Curriculum

Giorgio Ottaviani

Born in Florence, October 1st, 1960.

Research area

Main research area is Algebraic Geometry and its applications. In particular, projective subvarieties and vector bundles. Homogeneous vector bundles on rational homogeneous varieties. Secant varieties and tensor decomposition. Tensor rank. Identifiability of tensors. Complexity of matrix multiplication algorithm. Entanglement and applications to Quantum Information. Developing algorithms by current symbolic software (Macaulay2.

Conference Talks and Seminars (main)


"Analisi complessa e geometria 6" CIRM Trento 1987,
"Giornate di Geometria Algebrica" L'Aquila 1991,
"Classification of algebraic Varieties" L'Aquila 1992,
"Vector bundles in Algebraic Geometry" Durham 1993,
"Vector bundles on Fano 3-folds" Trento 1994,
"Algebraic Geometry and Physics" Trieste 1996,
"Conference in Algebraic Geometry", Roma 1998,
Algebraic Geometry and Commutative Algebra" Madrid 1998,
"Global Geometry of Algebraic Varieties", Madrid 2002,
Geometry of Algebraic Varieties AGAFE 2005, Ferrara 2005,
"Vector Bundles and Low Codimensional Subvarieties", CIRM Trento 2006,
Algebraic Geometry Conference ABB70, Bedlewo (Polonia), 2006,
Algebraic Geometry in higher dimension, Levico 2007;
Special session on Secant Varieties and Applications at AMS Joint Meeting, San Diego California (2008);
Moduli spaces of vector bundles: algebro-geometric aspects, Barcelona 2008
International Conference in Algebraic Geometry, Bucharest, 2008
Workshop on Geometry and Representation Theory of tensors for computer science, statistics and other areas, AIM Palo Alto (California), 2008,
Geometry of Projective Varieties (Rome, 2008),
Workshop on tensors and interpolation, (Nice, 2009),
Algebraic Geometry Party after Carnival (Torino, 2010),
Journ?s Paloises de G?m?rie alg?rique, (Pau, 2010),
Solving Polynomial Equations (KTH Stockholm, 2011),
Texas Algebraic Geometry Seminar (Rice University, Houston, Texas, 2011),
Foundations of Computational Mathematics Conference, (Budapest 2011),
Western Algebraic Geometry Seminar (Colorado State University, 2011),
SIAM Meeting on Applied Algebraic Geometry (North Carolina State University, 2011)
International Conference on the Spectral Theory of Tensors (Nankai University, Tianjin, 2012)
Algebraic Statistics in the Alleghenies (Pennsylvania State University, 2012)
Convegno UMI-CIIM (Bergamo, 2012)
Varietà reali e complesse, geometria, topologia e analisi armonica, Scuola Normale Superiore, Pisa, 2013
MEGA (Effective methods in Algebraic Geometry), Frankfurt 2013 (plenary)
SIAM Meeting on Applied Algebraic Geometry (Colorado State University, 2013)
International Conference on Engineering and Computational Mathematics (Hong Kong, 2013)
Vector Bundles Days II, Mezzetti 60th, Trieste 2014
Computational Nonlinear Algebra, ICERM, Providence, 2014
Effective moduli spaces and applications to cryptography, Rennes, 2014
Program Algorithms and Complexity in Algebraic Geometry, Simons Institute, Berkeley, 2014
Theory and Applications of Syzygies, Schreyer 60th, Saarbruecken, 2015
SIAM Conference on Applied Algebraic Geometry, NIMS, Daejeon, 2015 (plenary)
Geometry of Algebraic Varieties, Verra 65th, Berlin, 2015
Coloquio Latinoamericano de Algebra, Buenos Aires, 2016
Tensors: Algebra meets Numerics, MPI Leipzig, 2016
On crossroads of Algebra, Analysis and Geometry, Shapiro 60th, Stockholm, 2017
Modern Algebra and Classical Geometry, together with Edoardo, Sernesi 70th, Trento, 2017
FOCM Barcelona, 2017 (semiplenary)
Tensors, Turin, 2018
Italian-Polish meeting, Wroclaw, 2018 (plenary)
Nonlinear algebra in applications, ICERM, Providence, 2018
A journey through projective and birational Geometry (Andreatta 60th), Trento, 2019
POEMA 1st workshop, Florence, 2020
Webinar at Università dell'Insubria, Novembre 2020
Università di Trento, PhD day, Marzo 2021
Projective and birational higher dimensional geometry, (online) April 9, 2021.
Tensor Methods and Emerging Applications to the Physical and Data Sciences MARCH 8 - JUNE 11, 2021, IPAM (online)
Tensor Networks: Quantum Physics, Geometry and Applications, Levico Terme (Trento), July 26-28, 2021
SIAM Applied Algebraic Geometry, Texas A&M, Agosto 2021
Algebraic Geometry in Ischia, Ottobre 2021
Jornada de Jovenes Doctores en Geometrıa Algebraica Barcelona, November 4-5th, 2021
POEMA 1st workshop, Florence, January 2020
Webinar at Università dell'Insubria, Novembre 2020
Università di Trento, PhD day, Marzo 2021
Projective and birational higher dimensional geometry, (online) April 9, 2021.
Tensor Methods and Emerging Applications to the Physical and Data Sciences MARCH 8 - JUNE 11, 2021, IPAM (online)
Tensor Networks: Quantum Physics, Geometry and Applications, Levico Terme (Trento), July 26-28, 2021
SIAM Applied Algebraic Geometry, Texas A&M, Agosto 2021
Algebraic Geometry in Ischia, Ottobre 2021
Jornada de Jovenes Doctores en Geometria Algebraica Barcelona, November 4-5th, 2021
Workshop on Geometry and Complexity Theory, Toulouse (France), April 2022
Bandoleros 2022, Conference on Vector Bundles, Ankara (Turkey), May 2022
Agates 2022, Geometry of secants workshop, Warsaw (Poland), October 2022
Homemade Algebraic Geometry, Celebrating Enrique Arrondo's 60th birthday, Alcalà de Henares, July 2023
Algebraic Geometry in L'Aquila, July 2023


