## Columbia Mathematics
Department Colloquium

*"From rough space-time to
black holes.*

*
Evolution problem in General Relativity"*

### by

### Igor Rodnianski

### Princeton

Abstract:

I will start by
explaining basic principles of General Relativity.

I will review the all
familiar Einstein-vacuum space-times: Minkowski
and

Schwarzschild, the latter
giving the simplest example of a black hole

space-time, describe basic monotonicity property of the Einstein
equations

and its use in the Penrose
incompleteness theorem. I will then discuss the

evolution problem in General
Relativity, explain how to construct rough

space-times and trapped surfaces, and
explore several stability problems,

including that of black holes. In that context I will examine
global

behavior of linear waves and explain
the role of the celebrated red-shift effect.

**November 12th,
Wednesday, 5:00-6:00 pm**

**Mathematics
520**

**Tea will be served at
4:30pm**