## Notiziario Scientifico

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

Settimana dal 05-12-2022 al 11-12-2022

Lunedì 05 dicembre 2022
Ore 8:30-18:00, Aula Seminari (in RM004, ex palazzina E, via Scarpa), Dipartimento SBAI, Sapienza Università di Roma
Workshop
Recent advances in direct and inverse problems for PDEs and applications
Per maggiori informazioni consultare la web page https://sites.google.com/uniroma1.it/direct-inverse-problems-pdes/home-page
Organizers: Giuseppe Floridia (Sapienza Università di Roma), Paola Loreti (Sapienza Università di Roma), Masahiro Yamamoto (The University of Tokyo). Aims, scope, and information: The workshop will cover several topics of applied mathematics, including Inverse Problems, Control and Stabilization, Optimal Control Theory, and also Fractional PDEs. It is supported by GNAMPA-INdAM, LIA COPDESC, JSPS, and SAPIENZA. You can participate in hybrid way, face-to-face or online. Participation is free but registration is mandatory to receive the Zoom link or to follow in presence. All the interested participants are invited to register at their earliest convenience filling the registration form https://forms.gle/kRtdbBMa9HME8AnM6.

Lunedì 05 dicembre 2022
Ore 11:30, Aula 009, Dipartimento di Matematica e Fisica, Universita' degli Studi Roma Tre, e via Teams al seguente link
Seminario di Fisica Matematica
Sergio Simonella (Sapienza Universita' di Roma)
Global-in-time fluctuations of the empirical measure at low density
We consider dynamical fluctuations of the hard sphere gas at low density (Boltzmann-Grad limit), with random initial data distributed according to the Gibbs equilibrium measure. This is one of the few cases in which the small time restriction intrinsic to the dynamical perturbation theory can be lifted. We shall explain the main features of the proof, which is based on an $$L^2$$ (entropy-type) bound, together with a suitable coupling of deterministic and stochastic dynamics.

Lunedì 05 dicembre 2022
Ore 14:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di Analisi Matematica
Pierpaolo Esposito (Università degli Studi Roma Tre)
Green functions for a quasilinear operator and applications
We discuss existence, uniqueness and "regularity" issues for the Green function of the quasi-linear operator $$u \to -\Delta_p u-\lambda |u|^{p-2}u$$ with $$1 < p \leq N$$ on a bounded N-dimensional domain with Dirichlet boundary condition. Of independent interest, these properties represent a fundamental tool to discuss, as a non-trivial application, existence results for the quasi-linear Brezis-Nirenberg problem in the low-dimensional case, where the problem has a global character which is encoded, as we will see, in the "regular" part of the Green function.
Per informazioni, rivolgersi a: spadaro@mat.uniroma1.it

Martedì 06 dicembre 2022
Ore 8:30-18:10, Aula Seminari (in RM004, ex palazzina E, via Scarpa), Dipartimento SBAI, Sapienza Università di Roma
Workshop
Recent advances in direct and inverse problems for PDEs and applications
Per maggiori informazioni consultare la web page https://sites.google.com/uniroma1.it/direct-inverse-problems-pdes/home-page
Organizers: Giuseppe Floridia (Sapienza Università di Roma), Paola Loreti (Sapienza Università di Roma), Masahiro Yamamoto (The University of Tokyo). Aims, scope, and information: The workshop will cover several topics of applied mathematics, including Inverse Problems, Control and Stabilization, Optimal Control Theory, and also Fractional PDEs. It is supported by GNAMPA-INdAM, LIA COPDESC, JSPS, and SAPIENZA. You can participate in hybrid way, face-to-face or online. Participation is free but registration is mandatory to receive the Zoom link or to follow in presence. All the interested participants are invited to register at their earliest convenience filling the registration form https://forms.gle/kRtdbBMa9HME8AnM6.

Martedì 06 dicembre 2022
Ore 12:00, 1/B1-B2 (palazzina B), Dipartimento SBAI, Sapienza Università di Roma
Seminario di Analisi Matematica
Ying Wang (Beijing Normal University (Cina))
Existence of solutions of Schrodinger-Poisson equations and Kirchhoff equations with critical terms
First, we consider a Schrodinger-Poisson equation with Sobolev critical terms and indefinite potentials in R^3. Applying the constraint minimization argument, we establish the existence of positive ground state solutions and ground state nodal solutions. Secondly, we prove the existence of positive solutions for a class of Kirchhoff equations with critical perturbations in an exterior domain (i.e. an unbounded domain whose complement is non-empty and bounded). Due to the particularity of the exterior domain, the general constraint minimization method is invalid at this time, so after showing the nonexistence of ground state solutions, we prove the existence of one positive solution with higher energy.
Per informazioni, rivolgersi a: isabella.ianni@uniroma1.it

