )

with Li linear forms on Pm (vi vectors over a vector field of dimension m+1 respectively),1 ≤ i ≤ t, that are uniquely determined (up to a constant).

16. Grassmann secants, identifiability, and linear systems of tensors.E. Ballico, A. Bernardi, M. V. Catalisano, L.Chiantini.Linear Algebra and its Applications 438 (2013) 121–135.URL: http://www.sciencedirect.com/science/article/pii/S0024379512006076DOI: 10.1016/j.laa.2012.07.045.ISSN: 0024-3795.



For any irreducible non-degenerate variety X ⊂ Pr, we relate the dimension of the s-thsecant varieties of the Segre embedding of Pk×X to the dimension of the (k, s)-Grassmannsecant variety GSX(k, s) of X. We also give a criterion for the s-identifiability of X.

17. On cactus rank of cubic forms.A. Bernardi, K. Ranestad.Journal of Symbolic Computation 50 (2013) 291–297.URL: http://www.sciencedirect.com/science/article/pii/S0747717112001332DOI: 10.1016/j.jsc.2012.08.001.ISSN. 0747-7171.

We prove that the smallest degree of an apolar 0-dimensional scheme of a general cubicform in n + 1 variables is at most 2n + 2, when n ≥ 8, and therefore smaller than therank of the form. For the general reducible cubic form the smallest degree of an apolarsubscheme is n+ 2, while the rank is at least 2n.

18. General Tensor Decomposition, Moment Matrices and Applications.A. Bernardi, J. Brachart, P. Comon, B. Mourrain.J. Symbolic Comput. Special Issue: ISSAC-2011. 52 (2013) 51–71.URL: http://www.sciencedirect.com/science/article/pii/S0747717112001290DOI: 10.1016/j.jsc.2012.05.012.ISSN: 978-1-4503-0675-1.

In the paper, we address the important problem of tensor decompositions which can be seenas a generalisation of Singular Value Decomposition for matrices. We consider generalmultilinear and multihomogeneous tensors. We show how to reduce the problem to atruncated moment matrix problem and give a new criterion for flat extension of Quasi-Hankel matrices. We connect this criterion to the commutation characterisation of borderbases. A new algorithm is described which applies for general multihomogeneous tensors,extending the approach of J.J. Sylvester on binary forms. An example illustrates thealgebraic operations involved in this approach and how the decomposition can be recoveredfrom eigenvector computation.

19. Real and complex rank for real symmetric tensors with low ranks.E. Ballico, A. Bernardi.Algebra, vol. 2013, Article ID 794054, 5 pages, 2013.URL: http://www.hindawi.com/journals/algebra/aip/794054/DOI:10.1155/2013/794054.ISSN: 2314-4106.

We study the case of real homogeneous polynomial P whose minimal real and complexdecompositions in terms of powers of linear forms are different. In particularly we willshow that, if the sum of the complex and the real ranks of P is smaller or equal than3 deg(P )−1, then the difference of the two decompositions is completely determined eitheron a line or on a conic.

20. Unique decomposition for a polynomial of low rank.E. Ballico, A. Bernardi.



Ann. Polon. Math. 108 (2013), 219–224.URL: http://journals.impan.pl/ap/Inf/108-3-2.htmlDOI: 10.4064/ap108-3-2.ISSN: 0066-2216.

Let F be a homogeneous polynomial of degree d in m + 1 variables defined over an al-gebraically closed field of characteristic 0 and suppose that F belongs to the s-th secant

variety of the d-uple Veronese embedding of Pm into P(m+dd )−1 but that its minimal decom-

position as a sum of d-th powers of linear forms requires more than s addenda. We showthat if s ≤ d then F can be uniquely written as F = Md

1 + · · ·+Mdt +Q, where M1, . . . ,Mt

are linear forms with t ≤ (d − 1)/2, and Q a binary form such that Q =∑q

i=1 ld−dii mi

with li’s linear forms and mi’s forms of degree di such that∑

(di + 1) = s− t.

21. Minimal decomposition of binary forms with respect to tangential projections.E. Ballico, A. Bernardi.Journal of Algebra and its Applications, 12, 6 (2013) 1350010 (8 pages).URL: http://dx.doi.org/10.1142/S0219498813500102DOI: 10.1142/S0219498813500102.ISSN: 0021-8693.

Let C ⊂ Pn+1 be a rational normal curve and let X ⊂ Pn be one of its tangentialprojection. We describe the X-rank of a point P ∈ Pn in terms of the schemes evincingthe C-rank or the border C-rank of the preimage of P .

22. Tensor ranks on tangent developable of Segre varieties.E. Ballico, A. Bernardi.Linear and Multilinear Algebra, 61 (7) , pp. 881–894 (2013).URL: http://www.tandfonline.com/doi/full/10.1080/03081087.2012.716430DOI: 10.1080/03081087.2012.716430.ISSN: 0308-1087.

