Born in Florence, October 1st, 1960.
July 1983 Degree in Mathematics at the University of Florence. Thesis: Fibrati vettoriali sugli spazi proiettivi, advisor Francesco Gherardelli.
1983-1987 Ph. D. in Mathematics at the University of Florence. Thesis: Vector bundles on grassmannians and quadrics, advisor Vincenzo Ancona
Teaching licence at high school for Mathematics and Physics
1987-1989 Teacher in Mathematics and Physics at Istituto Magistrale Rodari, Prato. Teacher in courses of Introduction to Computer Science at Scuola Elementare e Media S. Maria degli Angeli.
Fondazione Severi Prize 1988/89.
1989-1992 Researcher assistant in Geometry at Rome, University Tor Vergata.
1992-1994 Associate Professor in Geometry at Faculty of Engineering, University of Florence.
1994-1997 Full Professor at Faculty of Sciences, University of L' Aquila.
Since November 1st 1997 Full Professor at University of Florence .
Head of Department of Mathematics and Computer Science since November 2016.
Chairman of the Mathematics courses in Florence for the SSIS (Specialization School for Teaching in Higher School), 1999-2007. Coordinator of Mathematics-Physics-Computer Science SSIS in Tuscany since 2001 to 2003. Chairman of the Courses in Mathematics of University of Florence, 2008-2012.
Responsible of research funds ex 60% "Classificazione delle varietà reali e complesse" of Department of Mathematics of University of Florence, years 2003 2005 2007 2009 2011 2013
Local responsible (Florence) of MIUR PRIN research group "Geometry of Algebraic Varieties" (PI A. Verra). Member of the GNSAGA of Italian INDAM. Member of UMI, SIMAI, AMS and SIAM.
Executive Board member of Scuola Matematica Interuniversitaria (SMI) (2008-2017), Scientific Council member of Centro Internazionale Matematico Estivo (CIME) (2011-2017), member of Commissione Italiana per l'Insegnamento della Matematica (CIIM) since 2013.
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)
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.
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)
Jean Vallès (european grant)
Laura Costa (EAGER grant)
Pierre Emmanuel Chaput (EAGER grant)
Oskar Kedzierski (EAGER grant)
Beatriz Grana Otero (EAGER grant)
Luke Oeding (2 years through NSF grant)
Juan Luis Pons
Alicia Tocino Sanchez
Main Visiting Positions
Bayreuth, through the DFG program "Komplexe Mannigfaltigkeiten", 5 visits in period 1990-1996, invited by M. Schneider
research fellowship haute niveau CNRS at Versailles, one month in 2003
Colorado State University, one month in 2006
MSRI at Berkeley, one month in 2009, Algebraic Geometry
Mittag Leffler Institute, one month in 2011, Algebraic Geometry with a view toward applications
Simons Institute, Berkeley, three months in 2014, Program Algorithms and Complexity in Algebraic Geometry
Schools and Teaching activity for graduate students
1992/93 Algebra Commutativa Computazionale, Ph. D. course at the University of Florence
1993/94 INDAM course (intensive week) at Florence on "Varietà proiettive di codimensione piccola" , with V. Ancona
1994/95 INDAM course at Rome in Algebraic Geometry.
1995 SMI summer course in Cortona about "Rational Homogeneous Varieties" , with W. Decker
2001 Autumn School in Algebraic Geometry, Moduli of bundles and group actions, Wykno(Poland), with J. Vallès
2007 Scuola di dottorato: Geometria proiettiva e birazionale delle varietà algebriche. Gargnano, 2007, with P. Ionescu, M. Mella
Doctorate Course on Algebraic Geometry in Florence (several)
Doctorate Course on Geometric Invariant Theory, Pisa 2007 (repeated in Florence in 2009)
School on Geometry and Representation Theory of tensors for computer science, statistics and other areas, MSRI Berkeley (California), 2008, with P. Comon, J.M. Landsberg, J. Weyman.
Pragmatic School: Vector bundles, from classical techniques to new perspectives, Catania, 2009, with Rosa M. Mirò-Roig
Nordfjordeid summer school, Geometry of tensors and applications, 2010, with J.M. Landsberg, J. Weyman
School on Invariant Theory and Projective Geometry, Trento, 2012
Tensors and their geometry in high dimension, Berkeley 2012
Winter School on Algebraic Geometry KAIST (South Korea), 2013
Power sum decompositions and apolarity, a geometric approach; Lukecin (Poland), 2013
Tensors, geometric approach and its applications; Seoul, 2014
Quartiche piane, mappa di Scorza e argomenti correlati, Catania, 2016