Notiziario Scientifico

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

Settimana dal 28-04-2025 al 04-05-2025

Lunedì 28 aprile 2025
Ore 14:30, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
seminario di Analisi Matematica
Max Fathi (Université Paris Cité)
Cutoff phenomenon for nonlinear diffusion equations: a few examples
The cutoff phenomenon is a now classical topic in probability, that consists in proving an abrupt convergence to equilibrium for a sequence of Markovian dynamics. Classical examples include card shuffles, random walks on groups and graphs, or interacting particle systems. In this talk I will present an overview of the topic, and discuss some examples of cutoff for porous medium and fast diffusion equations in high dimension. Joint work with Djalil Chafaï and Nikita Simonov. This seminar is part of the activities of the Excellence Department Project CUP B83C23001390001 and it is funded by the European Union – Next Generation EU.
Per informazioni, rivolgersi a: azahara.delatorrepedraza@uniroma1.it

Lunedì 28 aprile 2025
Ore 14:30, Aula D'Antoni, Dipartimento di Matematica, Università degli Studi di Roma Tor Vergata
DocTorV Seminar
Nelson Alvarado (Università degli Studi di Roma Tor Vergata)
Abelian varieties and the Schottky problem
Roughly speaking, algebraic geometry studies geometric objects (called varieties) which are contained in the projective space and are defined by polynomial equations. One of the most special kind of varieties are the abelian ones, whose points have the structure of a commutative group. One of the historical reasons of why abelian varieties are studied is because given a curve C one can construct a (polarized) abelian variety, which is called the Jacobian of C, and it turns out that this abelian variety encodes the geometry of the curve in a very precise way. In this introductory seminar we will talk about how jacobians are constructed, both from the topological and algebraic point of view, and discuss why they are so special.
Per informazioni, rivolgersi a: doctorv.uniroma2@gmail.com

Lunedì 28 aprile 2025
Ore 16:00, aula M3, Dipartimento di Matematica e Fisica, Università di Roma Tre, Lungotevere Dante 376
seminario di probabilità
Lars Schroeder (University of Twente)
Stationary distribution of node2vec random walks on household models
Node2vec random walks are tuneable random walks that come from the popular computer science algorithm node2vec which is used for feature learning on networks. The transition probabilities of the random walks depend on the previous visited node and on the triangles that contain the current and the previous node. Even though the algorithm is widely used in practice, mathematical properties of node2vec random walks almost have not been investigated and even basic questions such as how the stationary distribution depends on the walk parameters are unexplored. We study household models, graphs with clique-structured communities, and we prove a theorem that gives an explicit formula for the stationary distribution of node2vec random walks on these models and compare it with the stationary distribution of the simple random walk.

Martedì 29 aprile 2025
Ore 10:00, Aula F, Dipartimento di Matematica, Sapienza Università di Roma
Corso di dottorato
Francesco Bei (Sapienza Università di Roma)
Introduzione alla coomologia L2 di varietà Riemanniane
La coomologia L2 di una varietà Riemanniana è un oggetto di natura analitica che contiene interessanti informazioni sulla geometria e la topologia della varietà sottostante. Informalmente possiamo definirla come un raffinamento dell'usuale coomologia di de Rham che in aggiunta tiene conto di condizioni di integrabilità indotte dalla metrica. L'obiettivo del corso è offrire un'introduzione a questo tema di ricerca, oggetto di numerosi lavori negli ultimi cinquant'anni. a) Richiami di analisi funzionale: operatori chiusi, operatori chiudibili, operatori essenzialmente autoaggiunti. Cenni di teoria spettrale. b) Complessi di Hilbert. Definizione e proprietà di base. c) Proprietà generali della coomologia L2 di una varietà Riemanniana. d) Alcuni esempi ed applicazioni notevoli.

Martedì 29 aprile 2025
Ore 14:30, Aula Dal Passo, Dipartimento di Matematica, Università di Roma Tor Vergata
Seminario di Analisi Matematica
Cristian Mendico (Université Bourgogne)
Nash equilibria, Mather measures and ergodic Mean-field games
In this presentation, we will analyze the various domains in which the ergodic mean field game (MFG) system arises. Specifically, we will explore how weak KAM theory can be used to study this system and derive results regarding long-time behavior or the approximation of Nash equilibria. Finally, we will introduce a quasi-stationary system—a model in which, at each moment, agents optimize their expected future cost under the assumption that their environment remains static.
NB: This talk is part of the activity of the MUR Excellence Department Project MATH@TOV CUP E83C23000330006
Per informazioni, rivolgersi a: molle@mat.uniroma2.it

Martedì 29 aprile 2025
Ore 15:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di Modellistica Numerica
Giulia Bertaglia (Università di Ferrara)
Gradient-based Monte Carlo methods for hyperbolic conservation laws
Originally developed to model reaction-diffusion systems, Gradient Random Walk methods are particle-based techniques that track the evolution of spatial derivatives of a solution. Inspired by vortex methods for the Navier-Stokes equations, these approaches emerged in the 1990s and attracted significant interest due to their advantageous properties: (i) they eliminate the need for a computational grid, (ii) they naturally adapt to solution features by concentrating particles where gradients are steep, and (iii) they offer a notable reduction in variance. In this seminar, we revisit and extend these ideas by demonstrating how the Gradient Random Walk framework can be adapted to a wider class of partial differential equations. To achieve this goal, we first extend the classical Monte Carlo method to the relaxation approximation of systems of conservation laws, and subsequently introduce a novel particle dynamics approach based on the spatial derivatives of the solution. This methodology, when combined with an asymptotic-preserving splitting discretization, enables the development of a new class of gradient-based Monte Carlo methods tailored for hyperbolic systems of conservation laws.

