Notiziario Scientifico
a cura del Dipartimento di Matematica Guido Castelnuovo, Sapienza Università di Roma
Settimana dal 30-05-2022 al 05-06-2022
Lunedì 30 maggio 2022
Ore 14:30, Aula II, Dipartimento di Matematica, Sapienza Università di Roma
Baby A&G Seminar
Guido Pezzini (Sapienza Università di Roma)
Solidi platonici, sottogruppi di SO(3) e singolarità
Storicamente la teoria dei gruppi ha avuto origini di natura geometrica, come simmetrie di figure, e algebrica, ad esempio nello studio delle equazioni polinomiali. Nel seminario ripercorreremo questi due aspetti e vedremo esempi della loro interazione. Vedremo come i solidi platonici ci aiutino a studiare i sottogruppi finiti di SO(3), e (passando attraverso la teoria degli invarianti) cosa c'entrino con la teoria delle singolarità.
Martedì 31 maggio 2022
Ore 14:30, Aula Dal Passo, Universita' di Tor Vergata
Seminario di Geometria
Annamaria Iezzi (Universita' di Napoli)
Computing the endomorphism ring of a supersingular elliptic curve
In recent years, isogeny-based cryptosystems have captured the attention of the math/crypto community for their conjectured resistance to quantum attacks. In this context, the most promising protocols have supersingular elliptic curves defined over finite fields as central objects, and their security is based on the mathematical problem of computing an isogeny between two supersingular elliptic curves E and E'. It has been shown that this problem can be reduced to the computation of the endomorphism rings of E and E'. In this talk, after reviewing the mathematical and cryptographic context, we will present an improved algorithm for computing the endomorphism ring of a supersingular elliptic curve over a finite field. This is a joint work with Jenny G. Fuselier, Mark Kozek, Travis Morrison and Changningphaabi Namoijam.
Per informazioni, rivolgersi a: onorati@mat.uniroma2.it
Martedì 31 maggio 2022
Ore 15:00, Aula 311, Dipartimento di Matematica e Fisica, Università degli Studi RomaTre
Seminario di Analisi Matematica
Frédéric Robert (Université de Lorraine)
Impact of localization of the Hardy potential on the stability of Pohozaev obstructions in low dimensions
Regarding the scalar curvature equation or the Brezis-Nirenberg problem, the classical existence results involve either local terms (in large dimension) or global terms (in low-dimension). Conversely, the Pohozaev obstructions yield nonexistence results. Druet-Laurain proved that these obstructions are stable in low-dimension. In this talk, we will discuss the same issue for Hardy-Sobolev equations. It turns out that when the singularity is in the domain, then a similar low-dimensional phenomenon occurs. When the singularity is on the boundary of the domain, we show that there is a universal stability independent of the dimension. Joint work with Nassif Ghoussoub (UBC) and Saikat Mazumdar (Bombay).
