Schedule of Capsule Research Talks

s: Amirali Abdullah Embedding results and lower bounds for Bregman divergences The Bregman divergences are a broad class of distance measures having high relevance in information theory, statistics and machine learning applications, and which include the Kullback-Leibler and Euclidean distance as special cases. The algorithmic tractability of these spaces is tightly linked with the underlying geometry, for example the embeddability of point sets into a low dimensional Euclidean space and isoperimetric properties of sets under perturbation. In this talk, I will discuss two of my results exploring the geometry of these spaces in an algorithmic context; namely lower bounds for near neighbor search under Bregman divergences, and upper bounds on dimensionality reduction for large sets of probability distributions. Matthieu Astorg Wandering domains and Teichmüller theory in complex dynamics When iterating holomorphic self maps, one defines the Fatou set as the the largest open set where the iterates form a relatively compact family. It is an open set where the dynamics is best understood. Sullivan famously proved in 1985 that every connected component of the Fatou set is preperiodic for rational maps on CP , notably leading to a complete description of the dynamics in the Fatou set, and introducing tools from Teichmller theory into complex dynamics. On the other hand, we will present recent joint work (with Buff, Dujardin, Peters and Raissy) proving that this is not the case in higher dimension. Efrat Bank: Number Theory in Function Fields. My research focuses on formulating and proving function field analogues of classical number theoretical problems. In this talk I will survey some of these problems; among which are the Hardy-Littlewood n-tuple conjecture, the Goldbach conjecture and conjectures on the number of primes in short interval and in arithmetic progressions. A key role in proving the function field analogues is played by the computation of some Galois groups. Deniz Bilman On long time asymptotics for integrable equations and their perturbations I will talk on obtaining long-time asymptotics for Hamiltonian perturbations of the Toda lattice, numerical inverse scattering, and some interesting problems which arise in these studies. Thomas Bothner On a Swiss army knife in integrable systems Seemingly unrelated questions in statistical mechanics can in fact be placed on common ground: they are related to Riemann-Hilbert problems (RHPs). These problems provide a common framework for aspects of the finite model and open the door to a rigorous analysis of the thermodynamical limit. We shall briefly sketch some known results in this field focusing on random matrix theory, the theory of exactly solvable lattice models and nonlinear wave equations. Sandrine Daurat Attracting sets in P C This talk is a discussion on the geometry and ergodic proprieties of attracting sets for endomorphisms of P C based on visual examples.