Martedì 29 aprile 2025
Ore 16:15, Aula riunioni I piano, Istituto per le Applicazioni del Calcolo IAC-CNR, via dei Taurini 19, Roma
Seminario Volterra
Riccardo Montalto (Università di Milano)
Small and large amplitude quasi-periodic waves in Fluid Mechanics
In this talk I shall discuss some recent results about the construction of small and large amplitude quasi-periodic waves in Euler equations and other hydro-dynamical models in dimension greater or equal than two. I shall discuss quasi-peridic solutions and vanishing viscosity limit for forced Euler and Navier-Stokes equations and the problem of constructing quasi-periodic traveling waves bifurcating from Couette flow (and connections with inviscid damping). I also discuss some results concerning the construction of large amplitude quasi-periodic waves in rotating fluids. The techniques are of several kinds: Nash-Moser iterations, micro-local analysis, analysis of resonances in higher dimension, normal form constructions and spectral theory.
Per informazioni, rivolgersi a: lucia.deluca777@gmail.com

Mercoledì 30 aprile 2025
Ore 11:00, Aula Dal Passo, Dipartimento di Matematica, Università di Roma Tor Vergata
Gerhard Huisken (MFO Oberwolfach e Università di Tubinga)
Concepts of quasi-local mass and quasi-local radius in Mathematical Relativity
In General Relativity, Euclidean 3-space is replaced by a 3-dimensional Riemannian manifold arising as a space-like hypersurface in a Lorentzian space-time. Energy conditions on the space-time matter lead to curvature restrictions on the 3-manifold such as non-negativity of the scalar curvature. In this context it is important to find geometric structures resembling classical physical concepts such as mass and momentum both locally and globally to describe physically interesting phenomena like gravitational collapse in a way that is independent of coordinates. The lecture discusses new geometric concepts for the mass and diameter of a finite region of a 3-manifold that aim in this direction.
Per informazioni, rivolgersi a: sinestra@mat.uniroma2.it

Mercoledì 30 aprile 2025
Ore 12:00, Aula Dal Passo, Dipartimento di Matematica, Università di Roma Tor Vergata
Luciano Mari (Università di Milano)
Prescribing the Lorentzian mean curvature of a spacelike hypersurface, and the Born-Infeld model
The talk aims to discuss the existence and regularity problem for spacelike hypersurfaces in Lorentz-Minkowski space whose mean curvature is a prescribed measure. The same equation also appears in Born-Infeld's theory of electrostatics, according to which the unknown describes the electric potential generated by a given charge. Even though the problem is formally the Euler-Lagrange equation of a nice convex functional, the lack of smoothness when the graph becomes lightlike in Lorentz-Minkowski space may prevent the unique variational minimizer to solve the equation. A chief difficulty comes from the possible presence of "light segments" in the graph of the solution, a fact that we will describe in detail. Various open problems and research directions will be discussed. The talk is based on joint works with J. Byeon, N. Ikoma, A. Malchiodi and L. Maniscalco.
Per informazioni, rivolgersi a: sinestra@mat.uniroma2.it

Mercoledì 30 aprile 2025
Ore 13:00, Aula Picone, Dipartimento di Matematica, Sapienza Università di Roma
Seminario del ciclo MATHtalks
Francesca Pieroni (Sapienza Università di Roma)
Random Matching Euclideo per densità Gaussiane
Il problema del Random Matching Euclideo consiste nel trovare il matching ottimale tra due insiemi di variabili aleatorie \(X_1,\ldots,X_n\) e \(Y_1,\ldots,Y_n\) indipendenti e distribuite su \(\mathbb{R}^d\) con una distribuzione di probabilità \(\rho\). Il primo passo è quello di minimizzare la quantità \(C_n(\pi):=\sum_{i=1}^n|X_i-Y_{\pi_i}|^p\) rispetto a tutte le possibili permutazioni \(\pi\) di \(\{1,...,n\}\), e poi considerare il valore atteso (rispetto a \(\rho\)) del minimo delle \(C_n(\pi)\), per \(p\) e \(d\) fissati e \(n\) molto grandi. L'obiettivo di questo seminario è di studiare il caso in cui le variabili aleatorie sono distribuite su \(\mathbb{R}^d\) con la densità di probabilità Gaussiana.
Per informazioni, rivolgersi a: MATHtalks@uniroma1.it

Mercoledì 30 aprile 2025
Ore 14:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di Algebra e Geometria
Antonio Trusiani (Chalmers University of Technology)
Extremal Kähler metrics on modifications
I will present the invariance of extremal Kähler manifolds under a suitable class of bimeromorphic morphisms. Focusing mostly on the cscK (constant scalar curvature Kähler) case, I will show how the main result is obtained as a consequence of a general uniform coercivity estimate for the Mabuchi energies of perturbed Kähler classes. I will then explain how such variational approach applies more generally to the class of weighted extremal metrics, modulo a log-concavity assumption on the first weight, and to any equivariant resolution of singularities of Fano type of a compact Kähler klt space whose weighted Mabuchi energy is assumed to be coercive. This is a joint work with S. Boucksom and M. Jonsson.

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