Notiziario Scientifico
a cura del Dipartimento di Matematica Guido Castelnuovo, Sapienza Università di Roma
Settimana dal 24-01-2022 al 30-01-2022
Lunedì 24 gennaio 2022
Ore 14:30, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
seminario di Analisi Matematica
Eris Runa (Deutsche Bank)
Symmetry breaking and pattern formation for local/nonlocal interaction functionals
In this talk we will review some recent results we obtained on the one-dimensionality of the minimizers of a family of continuous local/nonlocal interaction functionals in general dimension. Such functionals have a local term, typically the perimeter or its Modica-Mortola approximation, which penalizes interfaces, and a nonlocal term favouring oscillations which are high in frequency and in amplitude. The competition between the two terms is expected by experiments and simulations to give rise to periodic patterns at equilibrium. Functionals of this type are used to model pattern formation, either in material science or in biology. The difficulty in proving the emergence of such structures is due to the fact that the functionals are symmetric with respect to permutation of coordinates, while in more than one space dimensions minimizers are one-dimensional, thus losing the symmetry property of the functionals. We will present new techniques and results showing that for two classes of functionals (used to model generalized anti-ferromagnetic systems, respectively colloidal suspensions), both in sharp interface and in diffuse interface models, minimizers are one-dimensional and periodic, in general dimension and also while imposing a nontrivial volume constraint.
Martedì 25 gennaio 2022
Ore 14:30, Aula Dal Passo, Universita' di Tor Vergata, Dipartimento di Matematica
Seminario di Geometria
Simone Diverio (Sapienza Universita' di Roma)
Formule alla Gysin universali e positività di alcune forme caratteristiche
Negli ultimi anni si è visto un rinnovato interesse intorno a una congettura di Griffiths del 1969 che caratterizza esattamente quali dovrebbero essere le forme caratteristiche positive di un qualunque fibrato vettoriale olomorfo hermitiano positivo nel senso di Griffiths. Esse dovrebbero essere le forme caratteristiche che appartengono al cono positivo generato dalle forme di Schur. Dopo aver richiamato le varie nozioni di positività per i fibrati vettoriali olomorfi hermitiani e per (p,p)-forme, spiegheremo un risultato recente, ottenuto in collaborazione col mio studente di dottorato F. Fagioli, che fornisce una conferma parziale alla congettura di Griffiths. Tale risultato è un'applicazione di una formula alla Gysin di natura però puntuale e geometrico-differenziale per il push-forward della curvatura di fibrati tautologici sul fibrato delle bandiere.
Per informazioni, rivolgersi a: onorati@mat.uniroma2.it
Martedì 25 gennaio 2022
Ore 15:00, Sala di Consiglio e ZOOM, Dipartimento di Matematica
Seminario di Modellistica Differenziale Numerica
Benedetta Morini (Università di Firenze)
Unconstrained optimization methods based on probabilistic models for supervised machine learning
Stochastic optimization algorithms are widely employed for problems arising in machine learning but significant issues in their use are open. In fact, tuning these algorithms for each application may require an extremely high computational cost. Research for Green Artificial Intelligence aims to make efficiency an evaluation criterion along with accuracy. Adaptive optimization algorithms, borrowed from deterministic optimization and based on probabilistic models, are currently investigated as an alternative to avoid expensive tuning. In this talk we discuss these issues and present a first-order trust-region method where the models and the stepsize selection are adjusted dynamically along the iterations via the inexact restoration method and the trust-region machinery.
Per informazioni, rivolgersi a: falcone@mat.uniroma1.it
Martedì 25 gennaio 2022
Ore 16:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di Modellistica Differenziale Numerica
Michele Piana (Università di Genova)
Data-driven multi-scale modeling of cancer
In this talk I will present how proteomic, nuclear medicine and imaging data can be used to model the patho-physiology of cancer at different scales, from single cell, through tissues to organs. The mathematical approaches include chemical reaction network theory, compartmental analysis, and artificial intelligence methods for imaging.
Per informazioni, rivolgersi a: falcone@mat.uniroma1.it
Martedì 25 gennaio 2022
Ore 16:00, Aula Dal Passo + Streaming via MS Teams, Dipartimento di Matematica, Università degli Studi di Roma "Tor Vergata"
Seminario di equazioni differenziali
Rafael Ruggiero (PUC Rio de Janeiro (Brasile))
On the graph property for totally irrational Lagrangian invariant tori
We show that every C2 Lagrangian invariant torus W of a Tonelli Hamiltonian defined in the n-torus containing an orbit with totally irrational homology class is a graph of the canonical projection. This result extends the graph property obtained by Bangert and Bialy-Polterovich for Lagrangian minimizing tori without periodic orbits in the unit tangent bundle of a Riemannian metric in the two torus. Motivated by the famous Hedlund's examples of Riemannian metrics in the n-torus with n closed, homology independent, minimizing geodesics having minimizing tunnels, we also show the C1-generic nonexistence of Lagrangian invariant tori with "large" homology. Note: This talk is part of the activity of the MIUR Department of Excellence Project MATH@TOV CUP E83C18000100006 MS Teams Link for the streaming
Per informazioni, rivolgersi a: sorrentino@mat.uniroma2.it
Mercoledì 26 gennaio 2022
Ore 14:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
seminario di Algebra e Geometria
Paolo Aceto (Université de Lille)
Definite fillings of plumbed 3-manifolds
Motivated by the study of smoothings of rational surface singularities as well as symplectic fillings of plumbed 3-manifolds, we consider an analogue problem in a purely topological setting. The question of when a rational surface singularity admits a unique smoothing is of particular interest and has led to a conjecture of Kollár which has been proved in some cases. We look at smooth, definite fillings of certain plumbed manifolds and consider the question of which intersection forms can be realized by such fillings. We describe various constructions and an obstruction based on Donaldson's diagonalization theorem. Finally, we present a couple of uniqueness results and discuss their relevance for Kollár's conjecture as well as the problem of embedding lens spaces in certain 4-manifolds. While the main motivation lies in problems from singularity theory, our results are purely topological in nature and the main techniques used are algebro-combinatorial. This is joint work with Duncan McCoy and JungHwan Park.
