3:00pm Yuri Tomilov (Torun and IM PAN, Warsaw)
Rates of decay of operator semigroups.
Abstract: In the last years there has been an increasing interest to the study of the rates of decay of bounded C_0-semigroups motivated by concrete applications to PDE’s, e.g. to the study of energy decay for damped wave equations. We intend to review recent results and technique pertaining to decay of bounded C0- semigroups on Banach spaces obtained by Batty & Duyckaerts (2008) and Borichev & Tomilov (2010) and to discuss several notorious open problems in this domain.
4:30pm Daniel Lenz (Jena)
Large time behaviour of heat kernels.
Abstract: We study long time behaviour of heat kernels and show convergence of the semigroup to the ground state and convergence of suitably averaged logarithms of kernels to the ground state energy. The results hold for arbitrary selfadjoint positivity improving semigroups. This framework includes Laplace operator on manifolds, on graphs and on quantum graphs. (Joint work with Matthias Keller, Hendrik Vogt, Radoslaw Wojciechowski)