Dipartimento di Matematica -UTV-

Date	Type	Start	End	Room	Speaker	From	Title
03/02/26	Seminario	14:30	16:00	1101 D'Antoni	Tim Browning	IST Austria	Geometry Seminar Pairs of commuting matrices Abstract I'll discuss commuting varieties and a new upper bound for the density of pairs of commuting n x n matrices with integer entries. Our approach uses Fourier analysis and reduction modulo a suitably chosen prime, together with a result about the flatness of the commutator Lie bracket, which we also solve. This is joint work with Will Sawin and Victor Wang. <em> Note: </em> This talk is part of the activity of the MIUR Department of Excellence Project MatMod@TOV (2023-2027) and the PRIN 2022 Moduli Spaces and Birational Geometry and Prin PNRR 2022 Mathematical Primitives for Post Quantum Digital Signatures
03/02/26	Seminario	14:30	15:30	1201 Dal Passo	Daniel Tsodikovich	ISTA Austria	Seminario di Equazioni Differenziali Local rigidity of the Suris potential as an integrable standard twist map Abstract The Frenkel-Kontorova model is a standard model in condensed matter physics describing particles having nearest-neighbor spring-like interactions. Mathematical analysis of this model leads to studying standard-like twist maps. In the 80s, Suris found a remarkable family of potentials for this model with integrable dynamics. In some sense, this is similar to the role that ellipses play in planar billiards. In the talk, we will highlight this connection via the action-angle coordinates of the two systems. Then we will also show that an integrable perturbation of a Suris potential has to be a Suris potential itself. This is in the spirit of local results proven for the Birkhoff conjecture in billiards. The proof relies heavily on Fourier analysis, as well as the construction of a suitable basis for L2, which captures the dynamics of the system. Joint work with Corentin Fierobe. Note: This talk is part of the activity of the MIUR Department of Excellence Project MatMod@TOV (2023–2027).
27/01/26	Seminario	14:30	16:00	1101 D'Antoni	Andrea Ferraguti	Università di Torino	Geometry Seminar Abelian dynamical Galois groups Abstract Dynamical Galois groups are profinite groups that are constructed via iterations of rational functions. They are intimately connected with, and in a way they are a wild generalization of, Galois representations on Tate modules of elliptic curves. The problem of determining which rational functions yield abelian dynamical Galois groups has attracted quite some attention in recent years; in this talk I will survey on what is known about this problem, and explain how to solve certain instances of it over number fields and over function fields. This is based on joint works with P. Ingram, A. Ostafe, C. Pagano and U. Zannier. <em> Note: </em> This talk is part of the activity of the MIUR Department of Excellence Project MatMod@TOV (2023-2027) and the PRIN 2022 Moduli Spaces and Birational Geometry and Prin PNRR 2022 Mathematical Primitives for Post Quantum Digital Signatures
23/01/26	Seminario	16:00	17:00	1201 Dal Passo	Luca VITAGLIANO	Università di Salerno	Algebra & Representation Theory Seminar (ARTS) "Shifted Contact Structures on Differentiable Stacks" N.B.: this talk is part of the activity of the MIUR Excellence Department Project Mat-Mod@TOV (CUP E83C23000330006) Abstract Differentiable stacks are a class of singular spaces in differential geometry including orbifolds, leaf spaces of foliations and orbit spaces of Lie group actions. One possible definition is: a differentiable stack is a Morita equivalence class of Lie groupoids. It follows from this definition that geometry on differentiable stacks is more or less the same as Morita invariant geometry of Lie groupoids. Following this principle, several different geometries on differentiable stacks have been introduced and studied recently, including vector fields, differential forms, symplectic and Poisson structures, with several applications in Poisson geometry and mathematical physics. In this talk, I will first review Lie groupoids, Morita equivalence and differentiable stacks. In the second part of the talk, based on joint work with A. Maglio and A. Tortorella, I will briefly discuss contact structures on differentiable stacks. N.B.: this talk is part of the activity of the MIUR Excellence Department Project MatMod@TOV (CUP E83C23000330006)
23/01/26	Seminario	14:30	15:30	1201 Dal Passo	Peter Schauenburg	Université de Bourgogne	Algebra & Representation Theory Seminar (ARTS) Reflective centers as categories of modules N.B.: this talk is part of the activity of the MIUR Excellence Department Project Mat-Mod@TOV (CUP E83C23000330006) Abstract Tensor categories (and their module categories) take center stage in many interactions between algebra and low-dimensional topology inspired by physics. If we are lucky enough, a useful tensor category can be described neatly as the representation category of a suitable Hopf algebra, and any further embellishments of the situation can be described in terms of that Hopf algebra; in fact one can argue that this is exactly what Hopf algebras are for. We visit a recent installment of such a connection. Laugwitz-Walton-Yakimov introduce the "reflective center" of a module category over a braided tensor category (setting aside for this abstract any technical requirements of course). The notion of a braided tensor category is closely related to (representations of) the Artin braid group (of type A), and in the same fashion the braided module category constructed by Laugwitz-Walton-Yakimov is related to the Artin braid group of type B which is to a Weyl group of type B what the Artin braid group of type A is to the symmetric group. If the braided tensor category is the module category of a Hopf algebra H, and the module category is described by an algebra with an H-action, Laugwitz-Walton-Yakimov construct a new algebra with H-action describing the "reflective center". This "reflective algebra" is parallel in a sense to the famous Drinfeld double construction producing, from any Hopf algebra, a new Hopf algebra whose module category is braided. After explaining what all this is about, we humbly redo the reflective algebra construction of Laugwitz-Walton-Yakimov in a more conceptual (and slightly selfish) way, making full use of Majid's "transmuted" Hopf algebra and a peculiar and often overlooked structure the latter enjoys. N.B.: this talk is part of the activity of the MIUR Excellence Department Project MatMod@TOV (CUP E83C23000330006)