Martedì 31 maggio 2022
Ore 15:00, Sala di Consiglio e via zoom via zoom ID riunione: 867 4440 2839 Passcode: MDN, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di Modellistica Differenziale Numerica
Max Jensen (University of Sussex)
Dynamic Programming for Finite Ensembles of Nanomagnetic Particles
The stochastic Landau-Lifshitz-Gilbert equation describes magnetization dynamics in ferromagnetic materials in a thermal bath. In this presentation I discuss the optimal control of a finite spin system governed by the stochastic Landau-Lifshitz-Gilbert equation in order to guide the configuration optimally into a target state. At the heart of our analysis is the problem statement with a Bellman PDE on the state manifold. We show the wellposedness of the Bellman formulation and establish the regularity of the value function and the optimal controls to prove the existence of a strong solution of the optimal control problem. Numerical experiments in a high-dimensional setting are presented. The talk is based on joint work with Ananta Majee (IIT Delhi), Andreas Prohl and Christian Schellnegger (Universitaet Tuebingen)
Per informazioni, rivolgersi a: carlini@mat.uniroma1.it
Martedì 31 maggio 2022
Ore 16:00, Aula Dal Passo (+ Streaming via MS Teams), Dipartimento di Matematica, Università di Roma "Tor Vergata"
Seminario di Equazioni Differenziali
Anna Chiara Lai (Sapienza Università di Roma)
Converse Lyapunov theorems and optimal stabilizability for unbounded control systems
We review some recent results on the stabilizability of a wide class of control systems with unbounded inputs, including those with a polynomial dependence on the controls. We present an extension to these unbounded control systems of the well-known relations between the global asymptotic controllability, the sample stabilizability, and the existence of a control Lyapunov function. The results are based on a reparameterization technique commonly adopted in optimal impulsive control, and in particular, on showing that the unbounded setting can be equivalently recasted in terms of a related, extended control problem with bounded controls. Finally, we briefly discuss an integral cost associated to the control system and we establish sufficient conditions for the sample stabilizability of the system with regulated cost. This talk is based on a joint work with Monica Motta, Università di Padova. 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
Martedì 31 maggio 2022
Ore 16:15, Aula Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
seminario di Probabilità
Nicolas Forien (Sapienza Università di Roma)
On the phase transition of activated random walks
The Activated Random Walk model consists of particles which perform independent random walks on a graph and fall asleep with a certain rate. Sleeping particles stop moving and are awaken when another particle arrives on the same site. The model on Z^d presents a phase transition: depending on the density of particles (initially all active) and on the sleep rate, either almost surely each particle eventually falls asleep forever (fixating phase), or almost surely no particle falls asleep forever (active phase). In this talk, I will present a joint work with Alexandre Gaudillière (arxiv.org/abs/2203.02476) showing the existence of an active phase on Z^2: for every positive initial density of particles, for a sufficiently low sleep rate, almost surely no particle falls asleep forever.
Per informazioni, rivolgersi a: lorenzo.taggi@uniroma1.it
Mercoledì 01 giugno 2022
Ore 12:00, Aula 1B1, edificio RM002 , Dipartimento SBAI, Sapienza Università di Roma
Seminario PDE
Marcos Tadeu de Oliveira Pimenta (epartamento de Matemática e Computação Faculdade de Ciências e Tecnologia - Unesp)
Symmetry and symmetry breaking for Hénon type problems involving the 1-laplacian operator
In this work, we study a class of Hénon-type equations which involve the 1−laplacian operator in the unit ball. Under mild assumptions on the nonlinearity, it is proved the existence of radial solutions and, for a parameter in a certain range, it is proved the existence of symmetry breaking, through the presence of non-radial solutions. The approach is based on an approximation scheme, where a thorough analysis of the solutions of the associated p−laplacian problems is necessary.
Per informazioni, rivolgersi a: francesco.petitta@uniroma1.it
Mercoledì 01 giugno 2022
Ore 14:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
seminario di Algebra e Geometria
Thorsten Beckmann (Universität Bonn)
Atomic sheaves on hyper-Kähler manifolds
Motivated by the study of derived categories of hyper-Kähler manifolds, we introduced last year in an ad hoc way a Mukai vector in the Mukai lattice for certain sheaves. Guided by the curiosity of a more systematic understanding of this phenomenon, we introduced a new class of so called atomic sheaves on hyper-Kähler manifolds. Atomic sheaves behave in many ways like simple sheaves on K3 surfaces and we report on the ongoing journey of thoroughly understanding their properties.
Per informazioni, rivolgersi a: diverio@mat.uniroma1.it
Mercoledì 01 giugno 2022
Ore 15:30, Aula B, Dipartimento di Matematica, Sapienza Università di Roma
Mini-corso di dottorato (prima lezione)
Giacomo Micheli (University of South Florida)
Constructing Locally Recoverable Codes using Galois Theory over global function fields
In this course we will consider the problem of constructing optimal locally recoverable codes using number theoretical techniques. The first part of the course includes an introduction to the theory of locally recoverable codes and to the theory of global function fields (with particular emphasis on Galois extensions of global function fields). The second part of the course includes an effective method to construct new locally recoverable codes using Galois theory.
Per informazioni, rivolgersi a: bravi@mat.uniroma1.it
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