פעילויות השבוע

1. Coherence - classical.
2. Proof of Oka - sketch of classical (via Weierstrass preparation and division, etc).
3. Proof of definable Oka - sketch of steps and discussion of problematic points.

If time permits, I will report on the bourbaki text I sent during the previous lecture.

We prove the following conjecture of Margulis. Let M=Λ\G/K be a locally symmetric space where G is a simple Lie group of real rank at least 2. If M has infinite volume then it admits injected contractible balls of any radius. This generalizes the celebrated normal subgroup theorem of Margulis to the context of arbitrary discrete subgroups of G and has various other applications. We prove this result by studying random walks on the space of discrete subgroups of G and analysing the possible stationary limits.

This is a joint work with Mikolaj Fraczyk.