Project B4: Geodesic flows and Weyl chamber flows on affine buildings

Project B4, which is closely related to Project B3, deals with dynamical systems on Bruhat--Tits buildings, most notably with geodesic and Weyl chamber flows. One goal is to establish new dynamical estimates of geodesic flows on buildings which would allow us to derive isoperimetric inequalities. Furthermore, we want to develop a theory of Ruelle--Taylor resonances of Weyl chamber flows on quotients of buildings and study their relation to automorphic forms. Our strategy will be to start with known results from the Archimedean case of Riemannian symmetric spaces and transfer them to the case of buildings. We expect to take this farther, especially in situations where up until now analytical difficulties have impeded greater progress on the Archimedean side.