Alessandra Bernardi

• June 1996. Graduated from the high school Liceo Scientico of Polo Scolastico Maria Montessori in Porretta Terme, Bologna, Italy, with 60/60.
• March 16, 2001 Laurea degree in Mathematics with full marks and honors (110/110 with praise) from Alma Mater Studiorum Università degli Studi di Bologna. Thesis title: "Schemi 0-dimensionali e forme canoniche di polinomi omogenei", (i.e. "0-dimensional schemes and canonical forms of homogeneous polinomials"). Advisor: Prof. A. Gimigliano (University of Bologna).
• 2001-2005. PhD in Mathematics, Università degli Studi di Milano. Thesis title: "Varieties parameterizing forms and their secant varieties". Advisor: Prof. A. Gimigliano (University of Bologna).

Employment

• 2001-2005 PhD in Mathematics, Università 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 de Madrid, Spain), financed by GRUPO SANTANDER.
• November 2005-November 2009, Assegnista di ricerca; Alma Mater Studiorum Università degli studi 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 Ricerca Matematica) - Fondazione Bruno Kessler (Trento - Italy).
• November 8, 2010 - November 7, 2012: Individual Marie Curie Fellow (Post Doc) IEF (International European Fellowship), INRIA (Institut National de Recherche en Informatique et en Automatique) Sophia Antipolis - Mediterranee (France).
• January 17 - February 26, 2011: Visitor, Mittag-Leer Intitut (The Royal Swedish academy of sciences) invited by A. Dickenstein, S. Di Rocco, R. Piene, K. Ranestad and B. Sturmfels for the Spring Semester 2011 "Algebraic geometry with a view towards applications".
• November 2012 - December 2013, Researcher RTD a), University of Torino, Department of Mathematics "Giuseppe Peano", Italy.
• December 2013 - January 2016, Researcher RTD b), University of Bologna, Department of Mathematics, Italy.
• November 2014 - December 2014. Long-Term Participant at Simons Institute for Theory of Computing (Berkeley, CA, USA), in the framework of the Fall Program 2014 "Algorithms and Complexity in Algebraic Geometry", Invited by P. Burgisser, JM Landsberg, K. Mulmuley, B. Sturmfels.
• From February 2016, Associate Professor in Algebra, University of Trento, Department of Mathematics. Italy.

Teaching Activity

• Teaching activity abroad (for PhD Students or higher)
  • ​​Research Assistant for the American PhD course in Math.: MATH 689-computational complexity geometry, I Semester A.A. 2005-2006, Texas A&M University, College Station (Texas, USA); Teaching Professor: JM Landsberg (College Station, Texas, USA).
  • Teaching Assistant for JM Landsberg (Texas A&M, Texas, USA), L.-H. Lim (UC Berkeley, California, USA) and J. Morton (UC Berkeley, California, USA) during the Graduate Workshop "Geometry and representation theory of tensors for computer science, statistics and other areas", at MSRI (Mathematical Sciences Research Institute), Berkeley (California - USA). July 2008.
  •  Main Speaker at "36th Autumn School in Algebraic Geometry: Power sum decomposition and apolarity, a geometric approach". Advanced school for PhD students and higher. Lukecin, Poland, September 1-7, 2013.
• Teaching activity in Italy
  • Teaching Professor
    • Algebra 2, II year course of Mathematics, Univ. Torino, 2012-2013.
    • Geometria 1, I year course of Mathematics, Univ. Torino, 2012-2013.
    • Geometria, I year course of Engineering and architecture, Univ. Bologna, 2014-2015.
    • Teoria Algebrica dei Numeri, III year course of Mathematics, Univ. Trento, 2015-2018.
    • Geometria e algebra lineare, Engineering, Univ. Trento, 2016-2018.
    • Advances Commutative Algebra, Master and PhD in Mathematics, Univ. Trento 2016-2017.
    • Tensor Decomposition for Big Data Analysis, Master in Mathematics, Univ. Trento 2017-2018.
  • Tutorial Exercises 
    • Geometria e Algebra I, I year course of Mathematical and Physical Engineering, Politecnico di Milano, 2002-2003, teaching professor G. Bolondi.
    • Elementi di Analisi Matematica, Algebra e Geometria. I year course of Mechanical Engineering, Politecnico di Milano, 2003-2004, teaching professor F. Colombo.
    • Geometria e Algebra Lineare, (allievi A-K and L-Z). I year course of Management Engineering, Univ. Bologna, 2003-2004, 2006-2008 teaching professor A. Gimigliano.
    • Analisi Matematica B (allievi Ingegneri Civili). I year course of Ingegneria Civile, Milano Leonardo Politecnico (Italy), 2004-2005, teaching professor G. Verzini.
    • Geometria e Algebra (Corso integrato, moduli di Algebra e Geometria), I year course of Scienza della Formazione Primaria, Univ. Bologna, 2007-2008, teaching professor A. Gimigliano.
    • Analisi Matematica I, Geometria e Algebra Lineare (Corso integrato, moduli di Geometria e Algebra Lineare), (allievi A-K and L-Z). I year course of Management Engineering,Univ. Bologna, 2008-2010 teaching professor A. Gimigliano.

