Applied Math Colloquium | Hari Kunduri, Geometric inequalities in general relativity

Thursday, May 15, 2025 2:30 pm - 3:30 pm EDT (GMT -04:00)

MC 5501

Speaker

Hari Kunduri (Mathematics and Statistics, McMaster University)

Title

Geometric inequalities in general relativity

Abstract

General relativity is a geometric theory of gravity. Isolated gravitating systems (stars, black holes...) are modelled by manifolds which approach Euclidean space in an appropriate sense. These are called 'asymptotically flat' (AF). AF manifolds are characterized by geometric invariants which have the interpretation in general relativity as energy and angular momentum. I will discuss ideas behind the proof of geometric inequalities satisfied by these invariants, such as  the positive mass theorem and the Penrose inequality. The latter  conjectures a lower bound on the energy by a function of the area of black holes present in the spacetime. If time permits, I can discuss my recent work on a proof of the spacetime version of the Penrose inequality for cohomogeneity-one initial data sets.