**Curriculum**

**Giorgio Ottaviani **

Born in Florence, October 1^{st}, 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 1

^{st}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.

- Chair of MEGA (Effective Methods in Algebraic Geometry) 2015-2017, member of Advisory Board since 2013.
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.

**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 **

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, 2016Masterclass on Tensors: Geometry and Quantum Information, Copenhagen, 2018