Semyon Dyatlov - Spectral gaps for normally hyperbolic trapping

The Christodoulou Klainerman proof of existence of asymptotically simple space-­times shows that it is reasonable to consider the scattering of

In these lectures I will explain the basics of microlocal analysis, emphasizing non elliptic problems, such as wave propagation, both on manifolds without boundary, and on manifolds with boundary. In

I will explain how one can formulate and formalize the Gupta Bleuler framework for the Quantization of the electromagnetic field in an

I will discuss energy and Morawetz (or integrated local decay) estimates for fields outside black holes. These results build on results for

In order to control locally a space time which satisfies the Einstein equations, what are the minimal assumptions one should make on its

TBA

In this talk I will describe recent work with Peter Hintz on globally solving quasilinear wave equations in the presence of trapped rays,

In the algebraic approach to quantum field theory on curved backgrounds, there exists a special class of quantum states for free fields,

In these lectures I will explain the basics of microlocal analysis, emphasizing non elliptic problems, such as wave propagation, both on manifolds without boundary, and on manifolds with boundary. In

Dynamical zeta functions of Selberg, Smale and Ruelle are analogous to the Riemann zeta function with the product over primes replaced by

Conserved quantities, for example energy and momentum, play a fundamental role in the analysis of dynamics of particles and fields. For

In order to control locally a space time which satisfies the Einstein equations, what are the minimal assumptions one should make on its