Seminari di Geometria Algebrica a.a. 2016-2017

Pagina di Geometria Algebrica

7 Giugno 2017, ore 15.00, sala conferenze Tricerri, DiMaI
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
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
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
Alicia Tocino (UniversitÓ di Firenze) EIGENVECTORS AND BEST RANK K APPROXIMATION FOR BINARY FORMS
ABSTRACT. file.pdf
20 Gennaio 2017, ore 13.30, sala conferenze Tricerri, DiMaI
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.


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