Seminar:
Group Actions, Geometry and Dynamics
Event time:
Monday, March 4, 2024 - 4:00pm
Location:
KT205
Speaker:
Dongryul Kim
Speaker affiliation:
Yale
Event description:
In rank one, the Hopf-Tsuji-Sullivan dichotomy theorem states the dichotomy for the ergodicity of geodesic flow in terms of the divergence/convergence of the Poincaré series at the critical exponent. Burger-Landesberg-Lee-Oh initiated the study of higher rank version of the Hopf-Tsuji-Sullivan dichotomy for a one-dimensional diagonal flow and the associated Poincaré series. In this talk, we discuss the Hopf-Tsuji-Sullivan dichotomy for higher dimensional flows which we call subspace flows of Weyl chamber flows. Just like the dimension dichotomy for Brownian motions in RnRn, the codimension dichotomy of the flow occurs for Anosov homogeneous spaces. This is based on joint work with Hee Oh and Yahui (Amy) Wang.