Time: 3:48-3:56pm

Speaker: Jason Liu

Title: From complexity one spaces to toric manifolds

Abstract: A complexity k space is a 2n dimensional symplectic manifold equipped with an effective Hamiltonian action of a torus of dimension n-k. When k = 0, these spaces are also known as toric manifolds. Given a toric manifold, by considering the action of an (n-1)-dimensional subtorus, we get a complexity one space. A natural question to ask is: given a complexity one space, is there a way to extend it to a toric manifold? In a joint project with Joseph Palmer and Susan Tolman, we give a criterion for when such an extension exists under the assumption that the complexity one space is tall, i.e. each nonempty reduced space is a surface. In this talk, I will discuss how to generalize our result to any complexity one space.

Time: 3:59-4:07pm

Speaker: Ood Shabtai

Title: Off-diagonal estimates of partial Bergman kernels on $S^1$-symmetric K\"{a}hler manifolds

Abstract: We establish local asymptotic estimates of partial Bergman kernels on closed $S^1$-symmetric K\"{a}hler manifolds. The main result addresses the scaling asymptotics of partial Bergman kernels at generic off-diagonal points in which they are not negligible. The example of the two-dimensional sphere will be presented.