16/04/24  Seminario  16:00  17:00  1201 Dal Passo  Pietro Majer  Università di Pisa  Seminario di Equazioni Differenziali
On the CWstructure induced by a MorseSmale gradient flow
A classic yet delicate fact of Morse theory states that the unstable manifolds of a MorseSmale gradientflow on a closed manifold M are the open cells of a CWdecomposition of M.
I will describe a selfcontained proof by Abbondandolo and myself. The key tool is a "system of invariant stable foliations", which is analogous to the object introduced by Palis and Smale in their proof of structural stability of Morse Smale diffeomorphisms and flows, but with finer regularity and geometric properties.
[Stable foliations and CW structure induced by a MorseSmale gradient flow, A.Abbondandolo,P.Majer]
https://www.worldscientific.com/doi/10.1142/S1793525321500527
NB:This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C23000330006

16/04/24  Seminario  14:30  16:00  1101 D'Antoni  Elisabetta Colombo  Università degli studi di Milano  On the local geometry of the moduli spaces of cubic threefolds in
A_5 and of (2,2) threefolds in A_9
We will report on joint works with Paola Frediani, Juan Carlos Naranjo
and Gian Pietro Pirola. We study the second fundamental form of the
Siegel metric in A_5 restricted to the moduli space of the intermediate
jacobians cubic threefolds and the second fundamental form in A_9
restricted to the moduli of the the intermediate jacobians of (2,2)
threefolds in P^2xP^2 . In both case there is a natural composition with
a multiplication map. For cubic threefold this composition results to be
zero, while for (2,2) threefolds it gives a not zero holomorphic section
of a bundle. 
16/04/24  Seminario  14:30  15:30  1201 Dal Passo  Michael Barton  Basque Center for Applied Mathematics  Gaussian quadrature rules for univariate splines and their applications to tensorproduct isogeometric analysis
Univariate Gaussian quadrature rules for spline spaces that are frequently used in Galerkin discretizations to build mass and stiffness matrices will be discussed. Their computation is based on the homotopy continuation concept that transforms Gaussian quadrature rules from the so called source space to the target space. Starting with the classical Gaussian quadrature for polynomials, which is an optimal rule for a discontinuous odddegree space, and building the source space as a union of such discontinuous elements, we derive rules for target spline spaces with higher continuity across the elements. We demonstrate the concept by computing numerically Gaussian rules for spline spaces of various degrees, particularly those with nonuniform knot vectors and nonuniform knot multiplicities. We also discuss convergence of the spline rules over finite domains to their asymptotic counterparts, that is, the analogues of the halfpoint rule of Hughes et al., that are exact and Gaussian over the infinite domain. Finally, the application of spline Gaussian rules in the context of isogeometric analysis on subdivision surfaces will be discussed, showing the advantages and limitations of the tensor product Gaussian rules.
This talk is part of the activity of the MUR Excellence Department Project MatMod@TOV (CUP E83C23000330006). 
12/04/24  Seminario  16:00  17:00  1201 Dal Passo  Grant BARKLEY  University of Harvard 
Algebra & Representation Theory Seminar (ARTS)
"Hypercube decompositions and combinatorial invariance for elementary intervals"
N.B.: this talk is part of the activity of the MIUR Excellence Department Project MatMod@TOV (CUP E83C23000330006)
The combinatorial invariance conjecture asserts that the KazhdanLusztig (KL) polynomial of an interval [u,v] in Bruhat order can be determined just from the knowledge of the poset isomorphism type of [u,v]. Recent work of Blundell, Buesing, Davies, Velicković, and Williamson posed a conjectural recurrence for KL polynomials depending only on the poset structure of [u,v]. Their formula uses a new combinatorial structure, called a hypercube decomposition, that can be found in any interval of the symmetric group. We give a new, simpler, formula based on hypercube decompositions and prove it holds for "elementary" intervals: an interval [u,v] is elementary if it is isomorphic as a poset to an interval with linearly independent bottom edges. As a result, we prove combinatorial invariance for KazhdanLusztig Rpolynomials of elementary intervals in the symmetric group, generalizing the previously known case of lower intervals.
This is a joint work with Christian Gaetz. 
12/04/24  Seminario  14:30  15:30  1201 Dal Passo  Willem DE GRAAF  Università di Trento 
Algebra & Representation Theory Seminar (ARTS)
"Classifying orbits of complex and real Vinberg representations"
N.B.: this talk is part of the activity of the MIUR Excellence Department Project MatMod@TOV (CUP E83C23000330006)
Vinberg representations are representations of algebraic groups that arise from a cyclic grading of a semisimple Lie algebra. In the literature they are mainly known as thetagroups or Vinberg pairs. A distinguishing feature of these representations is that it is possible to classify the orbits of the algebraic group. We sketch how this can be done when the base field is the complex numbers. This mainly uses results of Vinberg of the 70's. Then we describe techniques for classifying the orbits when the base field is the real numbers. This talk is based on joint work with Mikhail Borovoi, Hong Van Le, Heiko Dietrich, Marcos Origlia, Alessio Marrani. 
10/04/24  Seminario  16:00  17:00  1101 D'Antoni  Fabio Ciolli  Università della Calabria 
Operator Algebras Seminar
Superselection theory as a covariant cohomology
Since 1976 J.E. Roberts introduced a nonAbelian 1cohomology of chargetransporters on the HaagKaster networks, and as early as 1990 he proved that this cohomology gives a category equivalent to the one of the DHR sectors of the (Haag dual) net of the observables on the Minkowski d=1+3.
In the DHR framework, the covariance of the sectors by the geometric symmetry is introduced through the vacuum representation and morphisms.
Quite recently, with G. Ruzzi and E. Vasselli, motivated by theories on a globally hyperbolic spacetime and by sectors with electric charges, as in the analysis by Buchholz and Roberts, we introduced a novel cohomology covariant under the geometric symmetry, for simply connected spacetimes.
I will discuss these recent results and some open problems about nonsimply connected spacetimes. 
09/04/24  Seminario  16:00  17:00  1201 Dal Passo  Luigi Appolloni  University of Leeds  Seminario di Equazioni Differenziali
Some existence results for the nonlinear Schrödinger equation on Riemannian manifolds
Over the last few decades, the study of the nonlinear Schrödinger equation on $mathbb{R}^N$ has been investigated by numerous researchers. However, very few results are known when the domain is nonEuclidean. In this talk, we will see some recent results regarding the existence and multiplicity of solutions for the nonlinear Schrödinger equation on noncompact Riemannian manifolds. In particular, we will focus our attention to the interplay between the necessary assumptions on the potential in the Schrödinger operator and those on the manifold.
NB:This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C23000330006

