29/04/19  Seminario  14:30  15:30  1201 Dal Passo  Carmelo Antonio FINOCCHIARO  Università di Catania  T.B.A.
T.B.A. 
15/04/19  Seminario  14:30  15:30  1201 Dal Passo  Andrea MAFFEI  Università di Pisa  T.B.A.
T.B.A. 
01/04/19  Seminario  14:30  15:30  1201 Dal Passo  Dmitriy RUMYNIN  University of Warwick  KacMoody Groups: representations, localisation, duality
We will look at representation theory of a complete KacMoody group G over a finite field. G is a locally compact totally disconnected group, similar, yet slightly different to the group of points of a reductive group scheme over a local field. After defining the group we will prove that the category of smooth representations has finite homological dimension. At the end we discuss localisation and homological duality for this category.
N.B.: this talk is part of the activity of the MIUR Excellence Department Project CUP E83C18000100006

26/03/19  Seminario  14:30  15:30  1201 Dal Passo  Alessandro Fortunati  University of Bristol (UK)  Arnold’s diffusion and variational methods: a constructive proof.
The talk is focused on the well known phenomenon of topological instability that can occour in a class of quasiintegrable systems, as pointed out by V.I. Arnold in 1964.
Right after the publication of the comprehensive work by Chierchia and Gallavotti in 1994 (based on geometric methods), a pioneering paper by U. Bessi proposed a variational formulation for the very same model studied in the original paper by Arnold. However, the constructivity of this approach is not as manifest as in techniques of geometric nature such as the ChierchiaGallavotti or the Windows methods.
The work presented is based on a revisitation of the tools proposed by Bessi then developed by Berti, Biasco and Bolle, in order to obtain a rigorous and constructive proof in the case of the Arnold example. New tools are introduced in order to formulate the quantitative estimates necessary for a machine implementation apt to construct the diffusing trajectories. 
25/03/19  Seminario  14:30  15:30  1201 Dal Passo  Claudio PROCESI  "Sapienza" Università di Roma  Accademia dei Lincei  Perpetuants: a lost treasure
Perpetuant is one of the several concepts invented (in 1882) by J. J. Sylvester in his investigations of covariants for binary forms. It appears in one of the first issues of the American Journal of Mathematics which he had founded a few years before. It is a name which will hardly appear in a mathematical paper of the last 70 years, due to the complex history of invariant theory which was at some time declared dead only to resurrect several decades later. I learned of this word from GianCarlo Rota who pronounced it with an enigmatic smile.
In this talk I want to explain the concept, a Theorem of Stroh, and some new explicit description.

20/03/19  Seminario  16:00  17:00  1201 Dal Passo  Valerio Proietti  East China Normal University  On the Ktheoretic approach to density of states in quasicrystals
One approach to generalizing Bloch theory to nonperiodic materials makes use of the standard tools of noncommutative topology, such as crossed product operator algebras, dual traces, and Ktheory. With this language, I will describe a model based on independent electron approximation, where the main properties of the motion of delocalized electrons are studied through the electronic band structure and the associated values of the integrated density of states (roughly, the number of available energy levels per unit volume). We will discuss the mathematical problems around this framework and some techniques for their solution. 
19/03/19  Seminario  16:00  17:00  1101 D'Antoni  Adriano Tomassini  Universita' di Parma  PROPRIETA' COOMOLOGICHE DI VARIETA' SIMPLETTICHE SPECIALI
Sia (M,?) una varieta' simplettica di dimensione 2n. Una struttura complessa J su M si dice ?simmetrica se, dato comunque x ? M, risulta
?(u, Jv) = ?(v, Ju),
per ogni coppia di vettori tangenti u,v ? TxM.
Si discuteranno alcuni risultati ottenuti recentemente in collaborazione con X. Wang, relativi alla coomologia di varieta' simplettiche compatte dotate di una struttura complessa ?simmetrica.
References
[1] A. Tomassini, X. Wang, Some results on Hard Lefschetz Condition, Internat. J. Math. 29, n. 13, (2018).
[2] A. Tomassini, X. Wang, in preparazione. 
19/03/19  Seminario  14:30  15:30  1201 Dal Passo  Marcello Lucia  The City University of New York  Some results related to Schiffer problem
Motivated by some earlier work by Schiffer, we consider an
overdetermined semilinear problem in a two dimensional bounded domain
where the Dirichlet data and Neumann boundary conditions are prescribed.
In this talk I will provide some conditions that ensure the domain to
be a disc. This is a joint work with B. Kawohl.

12/03/19  Seminario  14:30  15:30  1201 Dal Passo  Alessandra Lunardi  Universita' di Parma  Sobolev and BV functions in infinite dimension.
In Hilbert or Banach spaces $X$ endowed with a good probability measure $mu$ there are a few "natural"
definitions of Sobolev spaces and of spaces of bounded variation functions. The available theory deals
mainly with Gaussian measures and Sobolev and BV functions defined in the
whole $X$, while the study and Sobolev and BV spaces in domains, and/or with respect to non Gaussian
measures, is largely to be developed.
As in finite dimension, Sobolev and BV functions are tools for the study of different problems, in particular
for PDEs with infinitely many variables, arising in mathematical physics in the modeling of systems with an
infinite number of degrees of freedom, and in stochastic PDEs through Kolmogorov equations.
In this talk I will describe some of the main features and open problems concerning such function spaces. 
11/03/19  Colloquium  14:30  15:30  1201 Dal Passo  Wolfgang SOERGEL  Freiburg University  KazhdanLusztig Theory
The study of continous actions of groups like GL(n;R) and GL(n;C) on Banach spaces leads to interesting algebraic questions.
This field has seen great progress recently, and I want to talk on it.
N.B.: this talk is part of the activity of the MIUR Excellence Department Project CUP E83C18000100006
