Lawrence Mouillé, Syracuse University
The Grove-Searle Maximal Symmetry Rank Theorem (MSRT) is a foundational result in the study of manifolds with positive sectional curvature and large isometry groups. It provides a classification of closed, positively curved manifolds that admit isometric actions by tori of large rank. In this talk, I will present progress towards extending the MSRT to positive intermediate Ricci curvature, a condition that interpolates between positive sectional curvature and positive Ricci curvature. Grove and Searle were able to employ concavity of distance functions to establish their MSRT, but this feature is not available for positive intermediate Ricci curvature. I will discuss how we can overcome this barrier using a strengthening of Wilking's Connectedness Lemma. A portion of this talk is from joint work with Lee Kennard.
MC 5417