Notiziario Scientifico
a cura del Dipartimento di Matematica G. Castelnuovo, Sapienza Università di Roma
Settimana dal 10-02-2020 al 16-02-2020
Lunedì 10 febbraio 2020
Ore 14:00, aula Conversi, Dipartimento di Fisica, Università di Roma La Sapienza
seminario delle meccaniche
Emanuele Caglioti (Università di Roma La Sapienza)
Long time behavior of solutions of Vlasov-like equation
Vlasov-like equations, e.g. Vlasov Poisson Equation; 2D Euler; and the Hamiltonian mean field model (HMF) are non-linear Liouville equations with a mean-field Hamiltonian. For first I'll make a short review of known rigorous results about asymptotic behavior of the solutions of these systems: i.e. stationary solutions, BGK waves and Landau Damping. Then I'll present some conjectures on their long time behavior. Finally I'll discuss the possibility of building Eulerian periodic, and Langrangian chaotic, solutions for Vlasov like equations in the spirit of Morita and Kaneco 2006.
Lunedì 10 febbraio 2020
Ore 14:30, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma)
seminario di Analisi Matematica
Paolo Bonicatto (U. Basilea)
Uniqueness and non-uniqueness phenomena for the transport equation in R^d
Given \(d \geq 1\), \(T > 0\) and a vector field \(b\colon [0,T] \times\mathbb R^d \to\mathbb R^d\) , we study the problem of uniqueness of weak solutions to the associated transport equation \(\partial_t u+b\cdot\nabla u = 0\) where \(u\colon [0,T]\times\mathbb R^d \to\mathbb R\) is an unknown scalar function. In the classical setting, the method of characteristics is available and provides an explicit formula for the solution to the PDE, in terms of the flow of the vector field b. However, when we drop regularity assumptions on the velocity field, uniqueness is in general lost. In the talk we will present an approach to the problem of uniqueness based on the concept of Lagrangian representation: we will then give local conditions to ensure that this representation induces a partition of the space-time made up of disjoint trajectories, along which the PDE can be disintegrated into a family of 1-dimensional equations. If b is locally of class BV in the space variable, the decomposition satisfies this local structural assumption: this yields in particular the renormalization propertyfor nearly incompressible BV vector fields and thus gives a positive answer to the (weak) Bressan’s Compactness Conjecture. The talk is based on joint works with S. Bianchini and with N.A. Gusev.
Lunedì 10 febbraio 2020
Ore 15:30, Aula B, Dipartimento di Matematica, Sapienza Università di Roma
Corso di Dottorato
Maxime Hauray (Università d'Aix-Marseille), Mario Pulvirenti (Università di Roma La Sapienza)
Scaling limits and effective equation in kinetic theory
In this course I will discuss the scaling limits necessary to outline the physical regimes one wants to discuss, starting from large (classical) particle systems. The goal is to derive rigorously the effective equations which are largely used in kinetic theory, as the Boltzmann, Vlasov and Landau equations. From a mathematical side we have very few results and many open challenging problems. Per informazioni: https://phd.uniroma1.it/web/OFFERTA-FORMATIVA-EROGATA-MATEMATICA_nG3519_IT.aspx
Martedì 11 febbraio 2020
Ore 10:00, Aula M4, Dipartimento di Matematica e Fisica, Università di Roma Tre
Seminario dei Giovani Ricercatori
Matteo Quattropani (Università di Roma Tre)
How fast does a PageRank surfer mix?
The PageRank surfer is a simple stochastic process introduced by Brin and Page in their seminal paper [1], in which they present Google. Roughly, it is a discrete time irreducible Markov chain on an underlying directed graph, \(G\), where the vertices of \(G\) can be thought of as web pages, while the directed edges are hyperlinks between the pages. The surfer follows one uniformly random link leaving the page she is currently visiting with some probability \(\alpha\), while with complementary probability she will "teleport" to a random page, sampled accordingly to some fully supported measure \(\lambda\). The stationary distribution of such a Markov Chain, the so-called Generalized PageRank, can be thought of as a centrality measure over the vertex set of G. Numerical approximations of the stationary distribution can be obtained by running several independent copies of the PageRank surfer for "sufficiently long time" and collecting statistics about their locations. The goal of this talk is to quantify how long we should wait in order for the surfer to reach the equilibrium. In particular, we focus on two models of sparse random directed graphs in which the degrees are given, which we analyze in the asymptotic regime in which the number of vertices grows to infinity. We show that, regardless of the particular choice of \(\lambda\), the mixing behavior of the surfer depends on the asymptotic behavior of \(\alpha=\alpha(n)\). We exhibit two phase transitions with respect to the value of \(\alpha\). In each regime the convergence to equilibrium occurs in a different fashion. This is a joint work with P. Caputo. References: [1] S. Brin and L. Page, The anatomy of a large-scale hypertextual Web search engine, 1998, https://www.sciencedirect.com/science/article/pii/S016975529800110X [2] P. Caputo and M. Quattropani, Mixing time of PageRank surfers on sparse random digraphs, 2019, https://arxiv.org/abs/1905.04993
Martedì 11 febbraio 2020
Ore 11:25, Aula M4, Dipartimento di Matematica e Fisica, Università di Roma Tre
Seminario dei Giovani Ricercatori
Nico Michele Schiavone (Sapienza Università di Roma)
Heat versus Wave: blow-up of solutions
It is well known that the solutions to the heat and wave equations show completely different properties. We consider the two equations provided of the nonlinearity \(|u|^p\) and of small initial data. For large exponents, the solutions to the heat and wave equations exist globally, whereas they explode in finite time if \(p>1\) is small. The threshold is the so called critical exponent. We analyze the antagonism of the heat and wave equations studying the blow-up of the solutions, exploiting two techniques: the iteration argument and the test function method. Moreover, we will see how this competition continues in the study of scale-invariant wave equations with damping and mass terms.
