Speaker: Barbara Brandolini from University of Naples 3pm-4pm, Monday, 17 August 2009, Carslaw 454 Title: Some recent estimates on linear Neumann eigenvalues and eigenfunctions Abstract: We prove a reverse Holder inequality for the first nontrivial eigenfunction of the Neumann Laplacian. From this we deduce a lower bound for the first nontrivial eigenvalue in terms of the isoperimetric constant relative to the domain. We finally show that our results are asymptotically sharp at least in dimension two. Before the talk, we will take the Speaker to lunch at the restaurant Thai@home on Glebe Point Road. We will meet at 1pm on the outdoor Plaza on the 2nd floor of Carslaw.