Analysis Seminar

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Spectral Asymptotics for "April Fools" Wave Equations on Compact Spacetimes That Pretend to Be Elliptic

Speaker: Bob Strichartz, Cornell University

Location: Warren Weaver Hall 1302

Date: Tuesday, April 1, 2014, 11 a.m.

Synopsis:

The Weyl asymptotic law tells you about the spectrum of an elliptic pde on a compact manifold. You would not ordinarily think it would tell you anything about wave equations. Nevertheless, for certain compact spacetimes, such as the product of a circle and a 2-sphere, there is an asymptotic law for the spectrum (separately for the positive and negative part). However, "April Fools!", it gets the dimension wrong. The gist of the argument is elementary number theory (distictions between even and odd numbers). This is joint work with Jonathan Fox, and I will bring along some nice graphics that he has made.