Geometria Algebrica e Tensori a.a. 2018-2019

Ciclo di seminari di studio organizzato congiuntamente da E. Angelini, C. Bocci, C. Brambilla, A. Calabri, L. Chiantini, M. Mella, G. Ottaviani, E. Rubei .

Chiunque sia interessato a ricevere informazioni su questo ciclo di seminari contatti gli organizzatori via mail oppure si iscriva alla mailing list geometria.
I seminari si svolgono di norma ogni tre settimane, tra le sedi di Bologna e Firenze .

Quinto appuntamento:

venerdì 31 Maggio 2019, ore 12:00, sala Tricerri
Dipartimento di Matematica e Informatica "U. Dini", Università di Firenze
Nick Vannieuwenhoven (KU Leuven) terrà il seguente seminario:
Titolo: An introduction to tensor networks
Abstract: I will present an introduction to general tensor networks. We start with the easy case of networks that are a tree and discuss their algebraic and differential geometry. Then, we move to more complicated, general networks that include cycles, discussing their algebraic structure and presenting some open problems.

Quarto appuntamento:

venerdì 29 Febbraio 2019, ore 14:00, aula Seminario II
Dipartimento di Matematica, Università di Bologna
Alex Massarenti (Universitą di Ferrara) terrà il seguente seminario:
Titolo: Birational geometry of complete tensors
Abstract: The moduli space of complete collineations is roughly speaking a compactification of the space of linear maps between two fixed vector spaces, in which the boundary divisor is simple normal crossing. It has been constructed by I. Vainsencher as a sequence of blow-ups starting from the projective spaces parametrizing matrices modulo scalar along the Segre variety and its secants varieties in order of increasing dimension. This space is a spherical wonderful variety. Exploiting its spherical nature we will investigate its birational geometry. We will outline how these notions can be generalized to complete tensors and their relations with moduli spaces of vector bundles and Hilbert schemes of rational normal curves.

Terzo appuntamento:

venerdì 22 Febbraio 2019, ore 12:00, sala Tricerri
Dipartimento di Matematica e Informatica "U. Dini", Università di Firenze
Antonio Lerario (SISSA, Trieste) terrà il seguente seminario:
Titolo: Random algebraic geometry: from random polynomials to random tensors
Abstract: Over the past few years there has been an intense activity around the field of "Random Algebraic Geometry", whose main interest has been studying the zero set of random real algebraic equations. The main idea of this study is to approach real algebraic geometry replacing the notion of "generic", from complex algebraic geometry, with the notion of "random". In this talk I will adopt this philosophy for the study of properties of real tensors. For example: what is the expected real rank of a random symmetric tensor? The answer to this question is related to the volume of the secant locus of the Veronese variety (alternatively: to the number of multiple points of a random rational map...) I will present recent results on the subject of random tensor geometry, trying to explain some general principles and discussing why, in the large degree limit, random real algebraic geometry behaves as the "square root" of complex algebraic geometry.

Secondo appuntamento:

mercoledì 16 Gennaio 2019, ore 12:00, sala Tricerri
Dipartimento di Matematica e Informatica "U. Dini", Università di Firenze
Luca Sodomaco (Università di Firenze) terrà il seguente seminario:
Titolo: The ED polynomial of the dual varieties of Veronese varieties
Abstract: In the first part of this talk, we outline the main properties of the ED polynomial of a real algebraic variety, where ED stands for "Euclidean Distance". Then we focus on the ED polynomial of the dual of the d-th Veronese variety of P^n, showing its close relationship with the spectral theory of symmetric tensors. In particular, we investigate its lowest and highest coefficients and their corresponding vanishing loci. The main result is a closed formula for the product of the Euclidean eigenvalues of a symmetric tensor, which generalizes the known fact that the determinant of a symmetric matrix is the product of its eigenvalues.

Primo appuntamento:

venerdì 31 Ottobre 2018, ore 14:30, aula Arzelą
Dipartimento di Matematica, Università di Bologna
Francesco Galuppi (MPI Leipzig) terrà il seguente seminario:
Titolo: Introduction to moment varieties
Abstract: Moment varieties are geometric objects arising from algebraic statistic. The aim of this seminar is to present the basic definitions, the main examples and the state of the art of moment varieties, with special focus on defectivity and identifiability.

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