Weekly Bulletin (it)

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

Settimana dal 27-05-2024 al 02-06-2024

Lunedì 27 maggio 2024
Ore 14:30, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
seminario di Analisi Matematica
Vincent Millot (Université Paris-Est Créteil Val de Marne)
Fractional multiphase transitions & nonlocal minimal partitions: closed and open questions
I will first present a convergence result for solutions of Allen-Cahn type systems with a multiple-well potential involving the usual fractional Laplacian in the regime of the so-called nonlocal minimal surfaces. In the singular limit, solutions converge in a certain sense to stationary points of a nonlocal (or fractional) energy for partitions of the domain with (in general) non homogeneous surface tensions. Then I will present partially regularity results and open questions concerning the limiting problem underlying the new features compared to classical minimal partition problems. This talk is based on joint works with Thomas Gabard. This seminar is part of the activities of the Excellence Department Project CUP B83C23001390001 and the PRIN project 2022PJ9EFL, Geometric Measure Theory: Structure of Singular Measures, Regularity Theory and Applications in the Calculus of Variations.
Per informazioni, rivolgersi a: azahara.delatorrepedraza@uniroma1.it


Lunedì 27 maggio 2024
Sala conferenze INdAM, Dipartimento di Matematica, Sapienza Università di Roma
Mathematical Afternoon in Sapienza
Programma:

  • 15:30 Introduzione di Nicoletta Cantarini
  • 15:45 Friedrich Knop Classification of multiplicity free quasi-Hamiltonian manifolds
  • 16:45 Saluti finali
Pagina web: https://www1.mat.uniroma1.it/~desole/2024-volume-cdc/

Martedì 28 maggio 2024
Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Incontro scientifico in occasione dei 60 anni di Luigi Orsina
Programma

  • 10:00 Saluti della Direttrice del Dipartimento di Matematica "G. Castelnuovo"
  • 10:10 David Arcoya (Univ. di Granada) Back to Landesman-lazer conditions and quasilinear elliptic equations

    Abstract. For general (not necessarily smooth) bounded domains \(\Omega\) in \(\mathbb R^N\) and \(1 < p \leq N\) we present the joint work with M. C. M. Rezende and E. A. B. Silva (Universidade de Brasìlia) about the existence of solution for the quasilinear problem \(-\Delta_p u := \text{div}(|\nabla u|^{p-2}\nabla u)= \lambda |u|^{p-2} u+\mu h_\mu(x,u) \) in \(\Omega\), \(u=0\) on \(\partial\Omega\) when the positive parameters \(\mu\) and \(\lambda\) are closed, respectively, to zero and to the first eigenvalue \(\lambda_1\) of the \(p\)-Laplacian \(\Delta_p u \), and the Carathéodory function \(h_\mu:\overline{\Omega}\times\mathbb{R}\rightarrow\mathbb{R}\) is uniformly locally \(L^\sigma(\Omega)\)-bounded with \(\sigma> N/p\) and satisfies a local version of the classical Landesman-Lazer condition previously used in [1] for the p-Laplacian operator.
    [1] Arcoya, D. Orsina, L., Landesman-lazer conditions and quasilinear elliptic equations, Nonlinear Analysis, Theory, Methods and Applications 28 (1997), 1623–1632.
    [2] Stampacchia, G. Le problème de Dirichlet pour les équations elliptiques du second ordre à coefficients discontinus. Ann. Inst. Fourier (Grenoble) 15 (1965), 189–258.

  • 10.45: Marco Picerni (Sapienza) Existence and regularity of solutions of a parabolic-elliptic nonlinear system

    Abstract. We prove the existence of a solution of a parabolic-elliptic nonlinear system related to the Keller-Segel model for chemotaxis, which is the pairing of a Fokker-Planck type equation and a linear elliptic equation. We prove that such a solution obeys an equivalent of Stampacchia's regularity results for linear parabolic equations. This regularizing effect can be entirely attributed to the interplay between the two equations of the system, since it was shown that, without sufficient regularity of the drift term, it is only possible to find highly singular entropy solutions of the Fokker-Planck equation.

