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

07/05/19  Seminario  16:45  17:30  1101 D'Antoni  Haekan Samuelsson  Universita' di Goetemborg  A nonproper intersection product in $mathbb{P}^N$ based on current
calculus
Abstract: Let $Z_1$ and $Z_2$ be cycles in $mathbb{P}^N$ with supports of codimensions $k_1$ and
$k_2$, respectively. If the settheoretical intersection of their supports has codimension $k_1+k_2$,
then the intersection is said to be proper. In this case there is a canonical intersection cycle
$Z_1ullet Z_2$. In the case of nonproper intersection things are more involved. I will describe an
intersection product, based on the St\"uckradVogel procedure and calculus of currents, in the
nonproper case and discuss its relation to other nonproper intersection products. This is joint work
with M. Andersson, D. Eriksson, E. Wulcan, and A. Yger. 
07/05/19  Seminario  16:30  17:30  1201 Dal Passo  Jacques Franchi  I.R.M.A. Strasbourg  Small time equivalents for the density of a planar quadratic Langevin diffusion
Exact small time equivalents for the density of the (heat kernel) semigroup, with a control of the error term, are obtained for a quadratic planar analogue of the Langevin diffusion, which is strictly hypoelliptic and nonGaussian, hence of a different nature from the known Riemannian, subRiemannian and linearGaussian cases. Namely I consider the density p_t of X_t := ( B_t , int_0^t B_s^2 ds ), where B_t is real Brownian, and I obtain the asymptotic
behaviours, as t > 0, of p_t(0,(w,y)) and p_t(0,(w,ty)), which both can be seen as natural extensions beyond the degenerate LangevinGaussian framework. The result for the scaled regime is the first such one in a nonGaussian strictly hypoelliptic framework. The method is halfprobabilistic halfanalytic. 
07/05/19  Seminario  16:00  16:45  1101 D'Antoni  Erlend Wold  Universita' di Oslo  An embedding of the unit ball that does not embed into a Loewner
chain.
We will construct an embedding of the unit ball in C^3 that is not Runge in any strictly larger domain that contains it. This settles a central question in Loewner theory in dimension three. Joint work with J.E.
Fornaess. 
07/05/19  Seminario  15:15  16:15  1201 Dal Passo  Gastón Andrés GARCÍA  Universidad Nacional de La Plata  Pointed Hopf algebras, quantum groups and the lifting method
This talk will focus on the classification of pointed Hopf algebras and the description of a general method (called "lifting method") that was the key stone to solve the problem of classifying finitedimensional pointed Hopf algebras over Abelian groups. It turned out that Hopf algebras of this type are all isomorphic to variations of (Borel parts of) small quantum groups. The implementation of this method is based on the notions of Nichols algebras, braided spaces and PBWdeformations, and led to the development of generalized root systems and Weyl groupoids.
Time permitting, I will present a generalized lifting method that allows to construct new examples of nonpointed Hopf algebras related to quotients of quantized coordinate algebras over simple algebraic groups.
N.B.: this talk is part of the activity of the MIUR Excellence Department Project CUP E83C18000100006

07/05/19  Seminario  14:00  15:00  1201 Dal Passo  Gastón Andrés GARCÍA  Universidad Nacional de La Plata  Classifying finitedimensional Hopf algebras
In this talk I will introduce the problem of classifying (finitedimensional) Hopf algebras over an algebraically closed field of characteristic zero. This is a difficult question, since the theory of Hopf algebras includes as first examples group algebras and universal enveloping algebras of Lie algebras. Up to know, there are very few general results, hence all efforts are focused on solving the classification problem for certain families of Hopf algebras: e.g., the semisimple ones, the pointed ones, or those of small dimension.
The main obstruction lies in the lack of enough examples. Although the appearance of Quantum Groups gave a strong impulse to the theory, drawing the attention of mathematicians from different areas (representation theory, mathematical physics, QCFT, etc.), the problem is far from being solved.
In this talk I will present some structural results, different techniques for classifying particular families of Hopf algebras, and then describe the current situation of the classification problem for small dimension.
N.B.: this talk is part of the activity of the MIUR Excellence Department Project CUP E83C18000100006
