08/11/19  Seminario  14:30  15:30  1101 D'Antoni  Simon RICHE  Université Clermont Auvergne  Central sheaves on affine flag varieties
Gaitsgory's construction of "central sheaves" on the affine
flag variety of a reductive algebraic group is a fundamental tool in the
Geometric Langlands Program, with important applications to the geometry
of Shimura varieties. In this talk I will review this construction, and
explain how it generalizes to arbitrary rings of coefficients. I will
also explain its main application in Geometric Representation Theory,
namely an equivalence of categories due to ArkhipovBezrukavnikov
relating constructible sheaves on the affine flag variety to equivariant
coherent sheaves on the Springer resolution of the Langlands dual group,
together with an extension to modular coefficients. This will be based
on joint works in progress with Achar and with BezrukavnikovRider. 
07/11/19  Seminario  17:00  18:00  1101 D'Antoni  Emilio Porcu  Trinity College, Dublin  Modeling Temporally Evolving and Spatially Globally Dependent
Data
The last decades have seen an unprecedented increase in the
availability of data sets that are inherently global and temporally
evolving, from remotely sensed networks to climate model ensembles. This
paper provides an overview of statistical modeling techniques for
space–time processes, where space is the sphere representing our
planet. In particular, we make a distintion between (a) second
order?based approaches and (b) practical approaches to modeling
temporally evolving global processes. The former approaches are based on
the specification of a class of space–time covariance functions, with
space being the two?dimensional sphere. The latter are based on
explicit description of the dynamics of the space–time process, that
is, by specifying its evolution as a function of its past history with
added spatially dependent noise.
We focus primarily on approach (a), for which the literature has been
sparse. We provide new models of space–time covariance functions for
random fields defined on spheres cross time. Practical approaches (b)
are also discussed, with special emphasis on models built directly on
the sphere, without projecting spherical coordinates onto the plane.
We present a case study focused on the analysis of air pollution from
the 2015 wildfires in Equatorial Asia, an event that was classified as
the year's worst environmental disaster. The paper finishes with a list
of the main theoretical and applied research problems in the area, where
we expect the statistical community to engage over the next decade. 
07/11/19  Seminario  10:00  11:00  1201 Dal Passo  Annika Bach  Technisches Universität, Monaco di Baviera  Discretetocontinuum limits of multibody systems with bulk and surface longrange interactions
In this talk we study the atomistictocontinuum limit of a very general class of energy functionals for crystalline materials, where the energy densities may depend on interactions between all points of the lattice. The atomistictocontinuum limit is otained in terms of Gammaconvergence and in the first part of the talk we establish conditions on the discrete energy densities which ensure that the Gammalimit is a freediscontinuity functional defined on the space of special functions of bounded variation. In the second part we complement this abstract result by a homogenization theorem, where we provide sufficient conditions on the energy densities under which bulk and surface contributions decouple in the Gammalimit. This is joint work with Andrea Braides (Rome Tor Vergata) and Marco Cicalese (TU Munich).
This seminar is part of the MIUR Excellence Department Project awarded to the Department of Mathematics, University of Rome Tor Vergata, CUP E83C18000100006.

05/11/19  Seminario  14:30  15:30  1201 Dal Passo  Catherine Bandle  University of Basel  Large solutions of semilinear elliptic and parabolic equations
Semilinear elliptic equations of the type $Delta u = f(u)$ in a bounded smooth domain $Omega$ give rise to solutions which blow up at the boundary provided the nonlinearity is large at infinity. The existence of such solutions and their asymptotic behavior is well understood. Less is known about such phenomena for parabolic problems.
The goal of this talk is to summarize some old results and to indicate new developments. 