  • 11:00 Alessio Porretta (Univ. Tor Vergata) Diffusive effects in optimal transport with congestion

    Abstract. We discuss optimal transport problems with density dependent terms, penalizing congestion effects. Those terms enhance some form of dissipation compared to the classical Monge-Kantorovich transport. In particular we discuss properties like \(L^1-L^\infty\) regularization, displacement convexity, self-similar solutions and free boundary regularity when the support propagates with finite speed.

  • 11:35 Lucio Boccardo Some remarks on a paper by Fortunato-Pisani concerning Born–Infeld-Orsina type equations for electrostatic fields
  • 11:50 Saluti Finali.

Martedì 28 maggio 2024
Ore 14:30, aula d'Antoni, Dipartimento di Matematica, Università di Roma Tor Vergata
seminario di Geometria
Karl Christ (UT Austin)
Irreducibility of Severi varieties on toric surfaces
Severi varieties parametrize integral curves of fixed geometric genus in a given linear system on a surface. In this talk, I will discuss the classical question of whether Severi varieties are irreducible and its relation to the irreducibility of other moduli spaces of curves. I will indicate how tropical methods can be used to answer such irreducibility questions. The new results are from ongoing joint work with Xiang He and Ilya Tyomkin.
Per informazioni, rivolgersi a: guidomaria.lido@gmail.com


Martedì 28 maggio 2024
Ore 15:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di Modellistica Differenziale Numerica
Igor Voulis (Georg-August-Universität Göttingen)
An adaptive stochastic Galerkin method for elliptic PDEs
We model the uncertainties in (random) coefficient functions of an elliptic partial differential equation by expanding these coefficients as function series with scalar random coefficients. This gives us a deterministic formulation of a random PDE. Due to the combination of stochastic and spatial unknowns, this gives us a high-dimensional elliptic PDE. We present an adaptive stochastic Galerkin method for solving this PDE and discuss the optimality of this method. The method combines a multilevel representation of stationary random fields with a residual-based spatial adaptive scheme. An optimal operator compression is used for the stochastic operator. A Bramble-Pasciak-Xu (BPX)-frame is used to obtain a residual estimate and to achieve appropriate error reduction in the iterative linear solver. The numerical results and in the wavelet-case a complete rigorous analysis show that the obtained scheme is optimal. This talk is based on joint work with M. Bachmayr, M. Eigel and H. Eisenmann.


Martedì 28 maggio 2024
Ore 17:30, Aula C, Dipartimento di Matematica, Sapienza Università di Roma
YAMS - Young Algebraist Meetings in Sapienza
Davide Gori (Sapienza - Università di Roma)
Classical and tropical moduli spaces of curves, combinatorial aspects.
The aim of this seminar is to highlight the combinatorial aspects that arise from studying the compactifications of the moduli space of smooth curves. We will provide an overview of the construction of the tropical moduli space of curves, which can be developed in an entirely combinatorial manner. We will then explore how this relates to the classical Deligne-Mumford compactification, passing through Berkovich analytic spaces. If time permits, we will also introduce the notion of cone stacks, which serve as a tropical analogue to the Deligne-Mumford stacks.
Per informazioni, rivolgersi a: sabino.ditrani@uniroma1.it


Mercoledì 29 maggio 2024
Ore 14:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di Algebra e Geometria
Ralf Schiffler (University of Connecticut)
Cluster algebras and knot theory
Cluster algebras are commutative algebras with a special combinatorial structure. A cluster algebra is a subalgebra of a field of rational functions in several variables that is generated by a distinguished set of generators called cluster variables. These cluster variables are constructed recursively from an initial seed by a process called mutation. The algebra depends on the choice of an initial quiver (=oriented graph) which governs the mutation process. Cluster algebras are related to a number of research areas including representation theory of algebras and Lie algebras, combinatorics, algebraic and hyperbolic geometry, dynamical systems, and string theory. In this talk, we will present our recent work with Véronique Bazier-Matte establishing a connection between cluster algebras and knot theory. To every knot (or link) diagram, we associate a cluster algebra in which we identify a cluster whose cluster variables realize the Alexander polynomial of the knot. 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 29 maggio 2024
Ore 16:00, Aula Dal Passo, Dipartimento di Matematica, Università di Roma Tor Vergata
Seminario Algebre di Operatori
Stefaan Vaes (KU Leuven)
Ergodic states on type III_1 factors and ergodic actions
I will report on a joint work with Amine Marrakchi. Since the early days of Tomita-Takesaki theory, it is known that a von Neumann algebra that admits a state with trivial centralizer must be a type III_1 factor, but the converse remained open. I will present a solution of this problem, proving that such ergodic states form a dense G_\delta set among all normal states on any III_1 factor with separable predual. Through Connes' Radon-Nikodym cocycle theorem, this problem is related to the existence of ergodic cocycle perturbations for outer group actions, which I will discuss in the second half of the talk. Note: This talk is part of the activity of the MUR Excellence Department Project MatMod@TOV (CUP E83C23000330006) The Operator Algebra Seminar schedule is here: https://sites.google.com/view/oastorvergata/home-page?authuser=0


