Perspectives in geometric analysis on Sasakian manifolds

This workshop mainly focuses on finding canonical metrics on Sasaki manifolds which are base-manifolds of Kaehler orbifolds.

From the cohomological characterization of the Kaehler-Ricci flow, the behavior of the flow deeply reflects complex structures of the Kaehler manifold which is related to the Minimal Model Program in algebraic geometry. A Sasakian manifold is an odd dimensional counterpart of Kaehler geometry and a Sasaki-Einstein five-manifold provides interesting examples of the AdS/CFT correspondence.

In this workshop, we will study the classification of closed simply connected five-manifolds up to diffeomorphisms due to Smale and Barden, and discuss the analytic transverse MMP on Sasakian five-manifolds by using the Sasaki-Ricci flow. An independent episode related to isoperimetric inequality is also included. We sincerely invite everyone who is interested in this program to participate.