Per informazioni, rivolgersi a: diverio@mat.uniroma1.it
Mercoledì 26 gennaio 2022
Ore 14:30, Canale Youtube dell'IAC https://www.youtube.com/watch?v=1C1TJk1CZ98, 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
Massimo Fornasier (Technical University of Munich)
Consensus-Based Optimization in Machine Learning
Consensus-based optimization (CBO) is a multi-agent metaheuristic derivative-free optimization method that can globally minimize nonconvex nonsmooth functions and is amenable to theoretical analysis. In fact, optimizing agents (particles) move on the optimization domain driven by a drift towards an instantaneous consensus point, which is computed as a convex combination of particle locations, weighted by the cost function according to Laplace’s principle, and it represents an approximation to a global minimizer. The dynamics is further perturbed by a random vector field to favor exploration, whose variance is a function of the distance of the particles to the consensus point. In particular, as soon as the consensus is reached the stochastic component vanishes. Based on an experimentally supported intuition that CBO always performs on average a gradient descent of the squared Euclidean distance to the global minimizer, we show a novel technique for proving the global convergence to the global minimizer in mean-field law for a rich class of objective functions. The result unveils internal mechanisms of CBO that are responsible for the success of the method. In particular, we present the proof that CBO performs a convexification of a very large class of optimization problems as the number of optimizing agents goes to infinity. We further present formulations of CBO over compact hypersurfaces and the proof of convergence to global minimizers for nonconvex nonsmooth optimizations on the hypersphere. We conclude the talk with several numerical experiments, which show that CBO scales well with the dimension and is extremely versatile.
Per informazioni, rivolgersi a: roberto.natalini@cnr.it
Giovedì 27 gennaio 2022
Ore 14:30, Sala di Consiglio - https://meet.google.com/ads-dekx-bgm, Dipartimento di Matematica, Sapienza Università di Roma
Seminario P(n)
Gianmaria Verzini (Politecnico di Milano)
Singular analysis of the optimizers of the principal eigenvalue in indefinite weighted Neumann problems
When analyzing the survival threshold for a species in population dynamics, one is led to consider the principal eigenvalue of some indefinite weighted problems in a bounded domain. We study the minimization of such eigenvalue, associated with Neumann boundary conditions, performing the analysis of the singular limit in case of arbitrarily small favorable region. We show that, in this regime, the favorable region is connected and it concentrates on the boundary of the domain. Though widely expected, these properties are still unknown in the general case. This is a joint work with Dario Mazzoleni and Benedetta Pellacci.
Per informazioni, rivolgersi a: galise@mat.uniroma1.it
Giovedì 27 gennaio 2022
Ore 15:00, Il seminario sarà tenuto in modalità telematica, Il link per partecipare al seminario sarà condiviso con gli interessati
Seminari di Ricerca in Didattica e Storia della Matematica
Marta Menghini e Nicoletta Lanciano (Sapienza Università di Roma)
Costruire conoscenze geometriche in presenza di deficit visivo
Chi è interessato a partecipare può rivolgersi ad Annalisa Cusi (annalisa.cusi@uniroma1.it)
Venerdì 28 gennaio 2022
Ore 14:00, Aula B, Dipartimento di Matematica, Sapienza Università di Roma
Cristoforo Caffi (Sapienza Università di Roma)
Conformal embeddings in basic Lie superalgebras
Venerdì 28 gennaio 2022
Ore 14:30, Aula "Roberta Dal Passo", Dipartimento di Matematica, Università degli Studi di Roma "Tor Vergata"
Algebra and Representation Theory Seminar
Andrea Ferraguti (SNS PIsa)
Abelian dynamical Galois groups
Dynamical Galois groups are invariants associated to dynamical systems generated by the iteration of a self-rational map of P^1. These are still very mysterious objects, and it is conjectured that abelian groups only appear in very special cases. We will show how the problem is deeply related to a dynamical property of these rational maps (namely that of being post-critically finite) and we will explain how to approach and prove certain non-trivial cases of the conjecture. This is based on joint works with A. Ostafe, C. Pagano and U. Zannier.
Link per seguire in streaming
Venerdì 28 gennaio 2022
Ore 16:00, Aula "Roberta Dal Passo", Dipartimento di Matematica, Università degli Studi di Roma "Tor Vergata"
Algebra and Representation Theory Seminar
Rene' Schoof (Università degli Studi di Roma "Tor Vergata")
Class numbers of cyclotomic fields
It is notoriously difficult to compute class numbers of cyclotomic fields. In this expository lecture we describe an experimental approach to this problem.
Link per seguire in streaming
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