Notiziario Scientifico
a cura del Dipartimento di Matematica Guido Castelnuovo, Sapienza Università di Roma
Settimana dal 13-01-2025 al 19-01-2025
Lunedì 13 gennaio 2025
Ore 14:30, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
seminario di Analisi Matematica
Daniele Castorina (Università di Napoli Federico II)
Mean-field sparse optimal control of systems with additive white noise
We analyze the problem of controlling a multiagent system with additive white noise through parsimonious interventions on a selected subset of the agents (leaders). For such a controlled system with an SDE constraint, we introduce a rigorous limit process toward an infinite dimensional optimal control problem constrained by the coupling of a system of ODEs for the leaders with a McKean--Vlasov type of SDE, governing the dynamics of the prototypical follower. The latter is, under some assumptions on the distribution of the initial data, equivalent with a (nonlinear parabolic) PDE-ODE system. The derivation of the limit mean-field optimal control problem is achieved by linking the mean-field limit of the governing equations together with the Gamma-limit of the cost functionals for the finite-dimensional problems. This is a joint research project with Francesca Anceschi (Ancona), Giacomo Ascione (SSM Napoli) and Francesco Solombrino (Napoli Federico II). 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 13 gennaio 2025
Ore 17:00, aula Levi–Civita, Dipartimento di Matematica, Sapienza Università di Roma
Matematica, Scienza e Società
Mirko Degli Esposti (Università di Bologna)
A.I. Fakes you: Riflessioni su entropia, irreversibilità e intelligenza artificiale
Essere o non essere? vero o falso? creatività o plagio? opera originale o copia? Lo sviluppo di nuovi modelli di Intelligenza Artificiale Generativa ci pone quotidianamente difronte a ‘dati sintetici’ sempre più complessi e sempre più ‘indistinguibili’ da quelli reali. Da fisico matematico mi divertirò a descriverne il loro funzionamento, il loro impatto, e il loro prevedibile futuro, usando come guida due concetti fondamentali della fisica: l’entropia e l’irreversibilità.
Per informazioni, rivolgersi a: enrico.rogora@uniroma1.it
Martedì 14 gennaio 2025
Ore 10:30, sala conferenze INdAM, INdAM piazzale Aldo Moro 5, Roma
LYSeMinar
Loïc Foissy (Mathématiques Pures et Appliquées Joseph Liouville de l'Université du Littoral Côte d'Opale, Caen, France)
Double bialgebra of noncrossing partitions
In this talk, we will present a double bialgebra structure on the symmetric algebra generated by noncrossing partitions. The first coproduct is given by the separations of the blocks of the partitions, with respect to the entanglement, and the second one by fusions of blocks. This structure implies that there exists a unique polynomial invariant on noncrossing partitions which respects both coproducts: we will give some elements on this invariant, and applications to the antipode of noncrossing partitions.
Per informazioni: https://www.altamatematica.it/lysm/lyseminar/
Martedì 14 gennaio 2025
Ore 14:30, Aula Dal Passo, Dipartimento di Matematica, Università di Roma "Tor Vergata"
Seminario di Equazioni Differenziali
Riccardo Montalto (Università degli Studi di Milano Statale)
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. Note: This talk is part of the activity of the MIUR Department of Excellence Project MatMod@TOV (2023-2027)
Per informazioni, rivolgersi a: sorrentino@mat.uniroma2.it
Martedì 14 gennaio 2025
Ore 14:30, aula d'Antoni, Dipartimento di Matematica, Università di Roma Tor Vergata
seminario di Geometria
Francesco Tropeano (Università di Roma Tre)
Relative monodromy of ramified sections on abelian schemes
Let us consider a complex abelian scheme endowed with a section. On some suitable open subsets of the base it is possible to define the period map, i.e. a holomorphic map which marks a basis of the period lattice for each fiber. Since the abelian exponential map of the associated Lie algebra bundle is locally invertible, one can define a notion of abelian logarithm attached to the section. In general, the period map and the abelian logarithm cannot be globally defined on the base, in fact after analytic continuation they turn out to be multivalued functions: the obstruction to the global existence of such functions is measured by some monodromy groups. In the case when the abelian scheme has no fixed part and has maximal variation in moduli, we show that the relative monodromy group of ramified sections is non-trivial and, under some additional hypotheses, it is of full rank. As a consequence we deduce a new proof of Manin's kernel theorem and of the algebraic independence of the coordinates of abelian logarithms with respect to the coordinates of periods. (Joint work with Paolo Dolce, Westlake University.)
Per informazioni, rivolgersi a: guidomaria.lido@gmail.com
Martedì 14 gennaio 2025
Ore 15:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
MDN Seminars
Luca Saluzzi (Università di Roma La Sapienza)
A Data-Driven Tensor-Train Gradient Cross 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 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 an at most linear complexity in the dimension and a better stability in presence of noise. Moreover, I will present an application to an agent-based model and a comparison with Deep Learning techniques. Finally, time permitting, I will consider the coupling of the proposed method with Model Order Reduction techniques and their application to boundary feedback control for the Navier-Stokes equations.
