Entropy production under non-negative sectional curvature

COLLOQUIUM TALK

Title: Entropy production under non-negative sectional curvature

Abstract: It is known that non-negativity of the Ricci curvature on a complete Riemannian manifold can be characterised by convexity properties of entropy along optimal transport. In this talk, we will review this connection (including the relevant background) and discuss the corresponding picture for sectional curvature. Our main observation is that the convexity of entropy (which is a scalar-valued quantity) lifts to the convexity of a certain 2-tensor if non-negative sectional curvature is assumed. We will see how this stronger assumption leads to a refinement of contraction properties of the heat semigroup that are known to hold if the Ricci curvature is non-negative. This talk is based on joint work with Liran Rotem and Yair Shenfeld.

Speaker Bio: Gautam Aishwarya is a post-doctoral fellow at the Technion–Israel Institute of Technology, Haifa, Israel. He completed his Ph.D. in Mathematics at the University of Delaware, USA, in 2021, focusing on information-theoretic notions of size in the metric setting. His research interests include functional and geometric inequalities, with applications in combinatorics and number theory.