We describe the stratification by tensor rank of the points belonging to the tangent devel-opable of any Segre variety. We give algorithms to compute the rank and a decompositionof a tensor belonging to the secant variety of lines of any Segre variety. We prove Comon’sconjecture on the rank of symmetric tensors for those tensors belonging to tangential va-rieties to Veronese varieties.

23. Stratification of the fourth secant variety of Veronese variety via the symmetric rank.E. Ballico, A. Bernardi.Advances in Pure and Applied Mathematics 4 (2) 215–250 (2013).URL: http://www.degruyter.com/dg/viewarticle/j$002fapam.2013.4.issue-2$002fapam-2013-0015$002

fapam-2013-0015.xml

DOI: 10.1515/apam-2013-0015.ISSN: 1869-6090.

If X ⊂ Pn is a projective non degenerate variety, the X-rank of a point P ∈ Pn is definedto be the minimum integer r such that P belongs to the span of r points of X. We describe



the complete stratification of the fourth secant variety of any Veronese variety X via theX-rank. This result has an equivalent translation in terms both of symmetric tensors andhomogeneous polynomials. It allows to classify all the possible integers r that can occurin the minimal decomposition of either a symmetric tensor or a homogeneous polynomialof X-border rank 4 (i.e. contained in the fourth secant variety) as a linear combinationof either completely decomposable tensors or powers of linear forms respectively.

24. A comparison of different notions of ranks of symmetric tensors.A. Bernardi, J. Brachat, B. Mourrain.Linear Algebra and Its Applications, 460, 2014, 205–230.URL: http://www.sciencedirect.com/science/article/pii/S002437951400487XDoi:10.1016/j.laa.2014.07.036.ISSN: 0024-3795.

We introduce various notions of rank for a symmetric tensor, namely: rank, border rank,catalecticant rank, generalized rank, scheme length, border scheme length, extension rankand smoothable rank. We analyze the stratification induced by these ranks. The mutualrelations between these stratifications, allow us to describe the hierarchy among all theranks. We show that strict inequalities are possible between rank, border rank, extensionrank and catalecticant rank. Moreover we show that scheme length, generalized rank andextension rank coincide.

25. A Note on plane rational curves and the associated Poncelet Surfaces.A. Bernardi, A. Gimigliano, M. Ida.Rend. Istit. Mat. Univ. Trieste 47, 1–6 (2015).URL: http://hdl.handle.net/10077/11219DOI: 10.13137/0049-4704/11219.ISSN: 0049-4704.

We consider the parametrization (f0, f1, f2) of a plane rational curve C, and we wantto relate the splitting type of C (i.e. the second Betti numbers of the ideal (f0, f1, f2) ⊂K[P1]) with the singularities of the associated Poncelet surface in P3. We are able ofdoing this for Ascenzi curves. Moreover we prove that if the Poncelet surfaces S ⊂ P3 issingular then it is associated to a curve C which possesses at least a point of multiplicity≥ 3.

26. On Parameterizations of plane rational curves and their syzygies.A. Bernardi. A. Gimigliano, M. Ida.Accepted by Mathematische Nachrichten, July 20, 2015.URL: http://onlinelibrary.wiley.com/doi/10.1002/mana.201500264/abstractDOI: 10.1002/mana.201500264.

Let C be a plane rational curve of degree d and p : C → C its normalization. We areinterested in the splitting type (a, b) of C, where OP1(−a − d) ⊕ OP1(−b − d) gives thesyzigies of the ideal (f0, f1, f2) ⊂ K[s, t], and (f0, f1, f2) is a parameterization of C. Wewant to describe in which cases (a, b) = (k, d− k) (2k ≤ d), via a geometric description;namely we show that (a, b) = (k, d − k) if and only if C is the projection of a rationalcurve on a rational normal surface in Pk+1.


Alessandra Bernardi’s CV 12 REVIEWER AND REFEREE ACTIVITIES

11.5 Preprints

27. Curvilinear schemes and maximum rank of forms.E. Ballico, A. Bernardi.Preprint: http://arxiv.org/abs/1210.8171

We define the curvilinear rank of a degree d form P in n+ 1 variables as the minimumlength of a curvilinear scheme, contained in the d-th Veronese embedding of Pn, whosespan contains the projective class of P . Then, we give a bound for rank of any homogenouspolynomial, in dependance on its curvilinear rank.

28. Lecture notes on Waring problems, Secant varieties and Sylvester algorithm.A. Bernardi.Draft available at http://www.mimuw.edu.pl/ jabu/conf/2013/lukecin.html.

These are the Lecture notes on “Waring problems, Secant varieties and Sylvester algo-rithm” for the 36th Autumn School in Algebraic Geometry “Power sum decompositionand apolarity, a geometric approach” September 1st-7th, 2013 Lukecin, Poland.

