Notiziario Scientifico

Notiziario dei seminari di carattere matematico
a cura del Dipartimento di Matematica Guido Castelnuovo, Sapienza Università di Roma

Settimana dal 20-06-2022 al 26-06-2022

Martedì 21 giugno 2022
Ore 15:00, Sala di Consiglio e via zoom ID riunione: 867 4440 2839 Passcode: MDN, Sapienza Università di Roma
seminario di Modellistica Differenziale Numerica
Luca Saluzzi (Imperial College of London)
A Data-Driven Tensor Train Gradient Cross approximation for Hamilton-Jacobi-Bellman equations
Hamilton-Jacobi-Bellman (HJB) equation plays a central role in optimal control and differential games, enabling the computation of robust controls in feedback form. The main disadvantage for this approach depends on the so-called curse of dimensionality, since the HJB equation and the dynamical system live in the same, possibly high dimensional, space. In this talk, I will present a data-driven method for approximating high-dimensional HJB equations based on tensor decompositions. The application of tensor methods to the resolution of the HJB equation has been already studied recently via the application of the Policy Iteration Algorithm. The approach presented in this talk is based on the knowledge of the value function and its gradient on sample points and on a tensor train decomposition of the value function. The collection of the data will be derived by two possible techniques: Pontryagin Maximum Principle and State-Dependent Riccati Equations. The numerical experiments will demonstrate a linear complexity in the dimension and a better stability in presence of noise. Finally, I will present an application to an agent-based model and a comparison with a Deep Learning technique.
Per informazioni, rivolgersi a: carlini@mat.uniroma1.it

Mercoledì 22 giugno 2022
Ore 10:00, Aula B, Dipartimento di Matematica, Sapienza Università di Roma
Corso di dottorato (prima lezione)
Yohan Brunebarbe (CNRS, Bordeaux)
Hodge theory and tame geometry
https://phd.uniroma1.it/dottorati/cartellaDocumentiWeb/62870012-444a-4d43-bc63-3b6bbe7103ef.pdf
Per informazioni, rivolgersi a: bravi@mat.uniroma1.it

Mercoledì 22 giugno 2022
Ore 14:00, B1, Dipartimento SBAI
Seminario di Analisi Matematica
Alberto Saldana (UNAM, Mexico)
The role of the logarithmic Laplacian in the asymptotic analysis of fractional problems
Fractional derivatives are commonly used to model a variety of phenomena, but... what does it mean to have a logarithmic derivative? And what would it be used for? In this talk we focus on the logarithmic Laplacian, a pseudodifferential operator that appears as a first order expansion of the fractional Laplacian as the exponent s goes to zero. This operator can also be represented as an integrodifferential operator with a zero order kernel. We will discuss how the logarithmic Laplacian can be used to study the behavior of linear and nonlinear fractional problems in the small order limit. This analysis will also reveal a deep and interesting mathematical structure behind the set of solutions of Dirichlet logarithmic problems.

Mercoledì 22 giugno 2022
Ore 14:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
seminario di Algebra e Geometria
Margarida Melo (Università Roma Tre)
On the top weight rational cohomology of the moduli space of abelian varieties
In the last few years, tropical methods have been applied quite successfully in understanding the combinatorics behind compactification of moduli spaces, in particular by endowing them with a tropical modular interpretation. Consequently, one can study different properties of these (compactified) spaces by studying their tropical counterparts. In this talk, which is based in joint work with Madeleine Brandt, Juliette Bruce, Melody Chan, Gwyneth Moreland and Corey Wolfe, I will illustrate this phenomena for the moduli space \(A_g\) of abelian varieties of dimension \(g\). In particular, I will show how to apply the tropical understanding of the classical toroidal compactifications of \(A_g\) to compute, for small values of \(g\), the top weight cohomology of \(A_g\). We also show that our results can be used to study the stable cohomology of the Satake compactification of \(A_g\) and the cohomology of \(\operatorname{GL}_g(\mathbb Z)\).
Per informazioni, rivolgersi a: diverio@mat.uniroma1.it