20/01/26	Seminario	16:00	17:00	1201 Dal Passo	Wei Cheng	Nanjing University	Seminario di Equazioni Differenziali Singularities and generalized Hamiltonian gradient flow: From dynamics to transport Abstract We will begin by reviewing classical results in the dynamics of Lagrangian flows, primarily within the framework of Aubry-Mather theory and weak KAM theory. From the perspective of transport, the regular Lagrangian flow determined by these theories establishes a connection between viscosity solutions of the Hamilton-Jacobi equation and optimal transport. Over the past decade, we and our collaborators have developed an intrinsic approach to study the singularities and their evolution in the Hamilton-Jacobi equation. In particular, the theory of Hamiltonian generalized gradient flows that we have developed in recent years has preliminarily established a transport theory for the corresponding potential functionals in the context of irregular Lagrangian flows. We have reason to believe that we can further explore transport problems related to entropy functionals and free energy functionals, as well as issues ranging from the structure of the cut locus in deterministic systems, the existence of invariant measures beyond Mather, to vanishing viscosity and zero-temperature limits. This is a relatively open field, and we will discuss both existing achievements and future expectations. NB: This talk is part of the activity of the MUR Excellence Department Project MATH@TOV CUP E83C23000330006
20/01/26	Seminario	14:30	16:00	1101 D'Antoni	Madhavan Venkatesh	(MPI Saarbrücken)	Geometry Seminar Counting points on surfaces Abstract I will present a randomised algorithm to compute the local zeta function of a fixed smooth, projective surface over the rationals, at any large prime p of good reduction. The runtime of the algorithm is polynomial in log p, answering a question of Couveignes and Edixhoven. The main ingredient is to explicitly compute cocycles associated to a Lefschetz pencil on the surface. This is based on joint work with Nitin Saxena. Note: This talk is part of the activity of the MIUR Department of Excellence Project MatMod@TOV (2023-2027) and the PRIN 2022 Moduli Spaces and Birational Geometry and Prin PNRR 2022 Mathematical Primitives for Post Quantum Digital Signatures
20/01/26	Seminario	14:30	15:30	1201 Dal Passo	Francesca Prinari	Università di Pisa	Seminario di Equazioni Differenziali Extremals for Poincaré-Sobolev sharp constants in Steiner symmetric sets Abstract We prove existence of minimizers for the sharp Poincaré-Sobolev constant in general Steiner symmetric sets, in the subcritical and superhomogeneous regime. The sets considered are not necessarily bounded, thus the relevant embeddings may suffer from a lack of compactness. We prove existence by means of an elementary compactness method. We also prove an exponential decay at infinity for minimizers, showing that in the case of Steiner symmetric sets the relevant estimates only depend on the underlying geometry. Finally, we illustrate the optimality of the existence result, by means of some examples. Based on a joint work in collaboration with L. Brasco and L. Briani NB: This talk is part of the activity of the MUR Excellence Department Project MATH@TOV CUP E83C23000330006
15/01/26	Seminario	14:30	15:30	1101 D'Antoni	Espen Sande	Simula Research Laboratory, Oslo	On a robust inf-sup condition for the Stokes problem in slender domains – with application to preconditioning Abstract We identify a norm on the pressure variable in the Stokes equation that allows us to prove a continuous inf-sup condition with a constant independent of the domain's aspect ratio. This is in contrast to the standard inf-sup constant, which breaks down as the aspect ratio increases. We further apply our result to construct robust operator preconditioners for the Stokes problem in slender domains. Several numerical examples illustrate the theory. The talk is part of the activity of the MUR Excellence Department Project MatMod@TOV (CUP E83C23000330006).
14/01/26	Seminario	16:15	17:15	1201 Dal Passo	Giulio Tiozzo	Sapienza, Università di Roma	Seminario "Vito Volterra" On the singularity conjecture for random walks on groups Abstract Given a random walk on a group of isometries of hyperbolic (or other symmetric) space, one can consider its hitting measure, i.e. the probability that the walk converges to a given subset of the boundary. It has been discussed for several decades, starting with the work of Furstenberg in the late 60's, whether the hitting measure for a random walk can lie in the same measure class as a "nice" geometric measure, e.g. the Lebesgue measure on the boundary. It is a long-standing conjecture, formalized by Kaimanovich-Le Prince, that, if the group of isometries is discrete and the random walk is finitely supported, the hitting measure is always singular with respect to Lebesgue. We will explore this problem in various contexts, and discuss the state of the art and recent progress, based on joint works with N. Bogachev, P. Kosenko, H. Lee, and W. van Limbeek.