Hermann Weyl Lectures

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.

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...