23/05/19  Seminario  14:00  15:00  1201 Dal Passo  Mark Demers  Fairfield University  A measure of maximal entropy for the finite horizon periodic
Lorentz gas
While the existence and properties of the SRB measure for the
billiard map associated with a periodic Lorentz gas are well understood,
there are few results regarding other types of measures for dispersing
billiards. We begin by proposing a naive definition of topological entropy
for the billiard map, and show that it is equivalent to several classical
definitions. We then prove a variational principle for the topological
entropy and proceed to construct a measure which achieves the maximum.
This measure is Bernoulli and positive on open sets. An essential
ingredient is a proof of the absolute continuity of the unstable foliation with respect to the measure of maximal entropy. This is joint work with Viviane Baladi. 
21/05/19  Seminario  14:30  15:30  1201 Dal Passo  Alberto Farina  Université Picardie  Amiens  MONOTONICITY AND SYMMETRY OF SOLUTIONS TO A NONCOOPERATIVE SYSTEM OF GROSSPITAEVSKIITYPE
The talk is devoted to the study of the qualitative properties of solutions to a noncooperative elliptic system arising in BoseEinstein condensation. We show a universal and sharp L^{infty}estimate, as well as the monotonicity and the onedimensional symmetry of any solution satisfying the natural asymptotic conditions at infinity.
http://www.mat.uniroma2.it/~ricerca/analis/seminario_Farina.pdf
(*) this seminar is part of the activity of the MIUR Excellence Department
Project CUP E83C18000100006

20/05/19  Seminario  14:30  15:30  1201 Dal Passo  Gianluca MARZO  Università di Roma  Very easy functorial resolution of singularities of algebraic varieties in characteristic zero
According to J. Kollár (Lectures on Resolution of Singularities, Ex. pag 143144), a fully functorial procedure for the resolution of singularities of algebraic varieties is impossible, i.e. there cannot exist a smooth centre determined by purely local data blowing up in which one must improve some discrete measure of how far the singularity is from being smooth. This does not, however, precludes that there is such a centre in the 2category of algebraic champs (which turns out to be a categorical subterfuge that allows us to work with quotient singularities while doing linear algebra), i.e. a fully functorial resolution by blowing up in smooth centres is impossible, but by weighted centres is not.
The procedure of McQuillan and Panazzolo in [M. McQuillan, D. Panazzolo, "Almost Étale Resolution of Foliations", J. Differential Geom. 95 (2013), no. 2, 279–319] strongly suggested that such a functorial weighted centre should exist; the aim of the talk is to describe it and to show how fully functorial resolution of singularities in characteristic zero can be achieved.
This is a joint work with M. McQuillan. 
15/05/19  Seminario  16:00  17:00  1201 Dal Passo  Christian D. Ja?kel  Universidade de São Paulo  Stability of relativistic quantum electrodynamics in the Coulomb gauge
We show that relativistic quantum electrodynamics in the Coulomb gauge satisfies the following bound, which establishes stability: let H(?, V) denote the Hamiltonian of QED1+3 on the threedimensional torus of volume V and with ultraviolet cutoff ?. Then there exists a constant 0 < ?(?, V) < ? (the vacuum energy renormalization) such that the renormalized Hamiltonian is positive: Hren (?, V ) ? H?,V + ??,V · 1 ? 0.
(joint work with Walter F. Wreszinski) 
14/05/19  Seminario  15:00  16:00  1201 Dal Passo  Yeyao Hu  University of Texas at San Antonio  Uniqueness and symmetry of solutions to a mean
field equation on tori
We prove a sharp uniqueness result of a mean
field equation on arbitrary flat tori. We first establish the evenly
symmetry of the solutions by the newly invented sphere covering
inequality which is of independent interest. Then we employ a careful
nodal line analysis together with a homotopic argument to show the
uniqueness.
(*) This seminar is part of the activity of the MIUR Excellence Department Project CUP E83C18000100006

14/05/19  Seminario  14:00  15:00  1201 Dal Passo  Jingang Xiong  Beijing Normal University  On asymptotic behavior of solutions of conformally invariant equations with isolated singularities
I will review some classical results of conformally invariant equations with isolated singularities.
I will report a recent joint work with Tianling Jin, in which we solved the higher order case. Our approach
uses blow up analysis for local integral equations,
and is unified for all critical elliptic equations of order smaller than the dimension.
(*) This seminar is part of the activity of the MIUR Excellence Department Project CUP E83C18000100006

10/05/19  Seminario  16:30  17:30  1101 D'Antoni  Massimo Franchi  Sapienza Università di Roma  Cointegration in functional autoregressive processes
In this talk we define the class of Hvalued autoregressive (AR) processes with a unit root of finite type, where H is an infinite dimensional separable Hilbert space, and we derive a generalization of the GrangerJohansen Representation Theorem valid for any integration order d = 1, 2, . . . . An existence theorem shows that the solution of an AR with a unit root of finite type is necessarily integrated of some finite integer d and displays a common trends representation with a finite number of common stochastic trends of the type of (cumulated) bilateral random walks and an infinite dimensional cointegrating space. A characterization theorem clarifies the connections between the structure of the AR operators and (i) the order of integration, (ii) the structure of the attractor space and the cointegrating space, (iii) the expression of the cointegrating relations, and (iv) the Triangular representation of the process. 
10/05/19  Seminario  14:30  15:30  1101 D'Antoni  Chiara Camere  Università di Genova  Some isogenies between complex K3 surfaces [Algebraic Geometry Seminar  in the framework of the Research Project "Families of curves: their moduli and their related varieties"  Mission Sustainability Tor Vergata, CUP: E8118000100005, Principal Investigator: F. Flamini]
The aim of this talk is to construct special isogenies between K3 surfaces, obtained by following quotients by symplectic automorphisms, and to determine the families of K3 surfaces for which this construction is possible. To this purpose we will prove that there are families of K3 surfaces of large dimension which both admit a finite symplectic automorphism and are desingularization of quotients of other K3 surfaces by a symplectic automorphism. In the second part of the talk we will consider the special case of involutions, and exhibit infinitely many sets of infinitely many K3 surfaces which are isogenous to each other. This is joint work in progress with A. Garbagnati. Link: http://www.mat.uniroma2.it/~flamini/seminari/annuncio.html [Algebraic Geometry Seminar  in the framework of the Research Project "Families of curves: their moduli and their related varieties"  Mission Sustainability Tor Vergata, CUP: E8118000100005, Principal Investigator: F. Flamini] 
09/05/19  Seminario  16:00  17:00  1201 Dal Passo  Wei Cheng  University of Nanjing (China)  Herglotz variational principle and HamiltonJacobi equation of contact type
In this talk, I will discuss our recent work on the Herglotz' variational principle with the applications to HamiltonJacobi equations in the form D_tu(t,x)+H(t,x,u(t,x),D_xu((t,x))=0. We will mainly focus on the regularity of the minimizers of the variational problem. This is joint work with Piermarco Cannarsa, Liang Jin, Kaizhi Wang and Jun Yan.
(This seminar is part of the activity of the MIUR Excellence Department Project) 
09/05/19  Seminario  11:00  12:00  1201 Dal Passo  Jacques Franchi  I.R.M.A. Strasbourg  From Euclidian to Riemannian and Relativistic Diffusions