Mercoledì 22 giugno 2022
Ore 14:30, Canale Youtube dell'IAC https://www.youtube.com/watch?v=dS8ngH7u9cE, Istituto per le Applicazioni del Calcolo, Consiglio Nazionale delle Ricerche
Online Seminars on Artificial Intelligence and Mathematics 2022 https://www.aim.iac.cnr.it/home
Marco Cuturi (CREST - ENSAE, Institut Polytechnique de Paris)
Learning through ambiguity: differentiable matchings and mappings
Optimal transport (OT) theory is the branch of mathematics that aims at studying and generalizing the fundamental problem of matching optimally two groups of observations, covered in all CS 101 courses (remember the Hungarian algorithm!). Following a short introduction to that theory, I present use cases in ML when optimal matchings pop up in various applied areas in ML, where matchings are used to resolve labelling ambiguities. I will then show why a direct resolution of OT problems (using e.g. the Hungarian algorithm or more general network flows/linear programs) runs into several issues: computational complexity, sample complexity, poor parallelization and lack of a meaningful notion of differentiability (e.g. how an optimal matching varies with changes in inputs). I will then detail how regularization can help solve this issues, and present the implementation of these approaches in the ott-jax toolbox.
Per informazioni, rivolgersi a: roberto.natalini@cnr.it

Mercoledì 22 giugno 2022
Ore 16:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
seminario di Fisica Matematica
Alberto Fachechi (Sapienza Università di Roma)
PDE/Statistical Mechanics relation: from p-spin ferromagnets to dense associative memories
Spin-glass models have always been a challenge both for physicists and mathematicians, as they exhibit - also in their simplest version - complex, intriguing emergent behaviors whose rigorous description is particularly tricky. Among the techniques developed to deal with the thermodynamics of these systems, an important example is constituted by Guerra's interpolating techniques, which turn out to be connected with PDE systems. In this talk, we will present some recent results concerning the relation between Guerra’s interpolating partition functions of p-spin models and the Burgers hierarchy. Finally, we also discuss a generalization of these findings in some AI-relevant models, the so-called dense associative memories.

Giovedì 23 giugno 2022
aula degli Affreschi - Chiostro di San Pietro in Vincoli
Convegno
Two days of PDEs in heterogeneous and irregular structures
Programma:

9:25 Opening
9:30 Claudia Timofte (University of Bucharest, Romania)
10:15 Coffee break
11:00 Assegnazione premio "Tullio Levi-Civita" per le Scienze Matematiche e Meccaniche istituito dall' "International Research Center for Mathematics and Mechanics of Complex Systems", Università dell’Aquila MeMoCS e dalla fondazione MeMoCS
11:15 Claude Viterbo (Université de Paris-Saclay, Francia) - premio "Tullio Levi-Civita"
12:15 Francesco Dell'Isola (Università degli Studi dell’Aquila, Italy)
Lunch
14:30 Martin Ostoja-Starzewski (University of Illinois at Urbana-Champign, USA)
15:15 Gianpaolo Piscitelli (Università degli Studi di Napoli Federico II)
15:45 Giovanni Scilla ("Sapienza" Università di Roma)
16:15 Coffee Break
16:45 Simone Creo (Sapienza Università di Roma)

Sito web: https://sites.google.com/uniroma1.it/twodaysofpdes

Venerdì 24 giugno 2022
aula degli Affreschi - Chiostro di San Pietro in Vincoli
Convegno
Two days of PDEs in heterogeneous and irregular structures
Programma:

9:00 Josè Matias (Universidade de Lisboa, Portugal)
9:45 Alejandro Velez-Santiago (University of Puerto Rico at Mayagüez, Puerto Rico)
10:30 Coffee break
11:15 Adrian Muntean (Karlstad University, Svezia)
12:00 Sergio Polidoro (Università degli studi di Modena e Reggio Emilia, Italy)
Lunch
14:30 Maria-Magdalena Boureanu (University of Craiova, Romania)
15:15 Anna Chiara Lai (Sapienza Università di Roma)
15:45 Vishnu Raveendran (Karlstad University, Svezia)
16:15 Coffee Break

Sito web: https://sites.google.com/uniroma1.it/twodaysofpdes

Venerdì 24 giugno 2022
Ore 11:00, Aula M1, Dipartimento di Matematica e Fisica
Colloquium di Matematica
Umberto Zannier (Scuola Normale Superiore)
Dalle radici dell'unita' a Manin-Mumford e oltre. (Un survey sulla teoria dei punti di torsione su gruppi algebrici.)
Intendo presentare alcuni aspetti della teoria (aritmetica) dei punti di torsione su gruppi algebrici. Iniziero' dai casi piu' semplici, che risalgono a Gauss, per arrivare a studi recenti, tempo permettendo. Mi concentrero' soprattutto sulle 'relazioni algebriche tra punti di torsione'. Adottero' un linguaggio elementare, richiamando anche alcune nozioni di base, allo scopo di rendere il seminario accessibile anche a studenti e a chi opera in settori matematici di natura diversa
Ci sarà la possibilità di seguire il seminario in remoto, cliccando sul seguente link

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