| 03/02/26 | Seminario | 14:30 | 16:00 | 1101 D'Antoni | Tim Browning | IST Austria | Geometry Seminar
Pairs of commuting matrices
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 |
| 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)
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)
"TBA"
N.B.: this talk is part of the activity of the MIUR Excellence Department Project Mat-Mod@TOV (CUP E83C23000330006)
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
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
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
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
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
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.
|
| 13/01/26 | Seminario | 14:30 | 16:00 | 1101 D'Antoni | Fabio Bernasconi | La Sapienza Università di Roma | Geometry Seminar
Equisingular lifting of semi-log canonical F-split K-trivial surfaces
The Bogomolov–Tian–Todorov (BTT) theorem states that smooth Calabi–Yau (CY) varieties over the complex numbers have unobstructed deformation spaces. While this fails over fields of positive characteristic, recent results of Brantner–Taelman and Petrov show that the BTT theorem does hold in positive and mixed characteristics for ordinary CY varieties without crystalline torsion, implying that such varieties are liftable.
In this talk, we study the problem of liftability for singular CY surfaces over the ring of Witt vectors W(k). In earlier joint work with Brivio–Kawakami–Witaszek, we proved that normal globally $F$-split CY surfaces admit an equisingular lifting over W(k). Together with Q. Posva, building on the explicit birational geometry and the deformation theory of log CY surfaces, we further generalised this result to the case of globally $F$-split surfaces with semi-log canonical (in particular, not necessarily normal) singularities.
In the first part, I will recall the setup and definitions in positive characteristic algebraic geometry, giving an overview of the proofs of some of the previous results. In the second part, I will focus on joint work with Posva and highlight the difficulties that arise in the non-normal case.
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 |
| 09/01/26 | Seminario | 16:00 | 17:00 | 1201 Dal Passo | Francesco MEAZZINI | "Sapienza" Università di Roma |
Algebra & Representation Theory Seminar (ARTS)
"Deformations of monomial ideals"
N.B.: this talk is part of the activity of the MIUR Excellence Department Project Mat-Mod@TOV (CUP E83C23000330006)
We deal with infinitesimal deformations of affine schemes defined by a monomial ideal in a polynomial ring. We discuss a few applications: the cotangent cohomology for Stanley-Reisner schemes, some conjectures related to fat points, and some geometric properties of certain Hilbert schemes of points.
This is a joint work (partially in progress) with Nathan Ilten and Andrea Petracci.
N.B.: this talk is part of the activity of the MIUR Excellence Department Project MatMod@TOV (CUP E83C23000330006)
|