# Algebra and Geometry Seminar

### Event Description:

Title: Understanding the Sasaki Cone

Abstract: The Sasaki cone can be thought of as a premoduli space of Sasakian structures with a fixed underlying CR

structure. As such it can have dimension 1\leq k\leq n+1 where the dimension of the Sasaki manifold is 2n+1. We study various important functions on the Sasaki cone, the most important of which is the Einstein-Hilbert functional. I shall end with a conjecture which says that if the dimension of the Sasaki cone is greater than 1, then the manifold is covered (up to possible covering maps) by 3-dimensional spheres.