## Prossimi notiziari settimanali

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

Settimana dal 18-02-2019 al 24-02-2019

Lunedì 18 febbraio 2019
Ore 11:00, Aula Dal Passo, Dipartimento di Matematica dell’Università di Roma “Tor Vergata”
Vincenzo Basco
Infinite horizon control problems under state constraint and Hamilton-Jacobi-Bellman equations

Lunedì 18 febbraio 2019
Ore 14:15, Aula Consiglio, Dipartimento di Matematica
Seminario di Analisi Matematica
Giovanni Bellettini (DIISM, Universita' di Siena)
Does the N-clock model approximate the XY model?
In this seminar we will investigate the relationship between the N-clock model and the XY model (at zero temperature) through a Gamma-convergence analysis as both the number of particles and N diverge. The N-clock model is a two-dimensional nearest neighbors ferromagnetic spin system, in which the values of the spin field are constrained to lie in a set of N equispaced points of the unit circle. For N large enough, it is usually considered as an approximation of the XY model, for which the spin field is allowed to attain all the values of the unit circle. By suitably renormalizing the energy of the N-clock model, we will illustrate how its thermodynamic limit strongly depends on the rate of divergence of N with respect to the number of particles. We shall see that the N-clock model turns out to be a good approximation of the XY model only for N sufficiently large; in other regimes of N, we will show with the aid of cartesian currents that its asymptotic behavior can be described by an energy which may concentrate on geometric objects of different dimensions. The results presented in the talk are based on a work in collaboration with M. Cicalese and M. Ruf.

Lunedì 18 febbraio 2019
Ore 14:30, Aula 116 (1 piano), IAC-CNR
Seminario di Fisica-Matematica
Prof. Luciano Rezzolla (Institut fur Theoretische Physik, Frankfurt, Germany)
Relativistic hydrodynamics in strong gravitational fields
Relativistic hydrodynamics is an incredibly successful approach to study a large variety of problems that range from relativistic collisions of heavy ions to the inspiral and merger of neutron stars. I will review the basic mathematical and numerical frameworks for the solution of the equations of relativistic hydrodynamics in arbitrary spacetimes and discuss how the corresponding solutions can be used to answer fundamental questions in physics and astrophysics.

Lunedì 18 febbraio 2019
Ore 9:00:, Aula V, Dipartimento di Matematica, Sapienza Università di Roma
Convegno
Due giorni di Algebra Lineare Numerica
LUNEDI 18 FEBBRAIO mattina http://www.mat.uniroma1.it/rm2ggaln

Martedì 19 febbraio 2019
Ore 14:30, Aula D'Antoni, Dipartimento di Matematica, Università degli Studi di Roma "Tor Vergata"
Algebra and Representation Theory Seminar
Benoit Fresse (Università di Lille)
Kontsevich's graph complexes, operadic mapping spaces, and the Grothendieck-Teichmüller group
I will report on a joint work with Victor Turchin and Thomas Willwacher about the applications of graph complexes to the study of mapping spaces associated to $$E_n$$-operads. The class of $$E_n$$-operads consists of objects that are homotopy equivalent to a reference model, the operad of little $$n$$-disks, which was introduced by Boardman-Vogt in topology. I will briefly review the definition of these objects. The main goal of my talk is to explain that the rational homotopy of mapping spaces of $$E_n$$-operads has a combinatorial description in terms of the homology of Kontsevich's graph complexes. This approach can also be used for the study of homotopy automorphism spaces associated to $$E_n$$-operads. In the case $$n=2$$, one can identify the result of this computation with the pro-unipotent Grothedieck-Teichmüller group. The proof of these statements relies on results on the rational homotopy of $$E_n$$-operads which I will also briefly explain in my talk.

