Geometric Analysis Seminar This seminar is held on Tuesdays at 11:00 am in 210 Deady. 2011-2012 Winter-Schedule: JAN 17th, Peter Gilkey (local speaker) Title: Growth of heat trace asymptotics on rank 1 symmetric spaces . JAN 24th, Weiyong He (local speaker) Title: Nonnegative curvature in Sasaki geometry Jan 31, Peng Lu(local speaker) Title: TBA Feb 7th,Van den Berg Title: Heat content and Hardy inequality Abstract: Upper bounds are obtained for the heat content of an open set D in a geodesically complete Riemannian manifold M with Dirichlet boundary condition on the boundary of D, and non-negative initial condition. We show that these upper bounds are close to being sharp if (i) the Dirichlet-Laplace-Beltrami operator acting in L2(D) satisfies a strong Hardy inequality with weight d^{-2}, (ii) the initial temperature distribution, and the specific heat of D are given by d^{-a} and d^{-b} respectively, where d is the distance to the boundary of D, and 1 < a < 2, 1 < b < 2. Feb 14th, Boris Botvinnik (local speaker) Title: TBA Feb 21th, Thomas Bell Title: TBA Feb 28th, Jame Dilts Title: TBA TBA Title: TBA TBA Previous Schedule: 2011 Fall , 2010 Winter , 2010 Spring