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.

25/03/19  Seminario  14:00  17:00  1101 D'Antoni  Espen Sande  University of Oslo  Optimal spline spaces for L2 nwidth problems: I
This short course addresses the theory of Kolmogorov nwidths in the setting of Hilbert spaces. Starting from Kolmogorov's original paper we cover the main results up until the present day. The application of this theory to spline approximation and the modern field of Isogeometric Analysis will be explained

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

04/03/19  Seminario  14:30  15:30  1201 Dal Passo  Viola SICONOLFI  Università di Roma  Wonderful models for generalized Dowling lattices
Given a subspace arrangement, De Concini and Procesi in the '90s described the construction of a variety associated to it, namely its wonderful model. An important feature of these model is that some of its geometric aspects are linked to some combinatorical properties of the subspace arrangement, in particular the description of its boundary and its Betti numbers.
During the talk I will consider the subspace arrangement associated to a generalized Dowling lattice, a combinatorial object introduced by Hanlon.
The aim is to study the wonderful model associated to it and to give a description of its boundary. To deal with this I will use a bijection between the set of boundary components of the wonderful model and a family of graphs. This is a joint work with Giovanni Gaiffi.

27/02/19  Colloquium  14:30  15:30  1201 Dal Passo  Alberto ABBONDANDOLO  RuhrUniversität Bochum  Germany  On short closed geodesics, shadows of balls and polar bodies
How long is the shortest closed geodesic on a Riemannian sphere? How large is the shadow of a symplectic ball? How large is the volume of the polar of a centrally symmetric convex body? I will discuss how these seemingly different problems can be addressed within the setting of Reeb dynamics.
N.B.: this talk is part of the activity of the MIUR Excellence Department Project CUP E83C18000100006 
26/02/19  Seminario  16:00  17:00  1101 D'Antoni  Samuele Mongodi  Politecnico di Milano  Holomorphicity of sliceregular functions
Abstract: In 2010, Ghiloni and Perotti showed how a sliceregular function
f from a real alternative algebra A to itself is induced, in a suitable
sense, by a holomorphic function F from the complex numbers to the
complexification of A; however, there is no evident "holomorphic" link
between the values of f and the values of F.
I want to show, in the particular case where A is the algebra of
quaternions H, how the set of values of F which induce a zero of f is
actually a complex subspace of the complexification of H and how a number
of properties of sliceregular functions can be therefore deduced from the
classical properties of holomorphic functions.
Moreover, this approach gives an identification of the set of imaginary
units of H with a complex submanifold of a (complex) grassmannian, or, in
other words, how we obtain a natural complex structure on such set which is
compatible with sliceregularity; this point of view is linked to the work
of Gentili, Salamon, Stoppato on the twistorial lift of a sliceregular
function.
If time permits, I'll hint also to the general approach for the case of an
associative algebra. 