Noticias en español
Boundary controllability of critically singular parabolic equations on convex domains.
Abstract: In this talk I will discuss the null boundary control of heat-like equations on convex domains, featuring a singular potential that diverges as the inverse square of the distance to the boundary. For this purpose, I will establish global Carleman estimates for the associated operators by combining intermediate inequalities with distinct weights that involve non-smooth powers of the boundary distance. These estimates are sharp in the sense that they capture both the natural boundary conditions and the -energy for the problem. Additionally, I will describe the role of the potential...
Read MoreMatsumoto-Yor and Dufresne type theorems for a random walk on positive definite matrices.
Abstract: We establish analogues of the geometric Pitman 2M−X theorem of Matsumoto and Yor and of the classical Dufresne identity, for a multiplicative random walk on positive definite matrices with Beta type II distributed increments. The Dufresne type identity provides another example of a stochastic matrix recursion that admits an explicit solution.
Read MorePercolation games.
Abstract: Inspired by first-passage percolation models, we consider zero-sum games on Z^d and study their limit behavior when the game duration tends to infinity. After reviewing several fundamental results in this literature, we present a generalization and discuss connections with long-term behavior of Hamilton-Jacobi equations.
Read MoreScaling limits of individual-based models in adaptive dynamics allowing for local extinction or survival of population.
Abstract: Starting from an individual-based birth-death-mutation-selection model of adaptive dynamics with three scaling parameters (population size, mutation rate, mutation steps size), we will describe several scaling limits that can be applied to this model to obtain macroscopic models of different natures (PDE, stochastic adaptive walks), which allow to characterize long-term evolution of the population. Motivated by biological criticisms on the time-scale of evolution and the absence of local extinctions in the obtained macroscopic models, we propose a new parameter scalings under which...
Read MoreBraiding groups of homeomorphisms of the Cantor set.
Abstract: In this talk we will discuss some recent work on groups which connect self-similar and Higman-Thompson groups to big mapping class groups via “braiding”. We will explain some results on the topological finiteness properties of the resulting groups, which are topological generalizations of the algebraic properties of being finitely generated and finitely presented. The talk will involve recent joint works with Xiaolei Wu (Fudan) and Matthew Zaremsky (Albany).
Read MoreDynamics of Concentrated Vorticities In 2d and 3d Euler Flows.
Abstract: A classical problem that traces back to Helmholtz and Kirchhoff is the understanding of the dynamics of solutions to the Euler equations of an inviscid incompressible fluid when the vorticity of the solution is initially concentrated near isolated points in 2d or vortex lines in 3d. We discuss some recent results on these solutions’ existence and asymptotic behavior. We describe, with precise asymptotics, interacting vortices, and traveling helices, and extension of these results for the 2d generalized SQG. In particular we establish Helmholtz’ conjecture on...
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