Seminars Sorted by Series

By imposing symmetry on manifolds of exceptional holonomy we get a variety of differential geometric questions in lower dimensions. Related to that, one can consider “adiabatic limits”, where the manifold has a fibration and the fibre size is scaled...

Consider a system of small hard spheres, which are initially (almost) independent and identically distributed. Then, in the low density limit, their empirical measure $\frac1N \sum_{i=1}^N \delta_{x_i(t), v_i(t)}$ converges almost surely to a non...

Although the distribution of hard spheres remains essentially chaotic in this regime, collisions give birth to small correlations. The structure of these dynamical correlations is amazing, going through all scales. How combinatorial techniques can...

At leading order, the fluctuations around the typical dynamics are described by the second cumulant. They actually satisfy a stochastic PDE with time-space white noise. Can we say more using higher order cumulants?

The Riemann zeta function is the most important function of number theory, and a great part of modern research in number theory is dedicated to its study and the study of its relatives the L-functions. It was Riemann who revolutionized number theory...

Today the prevailing method in mathematics is 'analytic', in the sense that all mathematical objects are broken down into very small bits. For instance, a space or manifold is regarded as merely a set of points with structure. By contrast, in a...

The game of Prisoner's Dilemma is the simplest non-trivial game for two players. It has been studied by game-theory experts for fifty years. So it came as a big surprise this year when Bill Press discovered a new set of strategies which allow one...

Higher-order beliefs are of great importance in reasoning about agents’ strategic behavior, and have been long studied in epistemic game theory. Yet it was unclear whether eliciting such beliefs from the agents can help a social planner to better...

Black (or white) board is probably one of the most precious companions to many mathematicians. However, computers now also play an increasing role in the everyday activity of a researcher in mathematics: for typesetting articles, for testing...

Drawing on some recent work, I will try to explain how ideas from derived algebraic geometry shed new light on old constructions in arithmetic geometry, leading ultimately to a better understanding.