Seminari di Geometria Algebrica a.a. 2016-2017
- 7 Giugno 2017, ore 15.00, sala conferenze Tricerri, DiMaI
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Liqun Qi
(Hong Kong Polytechnic University)
Tensor Analysis: Spectral Theory and Special Tensors
Liqun Qi ha introdotto nel 2005 gli autovettori di tensori, che si riconducono nel caso di matrici agli autovettori classici.
E' un esperto a livello internazionale di analisi numerica multilineare.
ABSTRACT. Eigenvalues for tensors were introduced in 2005. Since then, a
rich theory on eigenvalues of tensors and special tensors has been
developed. This includes the characteristic polynomial theory,
the Perron-Frobenius theory for nonnegative tensors with
applications in spectral hypergraph theory and higher order Markov
chains, positive semi-definite tensors and sum-of-squares tensors,
completely positive tensors and copositive tensors, etc.
Eigenvalues of tensors also found their applications in magnetic
resonance imaging, elastic mechanics, liquid crystal study, quantum
entanglement and classicality problems, etc. A book ``Tensor
Analysis: Spectral Theory and Special Tensors'' is published by SIAM in April this year.
- 23 Maggio 2017, ore 14.30, sala conferenze Tricerri, DiMaI
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Nikolas Tziolas
(Cyprus)
Automorphisms and moduli of canonically polarized surfaces in positive
characteristic
ABSTRACT. In this talk I will discuss the moduli of canonically polarized surfaces
defined over an algebraically closed field of characteristic p>0 and the pathologies
that appear compared to the characteristic zero case. In particular, unlike the
characteristic zero case, there does not always exists a modular family.
A modular family is a family with the property that up to etale base change, every other
family is obtained from it by base change. I will explain the
relation between this pathology and the existence of canonically polarized surfaces with
nontrivial global vector fields, or equivalently with nonreduced
automorphism scheme. Moreover, several results regarding the geometry of such surfaces
will be presented.
- 21 Marzo 2017, ore 14.30, sala conferenze Tricerri, DiMaI
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Marcos Jardim
(Campinas, Brasile)
New moduli components of rank 2 bundles on projective space
ABSTRACT. We present a new family of monads whose cohomology is a stable
rank two vector bundle on the projective space. We also study the
irreducibility and smoothness together with a geometrical description of
some of these families. Such facts are used to prove that the moduli space
of stable rank two vector bundles with trivial determinant and second
Chern class equal to 5 has exactly three irreducible components. We
describe each of these components in terms of monads. This is joint work
with C. Almeida, A. Tikhomirov and S. Tikhomirov.
- 21 Febbraio 2017, ore 13.30, sala conferenze Tricerri, DiMaI
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Alicia Tocino
(Università di Firenze)
EIGENVECTORS AND BEST RANK K APPROXIMATION FOR BINARY
FORMS
ABSTRACT. file.pdf
- 20 Gennaio 2017, ore 13.30, sala conferenze Tricerri, DiMaI
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Fulvio Gesmundo
(Texas A&M)
Rigidita' di matrici e la complessita' del prodotto matrice-vettore
ABSTRACT. Negli anni 60, la scoperta dell'algoritmo FFT rivoluziono'
il mondo del signal processing portando la complessita' computazionale
della Trasformata Discreta di Fourier da O(n^2) a O(n log(n))
operazioni elementari. Negli anni successivi, L. Valiant congetturo'
che non fosse possibile trovare un algoritmo piu' veloce e propose un
programma per dimostrare questa congettura basandosi sulla nozione di
"rigidita' di una matrice", una misura della complessita' del prodotto
matrice vettore. Discutero' un approccio a questo problema che fa uso
di strumenti di geometria algebrica classica e moderna, basandosi
sullo studio di certi join tra la varieta' delle matrici di rango al
piu' r e degli spazi lineari. Parte di questo lavoro nasce da una
collaborazione con J. Hauenstein, C. Ikenmeyer e J.M. Landsberg.