Columbia Mathematics Department Colloquium


"From rough space-time to black holes.

                   Evolution problem in General Relativity"


Igor Rodnianski



 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