Speaker: Lawford Hatcher (Indiana University)
Title: The hot spots conjecture with mixed boundary conditions and small Dirichlet region
Abstract: The hot spots conjecture of Rauch states that a second Neumann eigenfunction of the Laplacian on a simply connected domain in Euclidean space has no interior extrema. In the past year or so, researchers have begun to consider an analogous question about the first mixed Dirichlet–Neumann eigenfunction. We will present a new theorem showing that on convex domains with connected and sufficiently small Dirichlet region, the first mixed eigenfunction indeed has no interior critical points.
Lunch: before the talk at 12pm at Shawarma Joint.