29. A uniqueness result on the decompositions of a bi-homogeneous polynomialE. Ballico, A. BernardiPreprint: http://arxiv.org/abs/1507.06083.

In the first part of this paper we give a precise description of all the minimal decom-positions of any bi-homogeneous polynomial p (i.e. a partially symmetric tensor ofSd1V1 ⊗ Sd2V2 where V1, V2 are two complex, finite dimensional vector spaces) if its

rank with respect to the Segre-Veronese variety Sd1,d2(V1, V2) is smaller than (d1+d2+1)2

and d1 and d2 differ at most by 2, or if its rank is smaller than (min{d1,d2}+1)2 . Such

a polynomial may not have a unique minimal decomposition as p =∑r

i=1 λipi withpi ∈ Sd1,d2

(V1, V2) and λi coefficients, but we can show that there exist unique p1, . . . , pr′ ,p′1, . . . , p

′r′′ ∈ Sd1,d2

(V1, V2) , two unique linear forms l ∈ V ∗1 , l′ ∈ V ∗2 , and two unique

bivariate polynomials q ∈ Sd2V ∗2 and q′ ∈ Sd1V ∗1 such that either p =∑r′

i=1 λipi + ld1q

or p =∑r′′

i=1 λ′ip′i + l′d2q′, (λi, λ

′i being appropriate coefficients).

In the second part of the paper we focus on the tangential variety of the Segre-Veronesevarieties. We compute the rank of their tensors (that is valid also in the case of Segre-Veronese of more factors) and we describe the structure of the decompositions of theelements in the tangential variety of the two-factors Segre-Veronese varieties.

12 Reviewer and Referee Activities

12.1 Referee

Referee for the following international organizations for research evaluation of fellowships and researchprojects:

• FWO Opening new horizons (Fonds Wetenschappelijk Onderzoek Vlaanderen) – (Flanders ResearchFoundation).


Alessandra Bernardi’s CV 13 APPENDIX

• ANR (L’Agence nationale de la recherche Des projets pour la science) – (French National Agencyfor Research of Projects for Science).

Referee for various journals among which (Class A and B in the ISI classification):

• Linear Algebra and its Applications (LAA).

• Numerical Linear Algebra with Applications (NLA).

• Algebra & Number Theory (ANT).

• Linear and Multilinear Algebra (LMA).

• Proceedings of the American Mathematical Society (Proc. Amer. Math. Soc.).

• Mediterranean Journal of Mathematics (MedJM).

12.2 Reviewer

Reviewer in the areas 14N05, 13D40, 14J26, 14M15, 13P10 (MSC 2000) for AMS Mathematical Reviewsand Zentralblatt MATH.

13 Appendix

13.1 Scientific Evaluation of the Marie Curie project by the European Com-munity

Total score: **86, 40/100, 00**of which:67

1. Scientific & Technological QUALITY (award): 4,50 / 5,00 (0,25 %);Strengths:

• The scientific quality of the proposal is very good, with multidisciplinary applications.

• The theme of the proposal is a modern approach situated in a classical research field.

• The methodology is appropriate, covering several topics, and is compatible with the objectives.

• Excellent host group, very qualified in the field of the proposal.

Weaknesses:

• The project might be over-ambitious for the length of the fellowship.

2. TRAINING (award): 4,50 / 5,00 (0,15 %);Strengths:

• The research training objectives are clearly stated and relevant.

• The additional scientific training and the complementary skills offered, mainly regarding themultidisciplinary applications, are of very good quality.


Alessandra Bernardi’s CV 13 APPENDIX

• The expertise of the supervisor and of the host group in training experienced researchers isgood.

Weaknesses:

• No major weakness.

RESEARCHER (award): 4,30 / 5,00 (0,25 %); Strengths:

• The research track record is very good, and the results obtained so far are very interesting.

• Good match between the fellow’s profile and project.

• The potential for reaching a position of professional maturity is high.

• The potential to acquire new knowledge is good.

• Independent thinking and leadership qualities are demonstrated.

Weaknesses:

• No major weakness.

3. IMPLEMENTATION (selection): 4,30 / 5,00 (0,15 %);Strengths:

• The quality of the infrastructures and facilities of the host institution is very high.

• The host is involved in many international collaborations.

• The practical arrangements for the implementation and management of the scientific projectare very good.

• The support for the hosting of the fellow is very good.

• The work plan is detailed.

Weaknesses:

• The feasibility of the project as a whole is not entirely convincing.

Comments:

• Even if partially successful, the outcome would still be substantial.

4. IMPACT (award): 4,00 / 5,00 (0,20 %)Strengths:

• The potential of acquiring competencies during the fellowship is high.

• The contribution to European excellence and European competitiveness is well documented.

Weaknesses:

• The description of the impact to the career development is not properly addressed: it ismerely a summary of the expected results, of the acquisition of complementary skills and ofsome general statements.


curriculum of scienti c and teaching activity of ...abernardi/encv.pdf · november 2005{november...

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