Seminários e cursos curtos

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.

We construct an action of sl(2) on equivariant Khovanov–Rozansky link homology. We will discuss some topological applications and show how the construction simplifies in characteristic p. This is joint with You Qi, Louis-Hadrien Robert, and Emmanuel Wagner.