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 real case (Veronese variety, Segre variety, Grassmannians, Flag varieties, Homogeneous varieties); Rank of symmetric tensors and structured tensors; Uniqueness of the decomposition of a tensor; algebraic and numerical algorithms for the tensor decomposition both in the complex and real case; Applications to telecommunications, complexity theory, data analysis, phylogenetics and quantum physics (entanglement and tensor networks).

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 real case (Veronese variety, Segre variety, Grassmannians, Flag varieties, Homogeneous varieties); Rank of symmetric tensors and structured tensors; Uniqueness of the decomposition of a tensor; algebraic and numerical algorithms for the tensor decomposition both in the complex and real case; Applications to telecommunications, complexity theory, data analysis, phylogenetics and quantum physics (entanglement and tensor networks).

Member of societies:

• UMI (Unione Matematica Italiana)
  • From May 2021, Secretary of UMI (Italian Mathematical Union).
  • From 2021, Member of the scientific committee of MaddMaths!.
  • From 2021, Member of Comitato per la Comunicazione e la Divulgazione UMI.
  • From 2021. Coordinator of Comitato di Gestione del Sito UMI.
  • From October 2021, Direttore Responsabile of Notiziario UMI.
  • From November 2021, Referente scientifico of Gruppo UMI “Crittografia e Codici”.
• SIAM (Society for Industrial and Applied Mathematics)
  • SIAM - AG (Algebraic Geometry activity group)
• EWM (European Women in Mathematics)

Scientific committees

• 2021. Component of the CAR (Committee of research areas) of the Math. Dept. of Trento for the

selection of the research products in the ANVUR program of VQR (Evalutaion of the Quality of

the research) 2015-2019.

• 2019. Reviewer for grant proposals for the National Science Center (Poland).

• 2019. Member of the jury of a HDR Mathématiques Appliquées diploma (France).

• 2019. Member of the eligibility jury of the recruitment competition for “chargé de recherche de

class normale” at the INRIA Sophia Antipolis Center.

• 2018. External referee of ANR (The French National Research Agency).

http://www.agence-nationale-recherche.fr/en/

• From June 2017. Member of the Scientific Advisory Board of MEGA (Effective Methods in Alge-

braic Geometry).

https://mega.sciencesconf.org/

• 2015, 2018. Member FWO-Expertpanel (Fonds Wetenschappelijk Onderzoek Vlaanderen) – (Flan-

ders Research Foundation) for the evaluation of applications for fellowships and research projects.

http://www.fwo.be/en/

• "Borsa di studio ENAM per studenti universitari meritevoli". Academic Years: 1996-1997, 1997-1998, 1998-1999, 1999-2000.
• Selected among the 100 best students of the Italian high schools by University Orientation Course for at Cortona (Italy). SCUOLA NORMALE SUPERIORE DI PISA. Summer 1995.
• Scholarship: "Best student of the Scientic Liceo, Polo Scolastico Maria Montessori" (Porretta Terme, Bologna, Italy). Financed by Lions Club of Granaglione Alto Reno, December 1996.
• Awards for the best student of the Scientic Liceo, Polo Scolastico Maria Montessori (Porretta Terme, Bologna, Italy). Financed by City Council of Gaggio Montano (Bologna, Italy). Years: 1991-1992, 1992-1993, 1993-1994, 1994-1995, 1995-1996.
• Award "VI Latinus Ludus". Financed by Lions Club Cattolica, Maggio 1992.
• Award for the best student of the Scuola Media Salvo D'Acquisto (Gaggio Montano, Bologna). Year 1991-1992.

