23/01/20  Seminario  16:30  17:30  1101 D'Antoni  Ernesto De Vito  Università di Genova  MultiScale Vector Quantization with Reconstruction Trees
The aim of vector quantization is a parsimonious reconstruction
of unsupervised data as provided by Kmeans and geometric
multiresolution analysis, to name a few. In the talk I will present a multiscale 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 finemultiscalefashion. 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 lowdensity limit.
In the first part of this lecture, I will discuss the proof of convergence of the Lorentz process, in the BoltzmannGrad 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 BoltzmannGrad 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 ParisDauphine  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 BakryEmery. 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

17/01/20  Seminario  14:30  15:30  1101 D'Antoni  Kenji IOHARA  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 curvaturedimension inequalities (due to BaudoinGarofalo), 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 timepreserving semiconjugate to an expansive flow acting on a compact 3dimensional manifold.
As a byproduct 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 KnieperClimegnagaKwar and independently LeddrapierLimaSarig, 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 BorelMoore homology or equivalently as the Extalgebra 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 highfrequency 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. 