Past Events

I will explain how one can combine algebro-geometric dichotomies and the Ratios Conjectures of Conrey, Farmer, and Zirnbauer, over a certain family of L-functions, to conditionally prove a conjectured asymptotic dichotomy, going back to Hooley and Manin, for the 6-variable cubic equation…

I will prove here the main theorems of the first talk, using two approaches: the first one is global while the second one, that does not give the optimal bounds of the first one, is locally topological. The interest of this second approach, based on induction on the genus…

Abstract: It is well known that solutions to the inviscid Burgers’ equation form shock singularities in finite time, even when launched from smooth data. A far less documented fact, at least in the popular works on 1D hyperbolic conservation laws, is that shock singularities are intimately tied…

Two recent and seemingly unrelated techniques for proving mixing bounds for Markov chains are: (i) the framework of "spectral independence", introduced by Anari, Liu and Oveis Gharan, and its numerous extensions, which have given rise to several breakthroughs in the analysis of mixing times of…

Quadratic twists of modular L-functions

Abstract:  The behavior of quadratic twists of modular L-functions is at the critical point is related both to coefficients of half integer weight modular forms and data on elliptic curves.  Here we describe a proof of an asymptotic for…

Suppose you like playing Werewolf, or "Mafia",  as this game is sometimes called. Is there a randomized optimal strategy you can follow if you are an innocent villager? When the total number of players is large, what is the size of the group of werewolves that guarantees comparable…

One motivation for this work is to launch a rocket from Earth carrying a satellite to be put in orbit on some other planet. There is then a main global Hamiltonian through Lagrange points, and a minimal set of smaller local Hamiltonians. In dimension 2, that main…

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