Giorgio Ottaviani

Born in Florence, October 1st, 1960.

Research area

Main research area is Algebraic Geometry and its applications. In particular, projective subvarieties of small codimension and vector bundles of small rank on projective spaces. Homogeneous vector bundles on rational homogeneous varieties. Instanton bundles on projective spaces and their moduli. Secant varieties and tensor decomposition. Tensor rank. Identifiability of tensors. Complexity of matrix multiplication algorithm. 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

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, 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

Main Visiting Positions

Schools and Teaching activity for graduate students