Notiziario Scientifico

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

Settimana dal 03-06-2019 al 09-06-2019

Lunedì 03 giugno 2019
Ore 12:00, Aula Dal Passo, Dipartimento di Matematica, Università degli Studi di Roma "Tor Vergata"
Algebra and Representation Theory Seminar
Rita Fioresi (Università di Bologna)
Quantum principal bundles over projective bases
In non commutative geometry, a quantum principal bundle over an affine base is recovered through a deformation of the algebra of its global sections: the property of being a principal bundle is encoded by the notion of Hopf Galois extension, while the local triviality is expressed by the cleft property. The quantum algebra of the base space is realized as suitable coinvariants inside the global sections of the quantum principal bundle. We want to examine the case of a projective base X in the special case X=G/P , where G is a complex semisimple group and P a parabolic subgroup. We will substitute the coordinate ring of X with the homogeneous coordinate ring of X with respect to a projective embedding, corresponding to a line bundle L obtained via a character of P. The quantization of the line bundle will come through the notion of quantum section and the quantizations of the base (a quantum flag) will be obtained as semi-coinvariants. The quantization of G will then be interpreted as the quantum principal bundle on the quantum base space X, obtained via a quantum section. (joint work with P. Aschieri and E. Latini)

Lunedì 03 giugno 2019
Ore 14:15, Aula Consiglio, Dipartimento di Matematica
Seminario di Analisi Matematica
Hitoshi Ishii (Waseda University)
The vanishing discount problem for weakly coupled systems of Hamilton-Jacobi equations
I discuss the recent development concerning the vanishing discount problem for Hamilton-Jacobi equations with an emphasis in the case of systems of Hamilton-Jacobi equations. The crucial tool in the development is the use of Mather measures from Aubry-Mather theory for Hamiltonian dynamics or their generalizations. I describe a way of constructing Mather measures and an approach to the vanishing discount problem.

Lunedì 03 giugno 2019
Ore 16:00, Sala delle Scienze Fisiche, Accademia dei Lincei, Palazzo Corsini
Tribute to Maryam Mirzakhani
Corinna Ulcigrai (University of Bristol & University of Zurich)
Billiards, Flat Surfaces and the Magic Wand Theorem

Martedì 04 giugno 2019
Ore 14:30, Aula 311, Dipartimento di Matematica e Fisica Largo S. L. Murialdo, 1
Seminario
Federico Bonetto ((Georgia Tech))
The Kac Model and (Non-)Equilibrium Statistical Mechanics
In 1959 Mark Kac introduced a simple model for the evolution of a gas of hard spheres undergoing elastic collisions. The main simplification consisted in replacing deterministic collisions with random Poisson distributed collisions. It is possible to obtain many interesting results for this simplified dynamics, like estimates on the rate of convergence to equilibrium and validity of the Boltzmann equation. The price paid is that this system has no space structure. I will review some classical results on the Kac model and report on an attempt to reintroduce some form of space structure and non-equilibrium evolution in a way that preserve the mathematical tractability of the system.

Martedì 04 giugno 2019
Ore 15:00, Aula di Consiglio, Dipartimento di Matematica Guido Castelnuovo, Sapienza Università di Roma
Seminario di Modellistica Differenziale Numerica
Michele Palladino (GSSI L'Aquila)
Alcuni problemi teorici sul Reinforcement Learning
Il Reinforcement Learning ha attirato l’attenzione in numerose discipline per via della sua velocità nel risolvere problemi computazionalmente costosi. Anche nella teoria del controllo, vari esperti hanno cominciato ad utilizzare questo metodo per risolvere problemi di controllo ottimo in cui il modello è fortemente influenzato da incertezze nei parametri. In questa presentazione, faremo una breve panoramica sui metodi di RL applicati al controllo e discuteremo un metodo per modellizzare le incertezze nei problemi di controllo ottimo.

Mercoledì 05 giugno 2019
Ore 14:00, Aula di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di Algebra e Geometria
Boris Botvinnik (University of Oregon, Eugene, USA)
Spaces and moduli spaces of metrics of positive scalar curvature
I will review several basic constructions related to positive scalar curvature metrics: surgery constructions, Dirac operator, index theory and some other relevant topological tools. Then we will discuss some recent results on the spaces and moduli spaces of metrics of positive scalar curvature.

Mercoledì 05 giugno 2019
Ore 16:30, aula di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
seminario di Fisica Matematica
Giovanni Gallavotti (INFN-Roma1 e Università di Roma La Sapienza)
Statistical ensembles in nonequilibrium: on turbulence and Navier-Stokes equation
How to formulate a theory of statistical ensembles analogous to that for equilibrium (\eg canonical or microcanonical ensembles) to describe the stationary states? Analysis of the Navier-Stokes equation provides a suggestion. It will be considered in the simple case of an incompressible fluid in a periodic container and subject to a constant force acting on the scale of the container. At strong turbulence the stationary states depend on a single parameter, R=Reynolds number, inverse of the viscosity and form a collection of probability distributions. The analysis will concern the possibility of existence of other PDEs which generate probability distributions that are -exactly- equivalent to the ones generated by the NS equation (in 2 or 3 dimensions) via a mechanism analogous to the equivalence of the equilibrium statistical ensembles in the thermodynamic limit (which will be proposed to be correspond to the limit in which the small scale regularization N is removed to infinity.

Giovedì 06 giugno 2019
Ore 14:30, Aula di consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario P(n)/N(p)
Rafael L ́opez Soriano (Universidad de Valencia)
Prescribed Gaussian and geodesic curvatures problem
This talk is concerned with a Liouville type problem on compact surfaces with boundary. More precisely, this equation allows us to assign Gauss and geodesic curvatures under a conformal change of the metric. We derive existence using the variational structure of the problem and compactness of solutions analyzing the blow-up phenomenon. Joint work with A. Malchiodi (SNS Pisa), D. Ruiz (Granada).

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