Martedì 06 dicembre 2022
Ore 14:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
seminario di Probabilità
Alberto Chiarini (Università di Padova)
On the cost of covering a fraction of a macroscopic body by a simple random walk.
In this talk we aim at establishing large deviation estimates for the probability that a simple random walk on the Euclidean lattice (d>2) covers a substantial fraction of a macroscopic body. It turns out that, when such rare event happens, the random walk is locally well approximated by random interlacements with a specific intensity, which can be used as a pivotal tool to obtain precise exponential rates. Random interlacements have been introduced by Sznitman in 2007 in order to describe the local picture left by the trace of a random walk on a large discrete torus when it runs up to times proportional to the volume of the torus, and has been since a popular object of study. In the first part of the talk we introduce random interlacements and give a brief account of some results surrounding this object. In the second part of the talk we study the event that random interlacements cover a substantial fraction of a macroscopic body. This allows to obtain an upper bound on the probability of the corresponding event for the random walk. Finally, by constructing a near-optimal strategy for the random walk to cover a macroscopic body, we discuss a matching large deviation lower bound. The talk is based on ongoing work with M. Nitzschner (NYU Courant).
Per informazioni, rivolgersi a: faggiona@mat.uniroma1.it

Martedì 06 dicembre 2022
Ore 15:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di Modellistica Differenziale Numerica
Matteo Piu (Sapienza Università di Roma)
Multi-lane vehicular flow models: the effects of lane changes on the traffic stability
This talk is devoted to the modeling and the stability of multi-lane traffic flow in the microscopic and macroscopic frameworks. First we present the study of a second order microscopic Follow-the-Leader Bando model in which we propose simple lane changing conditions. Afterwards we describe the derivation of a new first order macroscopic model which is obtained without postulating ad hoc micro-to-macro scalings. Further, we compute the equilibria for both models and we establish conditions for their stability. Finally we show some numerical examples that confirm the results of the theoretical analysis.
Per informazioni, rivolgersi a: giuseppe.visconti@uniroma1.it

Martedì 06 dicembre 2022
Ore 16:00, Aula "Dal Passo", Dipartimento di Matematica, Università di Roma "Tor Vergata"
Seminario di Analisi Matematica
Marco Ghimenti (Università di Pisa)
Compactness and blow up for Yamabe boundary problem
In 1992 Escobar extended the well known Yamabe problem to manifolds with boundary. The case of the scalar flat target manifold is particularly interesting since it also represents a generalization to Riemann mapping theorem to higher dimensions. In this talk we discuss when the solutions of the Yamabe boundary problem are a compact set, or when they form a blowing up sequence, underlining the affinities and the differences with the classical Yamabe problem.
NB:This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C18000100006
Per informazioni, rivolgersi a: molle@mat.uniroma2.it

Mercoledì 07 dicembre 2022
Ore 9:00-16:45, Aula Seminari (in RM004, ex palazzina E, via Scarpa), Dipartimento SBAI, Sapienza Università di Roma
Workshop
Recent advances in direct and inverse problems for PDEs and applications
Per maggiori informazioni consultare la web page https://sites.google.com/uniroma1.it/direct-inverse-problems-pdes/home-page
Organizers: Giuseppe Floridia (Sapienza Università di Roma), Paola Loreti (Sapienza Università di Roma), Masahiro Yamamoto (The University of Tokyo). Aims, scope, and information: The workshop will cover several topics of applied mathematics, including Inverse Problems, Control and Stabilization, Optimal Control Theory, and also Fractional PDEs. It is supported by GNAMPA-INdAM, LIA COPDESC, JSPS, and SAPIENZA. You can participate in hybrid way, face-to-face or online. Participation is free but registration is mandatory to receive the Zoom link or to follow in presence. All the interested participants are invited to register at their earliest convenience filling the registration form https://forms.gle/kRtdbBMa9HME8AnM6.

Mercoledì 07 dicembre 2022
Ore 14:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
seminario di Algebra e Geometria
Olivier Biquard (Sorbonne Université / IMJ-PRG)
Degenerations of conical Kähler-Einstein metrics
We study the degenerations of conical Kähler-Einstein metrics when the cone angle becomes small. In particular, in the Fano case, we solve a question of Donaldson (2012). Joint work with Henri Guenancia.
Per informazioni, rivolgersi a: diverio@mat.uniroma1.it

Mercoledì 07 dicembre 2022
Ore 16:15, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di Fisica Matematica
Marco Coco (Università Politecnica delle Marche)
Monte Carlo study of charge transport in graphene: computation and theoretical perspectives
The Ensemble Monte Carlo (EMC) method has become a standard tool for the study of transport problems in electronic devices. When the Pauli principle is no longer negligible, however, the EMC suffers from some drawbacks regarding the correct reconstruction of the carrier distribution. We will show a new Monte Carlo scheme which correctly takes into account the Pauli principle. Almost all of the previous approaches were based on some approximations in the description of the distribution function or of the scattering terms even if earlier a novel procedure was proposed for silicon, by adding the Pauli principle also at the end of the free flight. We address also the question of the correctness of representing the free flight in such a quantum view in place of the semiclassical one with the Liouville operator, in the case of a suspended monolayer graphene. Some theoretical perspectives arising from the presented numerical works will be discussed as well.

Le comunicazioni relative a seminari da includere in questo notiziario devono pervenire esclusivamente mediante apposita form da compilare online, entro le ore 24 del giovedì precedente la settimana interessata. Le comunicazioni pervenute in ritardo saranno ignorate. Per informazioni, rivolgersi all'indirizzo di posta elettronica seminari@mat.uniroma1.it.
Coloro che desiderano ricevere questo notiziario via e-mail sono pregati di comunicare il proprio indirizzo di posta elettronica a seminari@mat.uniroma1.it.

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