09h00 - 10h00: Piotr Biler - Large self-similar solutions of the parabolic-elliptic Keller-Segel model in higher dimensions;
Abstract: We construct radial self-similar solutions of the, so called, minimal parabolic-elliptic Keller-Segel model in several space dimensions with radial, nonnegative initial conditions which are below the Chandrasekhar solution - the singular stationary solution of this system.
10h00 - 11h00: Laurent Bétermin - Fekete points, vortices and crystallization problems;
Abstract: The main goal of this talk is to explain the connection between the discrete minimizers of the logarithmic energy on the 2-sphere (i.e. Fekete points) with the so-called ‘Vortex Conjecture’ (or Wigner/Abrikosov Conjecture) about the optimality of the triangular lattice at fixed density for a Coulombian two-dimensional renormalized energy. Other strongly related crystallization problems will be discussed in two and higher dimensions: Universal Optimality (Cohn-Kumar), crystallization for one-well potentials (e.g. Lennard-Jones type potentials) and minimization of energies among Bravais lattices.
11h00 - 11h15: pause café;
11h15 - 12h15: Oscar Dominguez Bonilla - Sparse John--Nirenberg spaces;
Abstract: We introduce John--Nirenberg-type spaces where oscillations of functions are controlled via sparse families of cubes. This construction gives new surprising results and clarifies classical inequalities. It is joint work with Mario Milman.
14h00 - 15h00: Gauthier Clerc - Longtime behaviour of entropic interpolations;
Abstract: The Schrödinger problem is an entropy minimisation problem on the space of probability measures. From a physical point of view, it consist to find the most likely evolution of a cloud of Brownian particles, given the two endpoints. Optimal curves of this problem are called entropic interpolations. In this talk I will introduce the Schrödinger problem, then I will present some new results about the longtime behaviour of entropic interpolations.
15h00 - 15h15: pause café;
15h15 - 16h15: Mickael De La Salle - Questions on the harmonic analysis on the sphere;
Abstract: One of my long-term projects is to develop tools to perform analysis with higher rank Lie and arithmetic groups (for example SL(3,R) and SL(3,Z)). Thanks to amazing discoveries by Vincent Lafforgue and other later progresses obtained by various authors, many of the questions can be reduced to simple-looking inequalities concerning vector-valued harmonic analysis on the euclidean spheres. I will try to explain all that and some progresses that I have made so far.