Department of Mathematics - Master Calendar

Title: Ricci Solitons and Isoparametric Functions

Abstract: In this talk, we will describe a connection between Ricci solitons and isoparametric functions.  The former comes from the theory of Ricci flows, initiated by R. Hamilton in the 80s, and played a key role in Perelman's resolution of the Poincaré conjecture.  The latter was motivated by questions in geometric optics, and the classification in an ambient round sphere is remarkably deep. We show that, for a Kahler gradient Ricci soliton in dimension four, either it is an integrable system and generically toric or its potential function is isoparametric. Furthermore, regular level sets of such a function are deformed Sasakian structures, leading to a complete classification.  In a real setup, the isoparametric condition also has interesting consequences.