Notiziario Scientifico
a cura del Dipartimento di Matematica G. Castelnuovo, Sapienza Università di Roma
Settimana dal 20-01-2020 al 26-01-2020
Lunedì 20 gennaio 2020
Ore 14:30, Aula C, Dipartimento di Matematica, Sapienza Università di Roma
Esame finale
Federico Caucci (Sapienza Università di Roma)
The basepoint-freeness threshold, derived invariants of irregular varieties, and stability of syzygy bundles
Lunedì 20 gennaio 2020
Ore 14:30, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
seminario di Analisi Matematica
Maria Esteban (U. Paris Dauphine)
Domains of singular Dirac operators and how to compute their eigenvalues
In this talk I will discuss how to find and compute the eigenvalues of Dirac operators in their spectral gaps. In order to do so in an optimal way, the delicate study of the domains of critical Dirac operators is important and necessary. The results are concerned with variational methods, spectral theory and the development of optimal algorithms to compute the eigenvalues in a robust and efficient manner.
Lunedì 20 gennaio 2020
Ore 14:30, aula 1200, Dipartimento di Matematica, Università di Roma "Tor Vergata"
Seminario di Geometria
Richard Schwartz (Brown University)
Polygonal outer billiards
In this talk I will discuss a dynamical system called outer billiards, which produces beautiful and mysterious tilings of the plane. In particular, I will sketch my solution of the Moser-Neumann Problem, which asks whether one can have an unbounded orbit for an outer billiards system. If time permits, I will explain what I call "the plaid model", which is a combinatorial model for the outer billiards orbits on kites. This talk will have a lot of computer demos.
Martedì 21 gennaio 2020
Ore 14:30, Aula Dal Passo, Dipartimento di Matematica, Universita' di Roma "Tor Vergata"
Colloquium di dipartimento
Maria J. Esteban (Universite' de Paris-Dauphine)
Optimal functional inequalities and improvements via the use of linear and nonlinear flows
In this talk I will present a family of methods that can be used to find optimal constants of functional inequalities, and the corresponding extremal functions. Surprisingly, they can also be used to obtain improvements of these optimal inequalities. They are based on well suited linear and nonlinear flows and related to the "carré du champ method" of Bakry-Emery. Applications of this theory to the case of functional inequalities on manifolds, inequalities with weights and inequalities with magnetic fields will show the strength, and also the limitations, of this approach. The results presented in this talk are concerned with the the field of nonlinear PDEs, but also with questions related to mathematical physics and differential spectral geometry.
This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C18000100006
Mercoledì 22 gennaio 2020
Ore 14:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di Geometria
Jonathan Rosenberg (University of Maryland)
Positive scalar curvature on manifolds with S^1-fibered singularities
This talk will describe recent work about the classification of simply connected manifolds of positive scalar curvature M, with a distinguished codimension 2 submanifold N, such that the metric on a tubular neighborhood of N has a natural specific form, and subject to a spin condition. This involves several interesting questions in algebraic topology and geometry of complex line bundles. This is joint work with Boris Botvinnik of the University of Oregon.
Mercoledì 22 gennaio 2020
Ore 16:30, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
seminario di Fisica Matematica
Jens Marklof (University of Bristol)
Kinetic theory for the low-density Lorentz gas
The Lorentz gas is one of the simplest and most widely-studied models for particle transport in matter. It describes a cloud of non-interacting gas particles in an infinitely extended array of identical spherical scatterers, whose radii are small compared to their mean separation. The model was introduced by Lorentz in 1905 who, following the pioneering ideas of Maxwell and Boltzmann, postulated that its macroscopic transport properties should be governed by a linear Boltzmann equation. A rigorous derivation of the linear Boltzmann equation from the underlying particle dynamics was given, for random scatterer configurations, in three seminal papers by Gallavotti, Spohn and Boldrighini-Bunimovich-Sinai. The objective of this lecture is to develop an approach for a large class of deterministic scatterer configurations, including various types of quasicrystals. We prove the convergence of the particle dynamics to transport processes that are in general (depending on the scatterer configuration) not described by the linear Boltzmann equation. This was previously understood only in the case of the periodic Lorentz gas through work of Caglioti-Golse and Marklof-Strombergsson. Our results extend beyond the classical Lorentz gas with hard sphere scatterers, and in particular hold for general classes of spherically symmetric finite-range potentials. We employ a rescaling technique that randomises the point configuration given by the scatterers' centers. The limiting transport process is then expressed in terms of a point process that arises as the limit of the randomised point configuration under a certain volume-preserving one-parameter linear group action. Based on joint work with Andreas Strombergsson (Uppsala).
Giovedì 23 gennaio 2020
Ore 14:30, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario P(n)/N(P)
Benedetta Pellacci (Università della Campania "Luigi Vanvitelli")
Shape optimization in some spectral optimization problems: Asymptotic spherical shapes
We study the positive principal eigenvalue of a weighted problem associated with the Neumann Laplacian. This analysis is related to the investigation of the survival threshold in population dynamics. When trying to minimize such eigenvalue with respect to the weight, one is lead to con- sider a shape optimization problem, which is known to admit spherical optimal shapes only in very specific cases. We investigate whether spherical shapes can be recovered in general situations, in some singular per- turbation limit. These are joint works with Dario Mazzoleni (Università Cattolica del Sacro Cuore) and Gianmaria Verzini (Politecnico di Milano).
Venerdì 24 gennaio 2020
Ore 14:00, Aula "Claudio D'Antoni", dipartimento di Matematica - Università di Roma "Tor Vergata"
seminario di Algebra e Teoria delle Rappresentazioni
Carlo Scoppola (Università de L'Aquila)
Classifying p-groups?
During the last 100 years several ideas were suggested to address the classification problem of finite p-groups. In this talk I will remind some of them (Hall's isoclinism, the coclass theory) and I will talk about some recent progress. Then I will define the p-groups of Frobenius type, and I will remind some recent results in this setting too.
Venerdì 24 gennaio 2020
Ore 15:15, Aula D'Antoni, Dipartimento di Matematica, Università di Roma Tor Vergata
Seminario di Geometria Algebrica
Fabrizio Barroero (Roma Tre)
On the Zilber-Pink conjecture for complex abelian varieties
La congettura di Zilber-Pink caratterizza le intersezioni di una sottovarietà di una varietà abeliana con i suoi sottogruppi algebrici di codimensione abbastanza grande. Nel caso unidimensionale, se tutto è definito sul campo dei numeri algebrici, Habegger e Pila hanno dimostrato la congettura nel 2016, mostrando dunque che l’intersezione di una curva con sottogruppi algebrici di codimensione almeno 2 è finita, a meno che la curva non sia contenuta in un sottogruppo algebrico proprio. In un lavoro in collaborazione con Gabriel Dill, grazie a un recente lavoro di Ziyang Gao, abbiamo esteso il risultato a varietà abeliane complesse. Più in generale, abbiamo dimostrato che la congettura generale può essere dedotta dal caso in cui la varietà ambiente è definita sul campo dei numeri algebrici.
Venerdì 24 gennaio 2020
Ore 16:00, Aula Picone, Dipartimento di Matematica, Sapienza Università di Roma
Seminari per docenti (PLS)
Ciro Ciliberto (Università di Tor Vergata)
Pensare proiettivo
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