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

02/05/19  Seminario  14:00  15:00  1201 Dal Passo  Michele Benzi  Scuola Normale Superiore Pisa  Solving differential equations on graphs
There is currently considerable interest in a class of models (known as Quantum Graphs) which can be described in terms of PDEs posed on large and possibly complex graphs. Such models have found applications in quantum chemistry, nanotechnology, solid state physics, neuroscience, network flow, and other areas. Both boundary and initial value problems are of interest in applications, as well as eigenvalue problems. In this talk I will present some methods for solving simple model PDEs on graphs. Discretization of PDEs posed on graphs using linear finite elements and implicit time stepping techniques leads to sparse systems of algebraic equations of huge size which, however, possess favorable properties for iterative solution of the reducedorder system obtained by Schur complement reduction.
The use of a preconditioned conjugate gradient method leads to optimal solution complexity in the elliptic case. Some results about diffusion on graphs will also be discussed.
This is joint work with Mario Arioli (LUM "Jean Monnet", Bari) 
30/04/19  Seminario  14:30  15:30  1201 Dal Passo  Nicola Gigli  SISSA  Functional analysis and metric geometry
Aim of the talk is to present some aspects of the important role that functional analysis has in the context of metric geometry. I shall discuss both the case of synthetic description of lower Ricci curvature bounds, where this role is by now well understood, and some potential applications to the world of lower sectional curvature bounds, where it might potentially lead to the solution of longstanding open problems.
(this seminar is part of the activity of the MIUR Excellence Department Project) 
29/04/19  Seminario  14:30  15:30  1201 Dal Passo  Carmelo Antonio FINOCCHIARO  Università di Catania  Spectral spaces of rings and modules and applications
Let K be a field and D be a subring of K. The space Zar(K/D) of all the valuation domains of K containing D as a subring can be endowed with the topology, called the Zariski topology, generated by the sets of the type Zar(K/D[x]) , for every x in K. In [C. A. Finocchiaro, M. Fontana, K. A. Loper, "The constructible topology on spaces of valuation domains", Trans. Amer. Math. Soc. 365, n. 12 (2013), 61996216] it was proved that Zar(K/D) is a spectral space and a ring whose prime spectrum is homeomorphic to Zar(K/D) was explicitly provided. In this talk we will introduce a spectral extension of Zar(K/D) , that is, the space of all Dsubmodules of K. More generally, given any ring A, a Zariskilike spectral topology can be given to the space S_{A}(M) of Asubmodules of an Amodule M. Some application to flat modules (see [C. A. Finocchiaro, D. Spirito, "Topology, intersection of modules and flat modules", Proc. Amer. Math. Soc. 144 (2016), no. 10, 41254133]) will be presented. 
17/04/19  Seminario  16:00  17:00  1201 Dal Passo  Gelu Popescu  University of Texas at San Antonio  Invariant subspaces and operator model theory on noncommutative varieties
We present recent results regarding the characterization of the joint invariant subspaces under the universal model (B_1, . . . , B_n) associated with a noncommutative variety V in a regular domain in B(H)^n. The main result
is a BeurlingLaxHalmos type representation which is used to parameterize the corresponding wandering subspaces of the joint invariant subspaces of (B1otimes I , . . . , Botimes I). We also present a characterization of the elements in the noncommutative variety V which admit characteristic functions. This leads to an operator model theory for completely noncoisometric elements which allows us to show that the characteristic function is a complete unitary invariant for this class of elements. Our results apply, in particular, in the commutative case. 
16/04/19  Seminario  14:30  15:30  1201 Dal Passo  Carlo Mercuri  Swansea University  Groundstate asymptotics for a class of singularly
perturbed pLaplacian problems in R^N
I will discuss the asymptotic behavior of positive groundstate solutions to a class of singularly perturbed problems involving the pLaplace operator and power nonlinearities. This behavior is classified in terms of three "regimes": subcritical, critical, and supercritical with respect to the classical Sobolev exponent. This is a joint work with W. Albalawi and V. Moroz.
