|23/01/20||Seminario||16:30||17:30||1101 D'Antoni||Ernesto De Vito||Università di Genova||Multi-Scale Vector Quantization with Reconstruction Trees
The aim of vector quantization is a parsimonious reconstruction
of unsupervised data as provided by K-means and geometric
multi-resolution analysis, to name a few. In the talk I will present a multi-scale algorithm for vector quantization and study its statistical properties. The proposed approach is inspired by decision trees and is based a family of given partitions, to quickly explore the data in a coarse to fine-multi-scale-fashion. The main technical contribution is an analysis of the expected distortion achieved by the proposed algorithm. Both asymptotic and finite sample results are derived. The presentation is based on a joint work with E. Cecini and L. Rosasco.
|23/01/20||Seminario||14:00||15:00||1201 Dal Passo|| Prof. Jens Marklof ||Bristol University||The classical and quantum Lorentz gas in the low-density limit.
In the first part of this lecture, I will discuss the proof of convergence of the Lorentz process, in the Boltzmann-Grad limit, to a random process governed by a generalised linear Boltzmann equation. This will hold for general scatterer configurations, including certain types of quasicrystals, and include the previously known cases of periodic and Poisson random scatterer configurations. The second part of the lecture will focus on quantum transport in the periodic Lorentz gas in the same Boltzmann-Grad limit, and I will report on some partial progress in this challenging problem. Based on joint work with Andreas Strombergsson (part I) and Jory Griffin (part II).
|21/01/20||Colloquium||14:30||15:30||1201 Dal Passo||Maria J. Esteban||Universite' de Paris-Dauphine||Optimal functional inequalities and improvements via the use of linear and nonlinear flows|
In this talk I will present a family of methods that can be used to find optimal constants of functional inequalities, and the corresponding extremal functions. Surprisingly, they can also be used to obtain improvements of these optimal inequalities. They are based on well suited linear and nonlinear flows and related to the "carré du champ method" of Bakry-Emery. Applications of this theory to the case of functional inequalities on manifolds, inequalities with weights and inequalities with magnetic fields will show the strength, and also the limitations, of this approach. The results presented in this talk are concerned with the the field of nonlinear PDEs, but also with questions related to mathematical physics and differential spectral geometry.
|17/01/20||Seminario||15:45||16:45||1101 D'Antoni||Richard SCHWARTZ ||Brown University||to be confirmed|
|Université Lyon 1||On elliptic root systems
Elliptic root systems are introduced in 1985 by K. Saito having simply elliptic singularities in mind. In this talk, the state of art around elliptic root systems will be explained.
|16/01/20||Seminario||16:30||18:00||1201 Dal Passo||Maria Gordina ||University of Connecticut ||Stochastic analysis and geometric functional inequalities|
We will survey different methods of proving functional inequalities for hypoelliptic diffusions and the corresponding heat kernels. Some of these methods rely on geometric methods such as curvature-dimension inequalities (due to Baudoin-Garofalo), and some are probabilistic such as coupling, and finally some use structure theory and a Fourier transform on Lie groups. For nilpotent groups, the latter can be interpreted as an eigenfunction expansion of the hypoelliptic heat kernel. This is based on joint work with F. Baudoin, B. Driver, T. Melcher, Ph. Mariano.
|14/01/20||Seminario||14:30||15:30||1201 Dal Passo||Rafael Ruggiero||PUC - Rio de Janeiro||Time preserving expansive models for geodesic flows of compact surfaces without conjugate points and the uniqueness of the measure of maximal entropy
We show that the geodesic flow of a compact surface of genus greater than one without conjugate points and continuous Green bundles is time-preserving semi-conjugate to an expansive flow acting on a compact 3-dimensional manifold.
As a by-product of this result we get a short proof of the uniqueness of the measure of maximal entropy of the geodesic flow,
a result proved by Knieper-Climegnaga-Kwar and independently Leddrapier-Lima-Sarig, by completely different methods.
|10/01/20||Seminario||15:45||16:45||1101 D'Antoni||Peter McNAMARA||University of Melbourne||Geometric Extension Algebras
A number of algebras that we study in Lie theory have geometric interpretations, appearing as a convolution algebra in Borel-Moore homology or equivalently as the Ext-algebra of a pushforward sheaf. We will discuss how information on the representation theoretic side (like being quasihereditary) is related to information on the geometric side (like odd cohomology vanishing). The primary application is to KLR and related algebras.
|10/01/20||Seminario||14:30||15:30||1101 D'Antoni||Markus REINEKE||University of Bochum||Cohomological Hall algebras of quivers
Cohomological Hall algebras form a class of graded algebras which are defined by a convolution operation on representation spaces of quivers. In the talk, we will motivate their definition, construct them, and review basic properties and known structural results. Then we turn to the special case of the Kronecker quiver and derive a description by generators and relations of the corresponding Cohomological Hall algebra, which is related to Yangians.
N.B.: this talk is part of the activity of the MIUR Excellence Department Project CUP E83C18000100006
|09/01/20||Seminario||15:00||16:00||1201 Dal Passo||Domenico Marinucci||University of Rome Tor Vergata||Critical points, multiple testing and point source detection for cosmological data|
In this talk, we shall review some mathematical issues arising in the analysis of Cosmic Microwave Background (CMB) radiation data; many of these issues can be related to the investigation of functionals of independent interest in random geometry. We will first review some results on harmonic analysis for spherical random fields, on the construction of spherical wavelets and on their stochastic properties; we will then show how to compute the asymptotic distribution of critical points for Fourier/wavelet components of random fields, and we will establish some ergodicity results, in the high-frequency limit. We will then investigate how to exploit these results to implement multiple testing procedures for detection of point sources (Galaxies) in CMB Data; the resulting tests will be shown to exhibit a number of optimality properties. Applications to CMB data from the Planck collaboration will also be briefly illustrated.
This talk is part of the activity of the MIUR Excellence Department Project CUP E83C18000100006.