Talks in Italian and international conferences

Plenary/Main Speaker

1. MEGA Effective Methods in Algebraic Geometry, “Tensor decomposition and homotopy continua-

tion”. Trento, 15–19 June, 2015.

2. MAG2015, December, 2-4 2015, Barcellona, Spagna.

3. “Fat points schemes”, Research Station on Commutative Algebra June 13-17, 2016, Seoul, Korea.

4. “Tensor decomposition and homotopy continuation”, British Mathematical Colloquium, April 3-7,

2017, Durham, UK.

Invited Speaker

5. “Secant Varieties and Ideals of varieties parameterizing certain symmetric tensors”, July 17, 2008,

MSRI (Mathematical Sciences Research Institute) (Berkeley, California, USA).

6. “Applicazioni recenti di risultati classici su varietà delle secanti a varietà che parametrizzano tensori.

Dal problema di Waring al rango di tensori”, November 22, 2010, Progressi Recenti in Geometria

Reale e Complessa, October 17–22, 2010, Levico Terme (Trento, Italy).

7. “Ranks of Tensors, related varieties and applications”, November 18, 2011, Genova-Torino-Milano

Seminar: some topics in Commutative Algebra and Algebraic Geometry, November 17–18, 2011,

Milano (Italy).

8. “Algebraic Geometry in Signal processing, Phylogenetic and Quantum Physics”, Colloquium Po-

litecnico di Torino, May 30, 2013, Politecnico di Torino, Italy.

9. “Tensor Ranks”, 2013 SIAM Conference on Applied Algebraic Geometry. August 1, 2013, Fort

Collins (Colorado, USA).

10. [Declined for family reasons (maternity leave)] to the “Tensors and Optimization” Conference, May

19–22, 2014 for the SIAM Optimization Meeting, San Diego (CA, USA).

11. [Declined for family reasons (maternity leave)] for Computational Nonlinear Algebra, for the ICERM

Conference, June 2–6, 2014, Brown University (Providence, USA).

12. “Cactus Varieties of Cubic Forms: Apolar Local Artinian Gorenstein Rings”, November 13, 2014,

inside the Workshop Tensors in Computer Science and Geometry in the framework of the fall

program 2014 at the Simons Institute for theory of Computing (Berkeley, USA) ”Algorithms and

Complexity in Algebraic Geometry“, Invited by P. Bürgisser, JM Landsberg, K. Mulmuley, B.

Sturmfels.

13. “Tensor Decomposition and Homotopy Continuation”, Tensors: Algebra meets Numerics, Max

Planck Institute for Mathematics in the Sciences, December 12-14, 2016, Leipzig, Germany.

14. “Algorithms for rank, tangential rank and cactus rank of a homogeneous polynomial”. Compu-

tational Nonlinear Algebra, for the ICERM Conference, November 12-16, 2018, Brown University

(Providence, USA).

15. “On the Dimension of Tensor Network Varieties”. Workshop IV: Efficient Tensor Representations

for Learning and Computational Complexity. Part of the Long Program Tensor Methods and

Emerging Applications to the Physical and Data Sciences. IPAM, UCLA (US), May 18, 2021.

16. “High order singular value decomposition for plant diversity estimation”. A New Paradigm for

Sustainable Development in Agriculture: Mathematics & AI get into the Field. December 2–3,

2021, Milano, Italy.

Schools

17. 36th Autumn School in Algebraic Geometry on “Power sum decomposition and apolarity, a geo-

metric approach”. September 1-7, 2013, Lukecin, Poland.

18. “Singular values decomposition and Applications”, INDAM school for II years undergraduate fel-

lowships. July 22–26, 2019, Perugia, Italy.

Organizations

Organization of Schools and Conferences

• Summer School: “An Interdisciplinary Approach to Tensor Decomposition”

Trento, Italy, July, 13–18, 2014.

Organizing Committee: A. Bernardi, A. Boralevi, E. Postinghel.

Financied by: FBK–CIRM, Compositio Mathematica, Dipartimento di Matematica “Giuseppe

Peano” Univ. Torino, GNSAGA.

• Workshop on “Symbolic and Numerical Methods for Tensors and Representation The-

ory”,

Simons Institute (Berkeley, CA, USA), 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).