09/04/24  Seminario  14:30  16:00  1101 D'Antoni  Ruijie Yang  HumboldtUniversität (Berlin)  Minimal exponent of a hypersurface
In this talk, I will go back to the origin of the minimal exponent and give a brief history on how it naturally arises in the context of integration over vanishing cycles (ArnoldVarchenko), counting integer solutions of congruence equations (Igusa) and Archimedean zeta functions (Atiyah, Bernstein, Loeser). Then I will talk about some joint work in progress with Dougal Davis (on birational formula of higher multiplier ideals via Beilinson’s formula from Jansen’s conjecture in geometry representation theory) and Ming Hao Quek (on birational characterization of minimal exponents via toric geometry and multi weighted blowups). 
08/04/24  Colloquium  14:30  15:30  1201 Dal Passo  Rostislav I. GRIGORCHUK  University of Texas A&M 
Colloquium di Dipartimento
"Fractal, liftable and scale groups"
Scale groups are closed subgroups of the group of isometries of a regular tree that fixes an end of the tree and are vertextransitive. They play an important role in the study of locally compact totally disconnected groups as was recently observed by PE. Caprace and G. Willis. In the 80’s they were studied by A. FigaTalamanca and C. Nebbia in the context of abstract harmonic analysis and amenability. It is a miracle that they are closely related to fractal groups, a special subclass of selfsimilar groups.
In my talk I will discuss two ways of building scale groups. One is based on the use of scaleinvariant groups studied by V. Nekrashevych and G. Pete, and a second is based on the use of liftable fractal groups. The examples based on both approaches will be demonstrated using such groups as Basilica, Hanoi Tower Group, and a group of intermediate growth (between polynomial and exponential). Additionally, the group of isometries of the ring of padics and the group of dilations of the field of padics will be mentioned in relation with the discussed topics.

03/04/24  Seminario  16:00  17:00  1201 Dal Passo  Florin Radulescu  Università di Roma Tor Vergata 
Operator Algebras Seminar
Automorphic forms design of free group factors and quantum dynamics
The role of automorphic forms as intertwiners between various representations of free group factors was discovered a long time ago by Vaughan Jones, starting with a remarkable formula relating Peterson scalar product with the intrinsical trace. The intertwiner associated to an automorphic form is an eclectic object, not much can be computed, but the Muray von Neuman dimension can be used to get hints on its image. Vaughan Jones used that to settle the problem of finding analytic functions vanishing on the orbit under the modular group of a point in the upper half plane. In past work of the speaker, it was put in evidence that this is related to equivariant Berezin quantization.
This leads to a different representation of free group factors and to the existence of a quantum dynamics whose associated unbounded Hochschild 2 cocycle is related to the isomorphism problem. I will explain some concrete formulae and some new interpretation of the associated quantum dynamics 