Martedì 19 febbraio 2019
Ore 14:30, Aula Dal Passo, Dipartimento di Matematica, Università degli Studi di Roma "Tor Vergata"
Seminario di Equazioni Differenziali
Pietro Baldi (Università di Napoli Federico II)
Control of water waves and quasilinear evolution PDEs
The talk deals with recent results of exact controllability, with internal control, for dispersive quasilinear evolution PDEs in the space-periodic setting: the gravity-capillary water wave equations, and quasilinear perturbations of the Korteweg-de Vries (KdV) and nonlinear Schrodinger (NLS) equations. Two different approaches are considered: the work [1] is based on microlocal analysis with a quasilinear scheme, while [2,3,4] rely on a new Nash-Moser theorem, which is sharp regarding a certain regularity issue. [1] T. Alazard, P. Baldi and D. Han-Kwan, Control of water waves, J. Eur. Math. Soc. (JEMS) 20 (2018), 657-745. [2] P. Baldi, G. Floridia, E. Haus, Exact controllability for quasi-linear perturbations of KdV, Anal. PDE 10 (2017), 281-322. [3] P. Baldi, E. Haus, A Nash-Moser-Hormander implicit function theorem with applications to control and Cauchy problems for PDEs, J. Funct. Anal. 273 (2017), 3875-3900. [4] P. Baldi, E. Haus, R. Montalto, Controllability of quasi-linear Hamiltonian NLS equations, J. Differential Equations 264 (2018), 1786-1840.

Martedì 19 febbraio 2019
Ore 14:30, stanza 311, Dipartimento di Matematica e Fisica, Universita' degli Studi Roma Tre, Largo San Leonardo Murialdo 1
Seminario di Fisica Matematica
Prof. G. Gallavotti (Univ. Roma Sapienza)
Navier-Stokes equation: irreversibility, turbulence and ensembles equivalence
The NS equation is considered (in 2 & 3 dimensions) with a fixed forcing on large scale; the stationary states form a family of probability distributions on the fluid velocity fields depending on a parameter R (Reynolds number). It is proposed that other equations could lead to -exactly- the same distributions and that the mechanism is closelyanalogous to the coincidence of the canonical and microcanonical averages of local observables in statistical mechanics in the thermodynamic limit (which in NS is proposed to correspond to the limit in which the UV cut-off N is removed to infinity).

Martedì 19 febbraio 2019
Ore 15:30, Dal Passo (1201), Dipartimento di Matematica, Università di Roma Tor Vergata
Seminario Dipartimentale
Gilberto Bini (Università di Milano Statale)
Invariants and Classification
Classification is extremely important in various scientific disciplines, such as Chemistry and Biology, as well as Mathematics. In this talk, we will recall some examples and give some more, specially in relation with projective geometry and birational geometry, in order to give a classification of low dimensional complex projective varieties with respect to suitable invariants. [Department Seminar (general audience talk) - in the framework of the Research Project "Families of curves: their moduli and their related varieties" - Mission Sustainability Tor Vergata, CUP: E81|18000100005, Principal Investigator: F. Flamini]

Martedì 19 febbraio 2019
Ore 16:00, Aula di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Esame finale di Dottorato
Federico Luigi Dipasquale (Dipartimento di Matematica, Sapienza Università di Roma)
Variational methods in the Landau-de Gennes theory of nematic liquid crystals
In this talk, I will present the main results of my Ph.D. thesis, focused on biaxial torus solutions in the Landau-de Gennes (LdG) model for nematic liquid crystals. These are smooth minimizers, so far only known through numerical experiments, of a widely-studied LdG energy functional w.r.t. a radial Dirichlet boundary datum, in conditions of "low temperature", with a very rich structure and a peculiar S^1-equivariant profile. We analytically prove that minimizing the energy in the class of S^1-equivariant Q-tensors of constant pointwise norm (which is, surprisingly, physically reasonable) agreeing the assigned boundary condition on the boundary gives back either biaxial torus solutions or the analogue of a special kind of singular solution, also expected from simulations. We then investigate the behavior of minimizers w.r.t. deformations of the boundary datum and, exploiting the very precise classification we got of the possible singularities, we also establish counterparts of some well-known theorems in harmonic maps. Joint work with Vincent Millot (Paris Diderot) and Adriano Pisante (Sapienza).