• International workshop on “Quantum Physics and Geometry”

Levico Terme (Trento, Italy), July 4–6, 2017.

Organizing Committee: E. Ballico, A. Bernardi, I. Carusotto, S. Mazzucchi, V. Moretti.

Webpage: http://www.science.unitn.it/~carusott/QUANTUMGEO17/index.html

Financed by: CIRM, INDAM, Siquro Project, BEC Center, University of Trento, INFN.

• Session in the SIMAI-UMI-PTM Joint Meeting: “Algebraic geometry and interdisci-

pliary applications”

Wroclaw, Poland, September 16–20, 2018.

Organizers: Alessandra Bernardi and Weronika Buczyńska.

Invited Speakers: Mateusz Micha lek, Jarek Buczyński, Justyna Szpond, Marcin Dumnicki, M.V.

Catalisano, L. Chiantini, M. Gallet, F. Gesmundo.

• MEGA: Effective Methods in Algebraic Geometry 2019

Madrid, June 17–21, 2019.

Executive Committee: Carlos D’Andrea (Barcelona), Maria Emilia Alonso Garcia (Madrid, also

local chair), Alessandra Bernardi (Trento), Frederic Bihan (Univ. de Savoie), Sandra Di Rocco

(KTH Stockholm), Mauricio Velasco (Bogota), Josephine Yu (Giorgia Tech), Thorsten Theobald

(Frankfurt)

Webpage: https://mega.sciencesconf.org/

• Special session at the UMI congress 2019: Algebra multilineare, Geometria Algebrica

e Applicazioni

Pavia, Italy, September 2–7, 2019

Organizers: Alessandra Bernardi and Luca Chiantini.

• Tensor Networks: Quantum Physics, Geometry and Applications

Levico (Trento), Italy, July 27–29, 2020

Organizers: Alessandra Bernardi, Iacopo Carusotto, Philipp Hauke

Webpage: https://sites.google.com/unitn.it/tensor-networks-quantum-geo/

• 100 years Unione Matematica Italiana 800 years Università di Padova

Padova, Italy, May 23–27, 2022

Organizing committee: Fabio Ancona, Martino Bardi, Alessandra Bernardi, Olga Bernardi, Alessan-

dra Bianchi, Giovanna Carnovale, Marco Ferrante, Fausto Ferrari, Antonia Larese, Francesco Rossi.

Webpage: https://www.100umi800unipd.it/.

Organization of PhD Courses and Masterclasses

• PhD Course: Quantum Information Theory and Geometry,

Teaching Professor: J.M. Landsberg (Texas A&M).

Univ. Trento. June-July 2017.

Financed by INDAM in the framework of “Programma professori visitatori”.

• PhD Course: The geometry of quantum algorithms

Teaching Professor: F. Holweck (Belfort, France)

Univ. Trento. April-May 2020.

Financed by Mathematical Department of Trento and Q@TN.

• Masterclass: Tensor decompositions and their applications (by Nick Vannieuwenhoven – KU Leuven,

Belgium) for the

Trento, Italy, November 2021

Organizers: Alessandra Bernardi and Alessandro Oneto

In the framework of the TensorDec Laboratory in Trento.

Organization of Workgroups

• Quantum Information, Geometry and Algebra Workgroup,

University of Trento, from 2016,

Interdisciplinary workgroup among Mathematical Department, Physics Department and CNR.

Organizers: A. Bernardi, I. Carusotto.

This is a series of interdisciplinary meetings where we try to build a common language among

Algebra, Geometry, Analysis, Physics starting on the base of the Quantum Information Theory.

Webpage: https://qi-geo-alg.maths.unitn.it/

• Tensor PhD Seminar

University of Trento

Organizers: A. Bernardi

From 2018/19 we run a cycle of seminars in which each PhD student reports to the group what is working on. From 2020/21 the initiative gather the all PhD students of the Italian tensor commu-

nity: https://sites.google.com/unitn.it/tensor-phd-seminar/home-page?authuser=1%20

Abilitazione to Professore Ordinario (Full Professor) in Mathematics in the Italian universities. Valid from 28/03/2017 to 28/03/2023.

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

Qualification to Maître de Conference in the section 25 (Pure Mathematics) in the French universities. Obtained in February 2012.

Leaves: From February 13 to July 13, 2014. Maternity Leave.