Massless field equations are fundamental in particle physics. In Clifford analysis, a version of these equations in Euclidean space of dimension 4 have been studied. In this talk, we shall discuss a recent development on this topic. In particular, for fields with values in a general irreducible spin module, as an analogue of massless field equations we propose the so-called generalized Cauchy-Riemann equations introduced by E. Stein and G. Weiss. Then we describe Fischer decompositions of massless fields up to spin 3/2. This is a joint work with V. Soucek, W. Wang, F. Brackx and H. De Schepper.
Le nuove tecnologie e l’Intelligenza Artificiale offrono oggi grandi opportunità di crescita economica e sociale, offrendo a tutti innovative soluzioni per migliorare le attività siano esse professionali o personali.
Di fronte a questi nuovi scenari si aprono importanti temi etici che vanno affrontati affinché l’impatto offerti da queste tecnologie possa portare i benefici attesi per migliorare la vita di tutti.
Con esempi e casi reali, durante l’intervento si valuteranno i molteplici ambiti di applicazione dell’AI, i progressi tecnologici fatti e i principi etici che guidano un’organizzazione come Microsoft nella definizione di sistemi di AI.
Sarà anche l’occasione per scoprire anche i vantaggi offerti dalle soluzioni di AI sui grandi urgenze mondiali, dalla crisi sanitaria a quelli legati ai temi della sostenibilità.
In this talk I will present some recent results on asymptotics of eigenvalues of the Dirichlet Laplacian when a small compact set is removed from the initial domain. If the small set is concentrating at a point in some sense, the eigenvalue variation is proved to be strictly related to the vanishing order of one of the relative eigenfunctions at that point. A good understanding of this asymptotics leads to new issues, for instance optimal location or optimal shape of the hole (open problem) as well as possible ramification of multiple eigenvalues.
Seminar The DPG Method for Convection-Reaction Problems Leszek Demkowicz, Oden Institute, The University of Texas at Austin lunedì 10 maggio 2021 alle ore 17:00 us02web.zoom.us/j/81021076857
We present a progress report on the development of Discontinuous Petrov-Galerkin methods for the convection-reaction problem in context of time-stepping and space-time discretizations of Boltzmann equations .
The work includes a complete analysis for both conforming (DPGc) and non-nonconforming (DPGd) versions of the DPG method employing either globally continuous or discontinuous piece-wise polynomials to discretize the traces.
The results include construction of a local Fortin operator for the case of constant convection and a global discrete stability analysis for both DPGc and DPGd methods.
The theoretical findings are illustrated with numerous numerical experiments in two space dimensions.
This is a joint work with Nathan Roberts from Sandia National Laboratories.
In the last two decades great progress has been made in the study of dispersive and wave equations. Over the years the toolbox used in order to attack highly nontrivial problems related to these equations has developed to include a collection of techniques: Fourier and harmonic analysis, analytic number theory, math physics, dynamical systems, probability and symplectic geometry. In this talk I will introduce a variety of results using as model problem mainly the periodic 2D cubic nonlinear Schrodinger equation. I will start by giving
a physical derivation of the equation from a quantum many-particles
system, I will introduce periodic Strichartz estimates along with some remarkable connections to analytic number theory, I will move on the concept of energy transfer and its connection to dynamical systems, and I will end with some results on the derivation of a wave kinetic equation.
In this talk, we present recent work on the hyperbolic Anderson model driven by a space-time colored Gaussian homogeneous noise with spatial dimension one and two. Under mild assumptions, we provide Lp-estimates of the iterated Malliavin derivatives of the solution in terms of the fundamental solution of the wave solution. We present two applications:
(1) We present quantitative central limit theorems for spatial averages of the solution to the hyperbolic Anderson model, where the rates of convergence are described by the total variation distance. These quantitative results have been elusive so far due to the temporal correlation of the noise blocking us from using the Itô calculus.
(2) We establish the absolute continuity of the law for the hyperbolic Anderson model. The Lp-estimates of Malliavin derivatives are crucial ingredients to verify a local version of Bouleau-Hirsch criterion for absolute continuity. Our approach substantially simplifies the arguments for the one-dimensional case, which has been studied in the recent work by Balan, Quer-Sardanyons and Song (2019).
This talk is based on the joint work (arXiv:2101.10957) with R. Balan, D. Nualart and L. Quer-Sardanyons (2021).
Seminar La delta di Dirac: storia di un mostro Marco Bramanti , Politecnico di Milano mercoledì 5 maggio 2021 alle ore 12:15 online: tiny.cc/fdsCM2021
At the time of writing, an ever-increasing amount of data is collected every day, with the volume of such generated records estimated to be doubling every two years. Datasets are becoming massive in terms of size and substantially more complex in nature. Nevertheless, this abundance of "raw information" does come at a price: wrong measurements, data-entry errors, breakdowns of automatic collection systems and several other causes may ultimately undermine the overall data quality. The talk will present novel methodologies for performing reliable inference, within the model-based classification and clustering framework, in presence of contaminated data. First a discriminant analysis method for anomaly and novelty detection will be introduced, with the final aim of discovering label noise, outliers and unobserved classes in a semi-supervised context. Secondly, two robust variable selection methods, effectively performing high-dimensional discrimination within an adulterated scenario, will be discussed.
Joint work with Francesca Greselin and Thomas Brendan Murphy
The talk is devoted to a mathematical introduction to Machine Learning
from the point of view of inverse problems. In the presentation, we focus on
supervised learning problems in the framework of kernel methods.