We introduce and study the class of Hausdorff-Berezin operators on the unit disc in the Lebesgue p-spaces with Haar measure. We discuss certain algebraic properties of such operators, and also give sufficient, and, in some cases necessary boundedness conditions for such operators. Joint work with Profs. K. Zhu and S. Samko.
Wednesday 16.5.2019 C124 14.15-15.15 o'clock (joint with Mathematical Physics seminar)
David Fisher (Indiana University): Arithmeticity, Superrigidity and Totally Geodesics Submanifolds
Abstract: All compact negatively curved manifolds admit infinitely many closed geodesics. I will discuss a recent result showing that hyperbolic manifolds admitting infinitely many closed totally geodesic submanifolds of codimension one are very special and in fact arithmetic. In fact a slightly more technical version holds for closed totally geodesic submanifolds of any dimension greater than 1. If time permits, I will explain how the proof involves a new superrigidity theorem and results from homogeneous dynamics.
Tuesday 14.5.2019 C124 14-16 o'clock