He gave seminar talks at the University of Milano, Roma, Firenze, L'Aquila, Poitiers, Trento, Trieste, Catania, Bayreuth, Kaiserslautern, Varsavia, Torun, Ferrara, Barcelona, Perugia, Pisa, Siena, Madrid, Grenoble, Versailles, Pau, Bucarest, Pavia, Genova, Fort Collins (Colorado), Denver (Colorado), Boulder (Colorado), College Station (Texas), Politecnico di Torino, Recife (Brasil), San Diego (California), MSRI Berkeley (California), AIM (California), Leuven (Belgio).

I have organized 4 international and 4 national conferences, often taking part in the Scientific Committee.

Doctoral Students

Chiara Brandigi, On the j-normality of small codimension projective varieties, Firenze, 1999
Carla Dionisi, Multidimensional matrices and minimal resolutions of vector bundles, Napoli, 2000
Daniele Faenzi, Vector bundles over Fano varieties, Firenze, 2003
Chiara Brambilla, Simplicity of vector bundles on Pn and exceptional bundles, Firenze, 2004
Ada Boralevi, Quiver representations and Homogeneous Vector Bundles on Flag Manifolds, Firenze, 2008
Alessandro Bernardi, Normal Bundle of rational Curves and the Waring Problem, Firenze, 2011
Elena Angelini, The Torelli problem for logarithmic bundles of hypersurfaces arrangements in the projective space, Firenze 2013
Maurizio Banchi, Typical ranks of ternary cubic forms over R, Firenze, 2013
Davide Vanzo, Instanton bundles and their moduli spaces, Firenze, 2017
Mauro Maccioni, Tensor rank and eigenvectors, Firenze 2017
Luca Sodomaco, The Distance Function from the Variety of partially symmetric rank-one Tensors, Firenze 2020
Ettore Turatti, Singular vector tuples and their geometry , H2020 grant Poema, Firenze, Novembre 2022
Cosimo Flavi, Decompositions of powers of quadratic forms (co-supervisor Alessandro Gimigliano), Bologna, 2023
Vincenzo Galgano, Secant varieties of Spinor varieties and of other generalized Grassmannians, (co-supervisor Alessandra Bernardi), Trento, 2023
Belal Sefatpanah, IASBS, Zanjan (Iran), current
Davide Furchí Università dell'Insubria, current

PostDoctoral Scholars and Fellows who have collaborated with me in Florence


Flavio Angelini (in L'Aquila)
Robert Braun
Jean Vallès (european grant)
Chiara Brandigi
Laura Costa (EAGER grant)
Carla Dionisi
Pierre Emmanuel Chaput (EAGER grant)
Daniele Faenzi
Oskar Kedzierski (EAGER grant)
Beatriz Grana Otero (EAGER grant)
Chiara Brambilla
Luke Oeding (2 years through NSF grant)
Juan Luis Pons
Simone Marchesi
Alessandra Bernardi
Nick Vannieuwenhoven
Kangjin Han
Pierre-Jean Spaenlehauer
Alicia Tocino Sanchez
Yang Qi
Zahra Shahidi

Main Visiting Positions

Schools and Teaching activity for graduate students