29/10/19  Seminario  14:30  15:30  1201 Dal Passo  Martin Mayer  Universita' di Roma "Tor Vergata"  A variational principle for critical points at infinity
After a brief introduction to the notion of critical points at infinity in comparison and contrast to classical critical points we shall expose a seemingly trivial variational principle and study its impact on critical points at infinity versus critical points. While in the latter case we obtain continuous stability of non degenerate critical points, the unstable nature of non degenerate critical points at infinity under continuous variation gives rise to non trivial existence results in the context of the prescribed scalar curvature problem. 
28/10/19  Seminario  14:00  15:00  1101 D'Antoni  Thomas Dedieu  Univ. P. Sabatier  Institut Math. de Toulouse  Estensioni di curve canoniche e mappe gaussiane
Data una varietà X in uno spazio proiettivo P^n, uno si chiede se esistono estensioni di X, cioè varietà Y in P^{n+k} che non sono coni e hanno X come sezione lineare. Nel caso in cui X è una curva di genere g canonicamente immersa in P^{g1}, le eventuali estensioni lisce di dimensioni 2 e 3 sono rispettivamente le superficie K3 e delle varietà di Fano. Un risultato recente di ArbarelloBrunoSernesi, il quale risolve una congettura di Wahl, afferma in sostanza che C si estende ad una superficie se e solo una certa mappa in coomologia, la cosidetta mappa gaussiana, non è suriettiva. Durante il seminario spiegherò come questo risultato si estende all'estendibilità di C a varietà di dimensioni superiori. Farò vedere alcune applicazioni, in particolare una condizione necessaria e sufficiente per l'estendibilità delle superficie K3. È un lavoro in collaborazione con C. Ciliberto e E. Sernesi. 
18/10/19  Seminario  15:00  16:00  1101 D'Antoni  Mark Andrea de Cataldo  Stony Brook University  La congettura P=W in teoria di Hodge non abeliana.
Discuto, in maniera spero accessibile ai non esperti, la congettura P=W in teoria di Hodge nonabeliana.
[Algebraic Geometry Seminar, in the framework of MIUR Excellence Project 20182022 Mat@Tov, CUPE83C18000100006] 
18/10/19  Seminario  14:00  15:00  1101 D'Antoni  Yusra NAQVI  University of Sydney  A gallery model for affine flag varieties
Positively folded galleries in Coxeter complexes play a role in many areas of maths, such as in the study of affine Hecke algebras, Macdonald polynomials, MVpolytopes, and affine DeligneLusztig varieties. In this talk, we will define positively folded galleries, and then look at a new recursive description of the set of end alcoves of folded galleries which are positive with respect to alcoveinduced orientations. This further allows us to find the images of retractions from points at infinity, giving us a combinatorial description of certain double coset intersections in the affine flag variety.
This talk is based on joint work with Elizabeth Mili?evi?, Petra Schwer and Anne Thomas.
N.B.: this talk is part of the activity of the MIUR Excellence Department Project CUP E83C18000100006 
16/10/19  Seminario  16:00  17:00  1201 Dal Passo  Pinhas Grossman  UNSW Sydney  (Conjectural) infinite families of quadratic categories
A fusion category is called quadratic if the set of simple objects has a unique nontrivial orbit under the tensor product action of the group of invertible objects. Examples of quadratic fusion categories are neargroup categories and HaagerupIzumi categories. In this talk we will discuss several conjectural families of quadratic categories and associated modular data, motivated by examples coming from the classification of smallindex subfactors. The formulas for the modular data generalize conjectures of Evans and Gannon. This is joint work with Masaki Izumi. 
16/10/19  Seminario  14:30  15:30  1201 Dal Passo  Bin Gui  Rutgers University  Categorical extensions of conformal nets
Given a conformal net A, its representation category Rep(A) is a braided tensor category by the DoplicherHaagRobert superselection theory (adapted to the low dimensional cases by FredenhagenRehrenSchroer). In this talk I give an alternative approach to the tensor and braid structure of Rep(A) by constructing a "universal", "free", and anyonic extension of A, called the categorical extension of A. I will explain the main idea of constructing categorical
extensions, and explain how this construction will be useful in solving many equivalence problems in conformal field theory.
