Alessandra Bernardi
Education 



Academic career and teaching activities 

Employment
Teaching Activity


Research interests 

Secant varieties, their dimensions and ideals; 0dimensional 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). 

Research work 

Secant varieties, their dimensions and ideals; 0dimensional 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). 

Memberships in societies and scientific committees 

Member of societies:
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) 20152019. • 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.agencenationalerecherche.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 FWOExpertpanel (Fonds Wetenschappelijk Onderzoek Vlaanderen) – (Flan ders Research Foundation) for the evaluation of applications for fellowships and research projects. http://www.fwo.be/en/ 

Awards and honours 



Conferences and lectures 

Talks in Italian and international conferencesPlenary/Main Speaker1. MEGA Effective Methods in Algebraic Geometry, “Tensor decomposition and homotopy continua tion”. Trento, 15–19 June, 2015. 2. MAG2015, December, 24 2015, Barcellona, Spagna. 3. “Fat points schemes”, Research Station on Commutative Algebra June 1317, 2016, Seoul, Korea. 4. “Tensor decomposition and homotopy continuation”, British Mathematical Colloquium, April 37, 2017, Durham, UK. Invited Speaker5. “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, GenovaTorinoMilano 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 1214, 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 1216, 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. Schools17. 36th Autumn School in Algebraic Geometry on “Power sum decomposition and apolarity, a geo metric approach”. September 17, 2013, Lukecin, Poland. 18. “Singular values decomposition and Applications”, INDAM school for II years undergraduate fel lowships. July 22–26, 2019, Perugia, Italy. 

Other work 

OrganizationsOrganization 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/algebraicgeometry20144 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 SIMAIUMIPTM 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/tensornetworksquantumgeo/ • 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. JuneJuly 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. AprilMay 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://qigeoalg.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/tensorphdseminar/homepage?authuser=1%20 

Notes 

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. 