Martedì 11 febbraio 2020
Ore 14:30, Aula Dal Passo, Dipartimento di Matematica, Università di Roma "Tor Vergata"
Seminario di equazioni differenziali
Beatrice Pelloni (Heriot-Watt University)
The mathematical theory of some geophysical flow models
The mathematical and numerical analysis of models for atmospheric flows is still a formidable mathematical challenge. The semi-geostrophic equations are a particular system of partial differential equations, widely used in the modelling of large-scale atmospheric flows. In this talk I will review the mathematical ideas and results that have enabled spectacular progress in the past 25 years, as well as discuss the many problems that are still open. Note: This talk is part of the activity of the MIUR Department of Excellence Grant 2018-2022, CUP E83C18000100006.
Mercoledì 12 febbraio 2020
Aula Dal Passo, Dipartimento di Matematica, Università di Roma Tor Vergata
Workshop
Regular and stochastic behaviour in dynamical systems
(Kick-off meeting for the PRIN 2017 grant "Regular and stochastic behaviour in dynamical systems")
Program:
- 10:00 - 11:00 Stefano Luzzatto (ICTP): Hyperbolic coordinates
- 11:00 - 11:30 Coffee break
- 11:30 - 12:30 Stefano Marò (Univ. Pisa): Symplectic methods for twist maps
- 12:30 - 14:30 Lunch break
- 14:30 - 15:30 Roberto Castorrini (Univ. Rome Tor Vergata): Statistical properties of partially expanding maps
- 15:30 - 16:30 Coffee break
- 16:00 - 17:00 Paolo Giulietti (SNS): Quantitative Global-Local mixing for accessible skew-products
Mercoledì 12 febbraio 2020
Ore 14:00, Aula B, Dipartimento di Matematica, Sapienza Università di Roma
Corso di Dottorato
Maxime Hauray (Università d'Aix-Marseille), Mario Pulvirenti (Università di Roma La Sapienza)
Scaling limits and effective equation in kinetic theory
In this course I will discuss the scaling limits necessary to outline the physical regimes one wants to discuss, starting from large (classical) particle systems. The goal is to derive rigorously the effective equations which are largely used in kinetic theory, as the Boltzmann, Vlasov and Landau equations. From a mathematical side we have very few results and many open challenging problems. Per informazioni: https://phd.uniroma1.it/web/OFFERTA-FORMATIVA-EROGATA-MATEMATICA_nG3519_IT.aspx
Mercoledì 12 febbraio 2020
Ore 14:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di Algebra e Geometria
Francesco Meazzini (Roma Sapienza)
On the Kaledin-Lehn formality conjecture
Kaledin and Lehn conjectured that (the homotopy class of) the DG-Lie algebra of derived endomorphisms of any polystable sheaf on a K3 surface is formal. The relevance of the formality conjecture relies on its consequences concerning the geometry of the moduli space of semistable sheaves on the K3. The conjecture was recently proven after several contributions mainly due to Kaledin-Lehn themselves, Zhang, Yoshioka, Arbarello-Saccà, Budur-Zhang. In this talk I will present a joint work with R. Bandiera and M. Manetti, where we introduce an alternative and more algebraic approach to the problem, eventually proving that the formality conjecture holds for polystable sheaves on any smooth minimal projective surface of Kodaira dimension 0.
