Seminars, for informal dissemination of research results, exploratory work by research teams, outreach activities, etc., constitute the simplest form of meetings at a Mathematics research centre.
CAMGSD has recorded the calendar of its seminars for a long time, this page serving both as a means of public announcement of forthcoming activities but also as a historic record.
The phenomenon of dispersion in a physical system occurs whenever the elementary building blocks of the system, whether they are particles or waves, overall move away from each other, because each evolves according to a distinct momentum. This physical process limits the superposition of particles or waves, and leads to remarkable mathematical properties of the densities or amplitudes, including local and global decay, Strichartz estimates, and smoothing.
In kinetic theory, the effects of dispersion in the whole space were notably well captured by the estimates developed by Castella and Perthame in 1996, which, for instance, are particularly useful in the analysis of the Boltzmann equation to construct global solutions. However, these estimates are based on the transfer of integrability of particle densities in mixed Lebesgue spaces, which fails to apply to general settings of kinetic dynamics.
Therefore, we are now interested in characterizing the kinetic dispersive effects in the whole space in cases where only natural principles of conservation of mass, momentum and energy, and decay of entropy seem to hold. Such general settings correspond to degenerate endpoint cases of the Castella–Perthame estimates where no dispersion is effectively measured. However, by introducing a suitable kinetic uncertainty principle, we will see how it is possible to extract some amount of entropic dispersion and, in essence, measure how particles tend to move away from each other, at least when they are not restricted by a spatial boundary.
A simple application of entropic dispersion will then show us how kinetic dynamics in the whole space inevitably leads, in infinite time, to an asymptotic thermodynamic equilibrium state with no particle interaction and no available heat to sustain thermodynamic processes, thereby providing a provocative interpretation of the heat death of the universe.
We present the theory of local and nonlocal minimal surfaces in relation to models of phase coexistence, with special attention to regularity and geometric properties.
The idea is to construct numerical integrator methods for Hamiltonian type of ODE’s which are defined in an ambient Poisson geometry. The goal is to approximate the exact dynamical solutions of this ODE while, at the same time, preserve the Poisson structure to a certain controlled degree. This is a non-trivial and long-range generalization of the notion of symplectic method in which the Poisson geometry is non-degenerate, thus, symplectic. We first outline a first approach to such methods which uses the geometry of so-called approximate symplectic realizations based on recent joint work with D. Martín de Diego and M. Vaquero. Finally, we describe a second approach based on theoretical results coming from Lie-theoretic aspects and which use an underlying groupoid multiplication, based on work in progress with D. Iglesias and J.C. Marrero.
I will discuss joint work with Agustina Czenky. We introduce a $(3-ε)$-dimensional TQFTs which is generated, in some sense, by the derived category of quantum group representations. This TQFT is valued in the $∞$-category of dg vector spaces, and the value on a genus $g$ surface is a $g$-th iterate of the Hochschild cohomology for the aforementioned category. I will explain how this TQFT arises as a derived variant of the usual Reshetikhin–Turaev theory and, if time allows, I will discuss the possibility of introducing local systems into the theory. Our interest in local systems comes from proposed relationships with 4-dimensional non-topological QFT.
We present the theory of local and nonlocal minimal surfaces in relation to models of phase coexistence, with special attention to regularity and geometric properties.
This lecture first provides an introduction to classical variational inference (VI), a key technique for approximating complex posterior distributions in Bayesian methods, typically by minimizing the Kullback-Leibler (KL) divergence. We'll discuss its principles and common uses.
Building on this, the lecture introduces Fenchel-Young variational inference (FYVI), a novel generalization that enhances flexibility. FYVI replaces the KL divergence with broader Fenchel-Young (FY) regularizers, with a special focus on those derived from Tsallis entropies. This approach enables learning posterior distributions with significantly smaller, or sparser, support than the prior, offering advantages in model interpretability and performance.
This lecture first provides an introduction to classical variational inference (VI), a key technique for approximating complex posterior distributions in Bayesian methods, typically by minimizing the Kullback-Leibler (KL) divergence. We'll discuss its principles and common uses.
Building on this, the lecture introduces Fenchel-Young variational inference (FYVI), a novel generalization that enhances flexibility.FYVI replaces the KL divergence with broader Fenchel-Young (FY) regularizers, with a special focus on those derived from Tsallisentropies. This approach enables learning posterior distributions with significantly smaller, or sparser, support than the prior, offering advantages in model interpretability and performance.
