Dipartimento di Matematica -UTV-

Date	Type	Start	End	Room	Speaker	From	Title
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 Mat-Mod@TOV (CUP E83C23000330006) Abstract 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 theta-groups 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 Abstract Since 1976 J.E. Roberts introduced a non-Abelian 1-cohomology of charge-transporters on the Haag-Kaster 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 non-simply 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 Abstract 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 non-Euclidean. In this talk, we will see some recent results regarding the existence and multiplicity of solutions for the nonlinear Schrödinger equation on non-compact 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	Humboldt-Universität (Berlin)	Minimal exponent of a hypersurface Abstract 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 (Arnold-Varchenko), 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 blow-ups).
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" Abstract Scale groups are closed subgroups of the group of isometries of a regular tree that fixes an end of the tree and are vertex-transitive. They play an important role in the study of locally compact totally di-sconnected groups as was recently observed by P-E. Caprace and G. Willis. In the 80’s they were studied by A. Figa-Talamanca 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 self-similar groups. In my talk I will discuss two ways of building scale groups. One is based on the use of scale-invariant 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 p-adics and the group of dilations of the field of p-adics 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 Abstract 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
02/04/24	Seminario	16:00	17:00	1201 Dal Passo	Donato Scarcella	UPC Barcelona	Seminario di Equazioni Differenziali Asymptotically quasiperiodic solutions for time-dependent Hamiltonians with a view to celestial mechanics Abstract Dynamical systems subject to perturbations that decay over time are relevant in the description of many physical models, e.g. when considering the effect of a laser pulse on a molecule, in epidemiological studies, as well as in celestial mechanics. For this reason, in the present talk, we consider a time-dependent perturbation of a Hamiltonian dynamical system having an invariant torus supporting quasiperiodic solutions. Assuming the perturbation decays polynomially fast as time tends to infinity, we prove the existence of orbits converging in time to the quasiperiodic solutions associated with the unperturbed system. This result generalizes the work of Canadell and de la Llave, where exponential decay in time was considered, and the one of Fortunati and Wiggins, where arithmetic, non-degeneracy conditions, and exponential decay in time are assumed. We apply this result to the example of the planar three-body problem perturbed by a given comet coming from and going back to infinity asymptotically along a hyperbolic Keplerian orbit (modeled as a time-dependent perturbation). Note: This talk is part of the activity of the MIUR Department of Excellence Project MatMod@TOV (2023-2027)
27/03/24	Seminario	16:00	17:00	1201 Dal Passo	Yasuyuki Kawahigashi	The University of Tokyo	Operator Algebras Seminar Quantum 6j-symbols and braiding Abstract Alpha-induction is a tensor functor producing a new fusion category from a modular tensor category and a Q-system. This can be formulated in terms of quantum 6j-symbols and braiding and gives alpha-induced bi-unitary connections. Last year, we showed that locality of the Q-system implies flatness of the alpha-induced connections. We now prove that the converse also holds. The Operator Algebra Seminar schedule is here: https://sites.google.com/view/oastorvergata/home-page?authuser=0
26/03/24	Seminario	14:30	16:00	1101 D'Antoni	Luca Schaffler	Roma Tre University	An explicit wall crossing for the moduli space of hyperplane arrangements Abstract Given the moduli space of hyperplanes in projective space, V. Alexeev constructed a family of compactifications parametrizing stable hyperplane arrangements with respect to given weights. In particular, there is a toric compactification that generalizes the Losev–Manin compactification for the moduli of points on the line. We study the first natural wall crossing that modifies this compactification into a non-toric one by varying the weights. In particular, we prove that in dimensions two the wall crossing corresponds to blowing up at the identity of the generalized Losev–Manin space. As an application, we show that any Q-factorialization of this blow-up is not a Mori dream space for a sufficiently high number of lines. This is joint work in progress with Patricio Gallardo.
25/03/24	Seminario	14:30	15:30	1201 Dal Passo	Hartmut Prautzsch	Karlsruhe Institute of Technology	The many aspects of de Casteljau's algorithm - A historical review Abstract Paul de Faget de Casteljau (1930-2022) was a highly gifted mathematician who worked in industry and made fundamental mathematical contributions. In this talk, I will focus on one central contribution that de Casteljau developed soon after he started working for Citroen in 1958. It is the algorithm of de Casteljau, a simple construction of polynomial curves from control points by iterated linear interpolation. This algorithm is not only very simple, very useful, and very well known, but it also has a great number of properties and generalizations that make it a fundamental and unifying theoretical tool for Geometric Design. As a tribute to an outstanding pioneer in CAGD, I will recall widely and little known generalizations and properties of this algorithm to remind us of its beauty, versatility and importance as THE algorithm and backbone of Computer Aided Geometric Design (CAGD).