Hermann Weyl Lectures

Can we reconstruct a function by knowing only a subset of its values and a subset of the values of the function's Fourier transform?

How many values do we need to know for such a reconstruction? Can we interpolate a given subset of values? What are...

Can we reconstruct a function by knowing only a subset of its values and a subset of the values of the function's Fourier transform?

How many values do we need to know for such a reconstruction? Can we interpolate a given subset of values? What are...

Can we reconstruct a function by knowing only a subset of its values and a subset of the values of the function's Fourier transform?

How many values do we need to know for such a reconstruction? Can we interpolate a given subset of values? What are...

Many important consequences of the Riemann Hypothesis would remain true even if there were some zeros off the critical line, provided these exceptions to the Riemann Hypothesis are suitably rare. We can unconditionally prove some results on the...

Given any non-negative function \f:ℤ→ℝ, it follows from basic ergodic ideas that either 100% of real numbers α have infinitely many rational approximations a/q with a,q coprime and |α−a/q|

I'll describe a recent resolution of this conjecture, which recasts the problem in combinatorial language, and then uses a general 'structure vs randomness' principle combined with an iterative argument to solve this combinatorial problem.

Given several real numbers α1,...,αk, how well can you simultaneously approximate all of them by rationals which each have the same square number as a denominator? Schmidt gave a clever iterative argument which showed that this can be done...

The defocusing Non Linear Schrödinger equation iut=Δu−u|u|p−1 is a classical model of mathematical physics. For energy subcritical non linearities, Ginibre and Velo proved in the ’80s that all solutions are global in time and asymptotically behave...

In the last forty years, the study of singularity formation has mostly concerned model problems and focusing non linearities. In this second lecture, we will try to give a unified overview on the known mechanisms of singularity formation, with in...

The 4th Clay Millenium problem has a very simple formulation: may viscous incompressible fluids form a singularity in finite time? The answer is no in dimension two as proved by Leray in 1932, but the three dimensional problem is out of reach. More...

The unique games conjecture gives a very strong PCP theorem, which, if true, leads to a clean understanding of a broad family of approximation problems. We will describe recent progress on the conjecture and how certain type of expansion and...