Mercoledì 20 febbraio 2019
Ore 14:00, Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di algebra e geometria
Tamas Hausel (Vienna)
Intersection of mirror branes on Higgs moduli spaces
I will discuss a computational approach for the semiclassical limit of mirror symmetry for Higgs moduli spaces for Langlands dual groups, by comparing the equivariant indices of intersections of mirror branes.

Giovedì 21 febbraio 2019
Ore 14:30, Aula di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Aula di Consiglio
Eugenio Vecchi (Università degli Studi di Trento)
Symmetry and rigidity for composite membranes and plates
The composite membrane problem is an eigenvalue optimization problem that can be formulated as follows: Build a body of prescribed shape out of given materials (of varying densities) in such a way that the body has a prescribed mass and so that the basic frequency of the resulting membrane (with fixed boundary) is as small as possible. In the first part of the talk we will review the known results and present a Faber-Krahn-type result obtained in collaboration with G. Cupini (Università di Bologna). A natural extension of the above problem to plates is the composite plate problem, which is an eigenvalue optimization problem involving the bilaplacian operator. The Euler-Lagrange equation associated to it is a fourth-order PDE that is coupled with Navier boundary conditions (for the hinged plate), or with Dirichlet boundary conditions (for the clamped plate). In the second part of the talk we will focus on symmetry properties of optimal pairs highlighting the differences between the hinged and the clamped case. These results have been obtained in collaboration with F. Colasuonno (Università di Torino).

Giovedì 21 febbraio 2019
Ore 15:00, Dal Passo (1201), Dipartimento di Matematica, Università di Roma Tor Vergata
Seminario di Geometria Algebrica
Gilberto Bini (Università Milano Statale)
A meaningful invariant in birational geometry
In this talk we will survey on the state of the art of some relevant conjectures for the birational classification of complex projective varieties with respect to an invariant that has not been completely utilised but seems to be potentially meaningful: the pseudo-effective dimension. [Algebraic Geometry Seminar - in the framework of the Research Project "Families of curves: their moduli and their related varieties" - Mission Sustainability Tor Vergata, CUP: E81|18000100005]

Venerdì 22 febbraio 2019
Ore 12:00, Aula di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminari MoMA
Karl Sigmund
Social learning leads to the recurrence of corruption
Cooperation can be sustained by institutions that punish free-riders. Such institutions, however, tend to be subverted by corruption if they are not closely watched. Monitoring can uphold a regime of honesty and cooperation, but usually comes at a price. The temptation to skip monitoring regularly leads to outbreaks of corruption and the breakdown of cooperation. We model the corresponding cycle by means of evolutionary game theory, using analytical methods and numerical simulations. The results confirm the view that transparency is a major factor in fighting corruption.

Venerdì 22 febbraio 2019
Ore 12:00, Aula di Consiglio, Dipartimento di Matematica
seminario MoMA
Karl Sigmund
Social learning leads to the recurrence of corruption
Cooperation can be sustained by institutions that punish free-riders. Such institutions, however, tend to be subverted by corruption if they are not closely watched. Monitoring can uphold a regime of honesty and cooperation, but usually comes at a price. The temptation to skip monitoring regularly leads to outbreaks of corruption and the breakdown of cooperation. We model the corresponding cycle by means of evolutionary game theory, using analytical methods and numerical simulations. The results confirm the view that transparency is a major factor in fighting corruption.

Venerdì 22 febbraio 2019
Ore 16:00, Aula Picone, Dipartimento di Matematica, Sapienza Università di Roma
Seminario per insegnanti (Piano Lauree Scientifiche)
Giuseppe Accascina*, Patrizia Berneschi**, Elena Possamai** (*Sapienza Università di Roma, **Liceo Nomentano)
Dalle immagini ai modelli

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