The Seminar of analysis IHP-Fondation Sciences Mathématiques de Paris is organized by Jean-Yves Chemin, director of the Fondation Sciences Mathématiques de Paris, Sergiu Klainerman, laureate in 2010 of the Foundation's Research Chair and Cédric Villani, Fields Medallist and director of the IHP, with the support of the Foundation and the IHP.
As a broad interest analysis seminar, it will bring high level mathematicians together talking about recent problems in fields connected to the subjects covered in the lectures.
The seminar is also open to master degree students.
The lectures format is 2 hours. The first hour is an overview of the subject and the second hour is more specialized.
All lectures are taking place in the IHP (11 rue Pierre et Marie Curie, 75005) or in Jussieu (4 place Jussieu, 75005 Paris).
21th of June 2011 from 4 p.m. to 6 p.m. in IHP room 314: New thoughts on Jacobian determinants, by Haïm Brezis (professor at Rutgers university, distinguished professor at university Pierre et Marie Curie, member of LJLL).
Videos of the lectures
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Lectures26th of april: Global dynamics above the ground state for the energy critical focussing NLW by Joachim Krieger (EPFL)
I'll discuss recent joint work with Kenji Nakanishi and Wilhelm Schlag on the existence of certain open data sets with energy strictly above that of the ground state for which one controls the global in time dynamics, in the context of the energy critical focussing nonlinear wave equation. This work builds in part on recent work by Duyckaerts, Kenig and Merle.
11th of april: On dynamical black holes by Igor Rodnianski (Princeton)
28th of march: Blow up for some energy critical geometrical models by Pierre Raphaël (Institut de Mathématiques de Toulouse (IMT), CNRS - Université Paul Sabatier UMR5219)
7th of march 2011: Optimal transport and rearrangement tools for some hamiltonian PDEs with dissipation by Yann Brenier (CNRS Nice et UPMC)
There are important hamiltonian PDEs that may produce singularities in finite time.
Sometimes, their solutions can be extended beyond singularities to the expense of some dissipation mechanism. A classical example is the so-called inviscid Burgers equation with the concepts of shock waves and entropy solutions.
A very ambitious goal would be to address the 3D Euler equations of incompressible fluid mechanics in a similar way, following Kolmogorov analysis of turbulence.
In this lecture, we present a somewhat simpler example where such a strategy can be followed using tools borrowed from rearrangement and optimal transport theories. This is related to the Vlasov-Poisson system with mono-kinetic distributions, and the related problem of "reconstructing the early universe", in cosmology, following Zeldovich, Peebles, and, more recently, Uriel Frisch.
28th of february 2011: The Dixmier unitarizability problem for group representations by Gilles Pisier (Texas A&M et Paris VI)
Abstract:A uniformly bounded representation of a group on Hilbert space is called unitarizable if it is similar to a unitary one. A group G is called unitarizable if every uniformly bounded representation on it is unitarizable. In 1950, Dixmier (as well as Day independently) proved that amenable implies unitarizable and then asked whether the converse holds. We will review the history of this problem, describe several partial results and discuss recent progress due to Ozawa and Monod based on the Gaboriau-Lyons result that the free group F2 ”randomly” embeds in any non-amenable group.
7th of february 2011: Hyperbolic dispersive estimates, topological pressure, and applications by Maciej Zworski (Berkeley University)
Following the work of Anantharaman and Nonnenmacher, Nonnenmacher and the speaker developed estimates for semiclassical propagators for open chaotic systems: under conditions on the topological pressure of the classical system one obtains exponential decay in time. This gives resonance free strips, resolvent estimates, local smoothing estimates. In related work of Wunsch and the speaker similar estimates are obtained for normally hyperbolic trapped sets. Dyatlov applied these to quasinormal modes for black holes which gives exponential decay of linear waves in Kerr-deSitter backgrounds.
24th of january 2011: On the uniqueness of stationary black holes in vacuum lecture by Alex Ionescu (Princeton University)
I will discuss first the concept of unique continuation and present some classical theorems in the subject. I will then discuss some recent work, joint with Sergiu Klainerman and Spyros Alexakis, on the uniqueness properties of the Kerr solutions in the class of regular stationary solutions of the Einstein vacuum equations.