Mercoledì 29 maggio 2024
Ore 17:30, Aula Dal Passo, Dipartimento di Matematica, Università di Roma Tor Vergata
Seminario Algebre di Operatori
Claudio Dappiaggi (Università di Pavia)
On the stochastic Sine-Gordon model: an AQFT perspective
We investigate the massive Sine-Gordon model in the finite ultraviolet regime on the two-dimensional Minkowski spacetime with an additive Gaussian white noise. In particular we construct the expectation value and the correlation functions of a solution of the underlying stochastic partial differential equation (SPDE) as a power series in the coupling constant, proving ultimately uniform convergence. This result is obtained combining an approach to study SPDEs at a perturbative level which a recent analysis of the quantum sine-Gordon model using techniques proper of the perturbative, algebraic approach to quantum field theory (pAQFT). This is a joint work with A. Bonicelli and P. Rinaldi, https://arxiv.org/pdf/2311.01558 Note: This talk is part of the activity of the MUR Excellence Department Project MatMod@TOV (CUP E83C23000330006) The Operator Algebra Seminar schedule is here: https://sites.google.com/view/oastorvergata/home-page?authuser=0


Giovedì 30 maggio 2024
Ore 14:30, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
P(n)/N(p): Problemi differenziali nonlineari/Nonlinear differential problems
Francesco Della Pietra (Università di Napoli Federico II)
Problemi di ottimizzazione di forma in modelli per la trasmissione del calore
In questo seminario presenterò alcuni problemi di ottimizzazione di forma per equazioni ellittiche con condizioni al bordo di tipo Robin. Problemi di questo tipo, nel caso di condizioni di tipo Dirichlet, sono stati ampiamente studiati nella letteratura. In questa presentazione, mi concentrerò sul caso di condizioni al bordo di tipo Robin. L'interesse per questo tipo di problemi deriva dalla loro applicazione in modelli di trasmissione del calore in questioni di isolamento termico. Dopo aver illustrato alcuni di questi modelli, presenterò i risultati di recenti ricerche sull'ottimizzazione di forma in questo contesto. I risultati che descriverò sono contenuti in lavori in collaborazione con Carlo Nitsch, Francescantonio Oliva, Riccardo Scala e Cristina Trombetti.
Per informazioni, rivolgersi a: galise@mat.uniroma1.it


Giovedì 30 maggio 2024
Ore 16:00, Sala di Consiglio (e tramite la piattaforma Zoom), Dipartimento di Matematica, Sapienza Università di Roma
Seminari di Ricerca in Didattica della Matematica
Elisabetta Robotti (Università di Genova)
L’inclusione scolastica e la Didattica della Matematica: prospettiva della ricerca

Per informazioni, rivolgersi a: annalisa.cusi@uniroma1.it


Venerdì 31 maggio 2024
Ore 16:00, Aula D'Antoni, Dipartimento di Matematica, Università di Roma Tor Vergata
DocTorV Seminars
Davide Gori (PhD Student, Sapienza Università di Roma)
Moduli spaces in algebraic geometry, with an emphasis on moduli of curves
The idea of moduli space is quite intuitive, you have surely encountered it multiple times. We will present a general overview of moduli spaces in an algebraic context, stressing the categorical point of view. In the second part of the talk, we will focus on the Deligne-Mumford compactification of the moduli space of smooth curves that appeared in '69. Time permitting, we will discuss a generalization of coarse moduli spaces, due to Alper ('13), and present some examples.
Per informazioni, rivolgersi a: vicari@mat.uniroma2.it


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.
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