Mercoledì 12 febbraio 2020
Ore 16:00, Aula D'Antoni, Dipartimento di Matematica di Tor Vergata
Minicorso di Dottorato
Yasuyuki Kawahigashi (University of Tokyo)
"Relative boundary-bulk duality and orbifold subfactors" Prima Lezione
Giovedì 13 febbraio 2020
Aula Dal Passo, Dipartimento di Matematica, Università di Roma Tor Vergata
Workshop
Regular and stochastic behaviour in dynamical systems
(Kick-off meeting for the PRIN 2017 grant "Regular and stochastic behaviour in dynamical systems")
Program:
- 10:00 - 11:00 Stefano Galatolo (Univ. Pisa): Linear response in random dynamical systems and control of the statistical properties of dynamics
- 11:00 - 11:30 Coffee break
- 11:30 - 12:30 Mattia Radice (Univ. dell'Insubria): Alcune proprietà statistiche di random walks non omogenei
- 12:30 - 14:30 Lunch break
- 14:30 - 15:30 Alfonso Sorrentino (Univ. Rome Tor Vergata): Inverse problems and rigidity questions in billiard dynamics
- 15:30 - 16:30 Coffee break
- 16:00 - 17:00 Tanja Schindler (SNS): Strong laws under triimming - comparison between iid random variables and dynamical systems
Giovedì 13 febbraio 2020
Ore 14:30, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario P(n)/N(p)
Edgar Pimentel (PUC, Rio de Janeiro)
A glimpse on regularity theory: from PDEs to interfaces
We consider elliptic equations in the double-divergence form and perform a two-fold analysis. First, we present results on the improved regularity of the solutions along zero level-sets. In this context, solutions become asymptotically Lipschitz; under further conditions on the data of the problem, we produce asymptotically-Lipschitz regularity for the gradient of the solutions. A second instance of analysis regards the geometric properties of nodal sets; our findings concern the (local) regularity and the Hausdorff dimension of those sets. We close the talk with a discussion on applications to solid mechanics, as well as with comments on further directions of research.
Giovedì 13 febbraio 2020
Ore 14:30, Aula 211, Dipartimento di Matematica e Fisica Largo S. L. Murialdo, 1
Seminario di Geometria
Barbara Bolognese (Università degli Studi Roma Tre)
A partial compactification of the stability manifold
Bridgeland stability manifolds of Calabi-Yau categories are of noticeable interest both in mathematics and in physics. By looking at some of the known example, a pattern clearly emerges and gives a fairly precise description of how they look like. In particular, they all seem to have missing loci, which tend to correspond to degenerate stability conditions vanishing on spherical objects. Describing such missing strata is also interesting from a mirror-symmetric perspective, as they conjecturally parametrize interesting types of degenerations of complex structures. All the naive attempts at constructing modular partial compactifications show how elusive and subtle the problem in fact is: ideally, the missing strata would correspond to stability manifolds of quotient triangulated categories, but establishing such correspondence on geometric level and viewing stability conditions on quotients of the original triangulated category as suitable degenerations of stability conditions is not straightforward. In this talk, I will present method to construct such partial compactifications if some additional hypoteses are satisfied, by realizing our space of interest as a suitable metric completion of the stability manifold.
Giovedì 13 febbraio 2020
Ore 15:00, Aula B, Dipartimento di Matematica, Sapienza Università di Roma
Seminari di ricerca in Didattica della Matematica
Nicoletta Lanciano (Sapienza Università di Roma)
Sui modi per conoscere le concezioni iniziali degli studenti: quello che pensano, conoscono, sanno, hanno visto o fatto, prima di affrontare a scuola una certa tematica
Venerdì 14 febbraio 2020
Aula Dal Passo, Dipartimento di Matematica, Università di Roma Tor Vergata
Workshop
Regular and stochastic behaviour in dynamical systems
(Kick-off meeting for the PRIN 2017 grant "Regular and stochastic behaviour in dynamical systems")
Program:
- 10:00 - 11:00 Marco Lenci (Univ. Bologna): Statistical properties of global observables in infinite-measure systems
- 11:00 - 11:30 Coffee break
- 11:30 - 12:30 Franco Cardin (Univ. Padova): Riduzione finito-dimensionale della Termodinamica di Giovanni Jona-Lasinio. Aspetti topologici.
- 12:30 - 14:30 Lunch break
Venerdì 14 febbraio 2020
Ore 14:00, Aula 1200, Università di Roma "Tor Vergata" - Dipartimento di Matematica
Algebra and Representation Theory Seminar - ARTS
Paolo PAPI ("Sapienza" Università di Roma)
Yangians vs. minimal W-algebras: a surprising coincidence
I will discuss a proof of the fact that the singularities of the R-matrix R(k) of the minimal quantization of the adjoint representation of the Yangian associated with a Lie algebra g are opposite to the roots of the monic polynomial that expresses the OPE of conformal fields with conformal weight 3/2 in the affine W-algebra of level k associated with g . I will then explain some interesting consequences. This is a joint work with V. G. Kac and P. Moseneder-Frajria.
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