14h00-15h30: Manon Costa,Point processes on the real line: from Poisson processes to Hawkes processes
16h00-17h30: Ariane Trescases, Models for chemotactic aggregation of cells
14h00-15h30: Guillaume Cébron, Spectra of large random matrices
Abstract : The concept of free independence was introduced by Voiculescu in the context of operator algebras. Later it was observed that it is also relevant for large random matrices. I will explain how freeness allows to address successfully the problem of determining the asymptotic eigenvalue distribution of general polynomials in independent random matrices.
16h00-17h30: Reda Chhaibi, The Toda lattice at the crossroads of classical and stochastic integrability, numerical analysis and representation theory
Abstract : In 1967, Morikazu Toda introduced a Hamiltonian dynamic on n points in order to model a unidimensional crystal, hence the name Toda lattice. The trajectories of these n particles via a seemingly unphysical potential proved surprisingly profound. - The Toda lattice is a beautiful instance of an integrable system. - Its flow is morally equivalent to the numerical diagonalization of matrices, via the Arnoldi-Lanczos-QR scheme. - It allows to explain the stochastic integrability of important reference models in Random Matrix Theory. - The Toda lattice generalizes to arbitrary complex Lie groups. And following Kostant, integrating the Toda system reflects the representation theory of the underlying group.
14h00-15h30: Jérôme Fehrenbach, Modélisation et optimisation pour enlever les rayures sur une image
16h00-17h30: Olivier Roustant, Global sensitivity analysis and Poincaré inequalities
14h00-15h30: Laure Coutin, Around Rough paths
16h00-17h30: Pascale Roesch, Sierpinsky carpets,topology and complex dynamics