Mercoledì 15 gennaio 2025
Ore 14:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di Algebra e Geometria
Fabrizio Barroero (Università Roma Tre)
On the Zilber-Pink conjecture for complex abelian varieties and distinguished categories
The Zilber-Pink conjecture is a very general statement that implies many well-known results in diophantine geometry, e.g., Manin-Mumford, Mordell-Lang, André-Oort and Falting's Theorem. It explains the behaviour of intersections between an algebraic variety and a countable family of "special varieties” in an ambient space that usually is an abelian variety, a Shimura variety or even a family of abelian varieties. After a general introduction to the problem, I will report on joint work with Gabriel Dill in which we proved that the Zilber-Pink conjecture for a complex abelian variety A can be deduced from the same statement for its trace, i.e., the largest abelian subvariety of A that can be defined over the algebraic numbers. This gives some unconditional results, e.g., the conjecture for curves in complex abelian varieties (over the algebraic numbers this is due to Habegger and Pila) and the conjecture for arbitrary subvarieties of powers of elliptic curves that have transcendental j-invariant. While working on this project we realised that many definitions, statements and proofs were formal in nature and we came up with a categorical setting that contains most known examples and in which (weakly) special subvarieties can be defined and Zilber-Pink and Mordell-Lang statements can be formulated. We obtained some conditional as well as some unconditional results .-- This seminar is part of the activities of the Dipartimento di Eccellenza CUP B83C23001390001 and it is funded by the European Union – Next Generation EU.
Mercoledì 15 gennaio 2025
Ore 14:30, online (zoom), registrazione disponibile alla pagina https://indico.gssi.it/event/410/
ciclo Mathematical Challenges in Quantum Mechanics
Robert Seiringer (Institute of Science and Technology Austria)
Spectral analysis of polaron models in the strong coupling limit
The Fröhlich polaron and related models of quantum field theory have played a prominent role in mathematical physics over several decades. In this talk, we shall explain recent bounds on the quantum corrections to the (classical) Pekar approximation of the ground state energy of the Fröhlich polaron model in the strong coupling limit, and their consequence on the existence of excited states and the polaron's effective mass.
Per informazioni, rivolgersi a: monaco@mat.uniroma1.it
Mercoledì 15 gennaio 2025
Ore 16:15, Aula primo piano, IAC-CNR Roma
Seminario Volterra
Sara Daneri (GSSI, L'Aquila)
Continuous symmetry breaking: a rigorous approach
At the base of spontaneous pattern formation is universally believed to be the competition between short range attractive and long range repulsive forces. Though such a phenomenon is observed in experiments and simulations, a rigorous understanding of the mechanisms at its base is still in most physical problems a challenging open problem. The main difficulties are due to the nonlocality of the interactions and, in more than one space dimensions, the symmetry breaking phenomenon (namely the fact that the interactions have a larger group of symmetries than that of their minimizers). In this talk we consider a general class of isotropic functionals in dimension \(d\geq 2\), typical in physical models, in which a surface term favouring pure phases competes with a nonlocal term with power law kernel favouring alternation between different phases. Close to the critical regime in which the two terms are of the same order, we give a rigorous proof of the conjectured symmetry breaking and pattern formation for global minimizers, in the shape of domains with flat boundary (e.g. stripes or lamellae). This is a recent work obtained in collaboration with E. Runa.
Per informazioni, rivolgersi a: lucia.deluca@cnr.it
Venerdì 17 gennaio 2025
Ore 14:30, Aula Dal Passo, Dipartimento di Matematica, U Roma Tor Vergata
Joint Topology & Algebra and Representation Theory Seminar (T-ARTS)
Andrea Pizzi (U Roma Tor Vergata)
(Multi-)Simplicial methods for configuration space recognition
The goal of this talk is to algebraically model the S_r-equivariant homotopy type of the configuration space of r labeled and distinct points in d-dimensional Euclidean space. We will present and compare two models: the Barratt-Eccles simplicial set and the multisimplicial set of 'surjections'. Moreover, we will introduce multisimplicial sets and discuss their connection to more well-known simplicial sets. Multisimplicial sets can model homotopy types using fewer cells, making them a highly useful tool. Following this, we will explore in detail how to recognize configuration spaces in the aforementioned models by playing with a graph poset. An explicit relationship between the models will also be presented. Joint work with Anibal M. Medina-Mardones and Paolo Salvatore.
Venerdì 17 gennaio 2025
Ore 16:00, Aula Dal Passo, Dipartimento di Matematica, U Roma Tor Vergata
Algebra and Representation Theory Seminar (ARTS)
Frédéric Patras (U Côte d'Azur)
How to recognize free Lie algebras?
Structure properties of free Lie algebras are a fundamental tool in group theory and its many applications. However, it is not always easy in practice to recognize that a Lie algebra is free. The talk will survey various results that allow to conclude to freeness, and various concrete examples. Based on joint work with L. Foissy.
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