30/05/19  Seminario  15:30  16:20  1200 Biblioteca Storica  Samuel Boissiere  Univ. Poitiers (France)  Some families of projective varieties uniformized by the 10dimensional complex ball
In a famous paper, Allock, Carlson and Toledo described the moduli space of cubic threefolds as the arithmetic quotient of the complementary of a hyperplane arrangement in the 10dimensional complex ball. I will present an interpretation of this moduli space as the one parametrizing a family of order three nonsymplectic automorphisms on hyperkaehler manifolds deformation equivalent to the Hilbert square of a K3 surface. This is a collaboration with Chiara Camere and Alessandra Sarti.
[Algebraic Geometry Seminar, in the framework of MIUR Excellence Project Math@Tov, CUP E83C18000100006] 
30/05/19  Seminario  14:30  15:20  1200 Biblioteca Storica  Alessandra Sarti  Univ. Poitiers (France)  On nonsymplectic automorphisms of K3 surfaces
Automorphisms of K3 surfaces were very much studied in the last years. Depending on the action on the holomorphic two form which can be trivial or not, they are called symplectic or nonsymplectic. The aim of the talk is to present recent results in the study of nonsymplectic automorphisms of 2power order. In particular in the case of the order 16 I completely describe the families of K3 surfaces carrying such automorphisms.
[Algebraic Geometry Seminar, in the framework of MIUR Excellence Project Math@Tov, CUP E83C18000100006] 
29/05/19  Colloquium  16:00  17:00  1201 Dal Passo  Albert Fathi  Georgia Institute of Technology (USA)  Singularities of solutions of the HamiltonJacobi equation. A toy model: distance to a closed subset
This is a joint work with Piermarco Cannarsa and Wei Cheng.
The distance function $d_F$ to a closed subset $F$ of Euclidean space ${f R}^k$ is given by
$$d_F(x)=inf_{fin F}xf.$$
It is a Lipschitz, hence differentiable almost everywhere. We will discuss some topological properties of the set ${
m Sing}(d_F)$ of points where $d_F$ is not differentiable.
More generally, we will discuss properties of the set of singularities of a viscosity solution of the HamiltonJacobi equation
$$partial_tU+H(x,partial_xU)=0,$$
when $H$ is a Tonelli Hamiltonian.
We will give applications in Riemannian geometry.
We will explain during the lecture all notions (beyond common knowledge) necessary to understand it. 
27/05/19  Seminario  14:00  15:00  1201 Dal Passo  Margherita PAOLINI   The integral form of the universal enveloping algebra of twisted affine sl_{3}
In the representation theory of a semisimple Lie algebra L, the subring of the universal enveloping algebra U(L) generated by suitable divided powers arises naturally, thus leading to construct an integral form of U(L). Kostant and Cartier indipendently defined this form and explicitly constructed integral bases when L is finite. Their construction has later been generalized to the untwisted affine case by Garland.
An analogous work by FisherVasta extends the construction of the integral form of U(L) to the affine twisted KacMoody algebra of rank 1 (type A^{2}_{2}). These works are based on complicated commutation formulas, whose regularity remains hidden; moreover, in the twisted case there are some problems both with the statement and the proof.
The aim of this talk is to give a correct description of the integral form of the enveloping algebra of type A^{2}_{2} , providing explicit and compact commutation relations, so to reach a deeper comprehension and drastic simplification of the problem. This is achieved by means of a careful use of the generating series of families of elements and of the properties of the ring of symmetric functions. 
23/05/19  Seminario  16:00  17:30  1101 D'Antoni  Alessia Caponera  Sapienza Università di Roma  Asymptotics for spherical autoregressions
We present a class of spacetime processes, which can be viewed as functional autoregressions taking values in the space of square integrable functions on the sphere. We exploit some natural isotropy requirements to obtain a neat expression for the autoregressive functionals, which are then estimated by a form of frequencydomain least squares. For our estimators, we are able to show consistency and limiting distributions. We prove indeed a quantitative version of the central limit theorem, thus deriving explicit bounds (in Wasserstein metric) for the rate of convergence to the limiting Gaussian distribution; to this aim we exploit the rich machinery of SteinMalliavin methods. Our results are then illustrated by numerical simulations. 
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
