## Special Colloquium

Dean Baskin

Northwestern University

Title: Decay of waves on conic manifolds

**Abstract:**The wave equation on flat space satisfies Huygens' principle (in odd spatial dimensions) and a weak Huygens' principle (in even spatial dimensions). Both the strong and weak Huygens' principles lead to non-trapping

*resolvent estimates*and hence to asymptotic expansions for the wave equation and a local smoothing estimate for the Schrödinger equation. In this talk I will first recall the strong and weak Huygens' principles in flat space and their applications. I will then describe recent work with Jared Wunsch establishing a "very weak" Huygens' principle (and the applications of this principle) for the wave equation on a class of manifolds with conic singularities.

Tea at 4:00

Friday November 30, 2012 at 3:00 PM in SEO 636