Please join us for the Clay Mathematics Institute Lectures with Professor Mohammed Abouzaid.

Bio: Mohammed Abouzaid joined Stanford University in 2023 as a Professor of Mathematics. He is currently teaching Topics in Symplectic Geometry. 

Mohammed completed his PhD at the University of Chicago in 2007. His primary research interest is in structures arising from studying Floer theory on Symplectic manifolds, as well as their applications.

Mohammed has received awards such as the Invited ICM Lecture (2014) and New Horizons Prize (2017).

Lecture 01: Bordism of manifolds

Abstract: In this introductory lecture, which should be accessible to a general mathematical audience, I will review the classical bordism theory of manifolds, from its origin in Poincare's work, to the subsequent development by Pontryagin, Thom, Milnor, Wall, and Quillen among others.

Lecture 02: Bordism of orbifolds

Abstract: An orbifold is a space with additional structure that describes it locally as the quotient of a manifold by a finite group. I will describe Pardon's recent result which reduces the study of orbifolds to the study of manifolds with Lie group actions. Then I will explain the relationship between equivariant and orbifold bordism, and formulation some structural properties of this theory.

Lecture 03: Bordism of derived orbifolds

Abstract: The notion of a derived orbifold arises naturally in pseudo-holomorphic curve theory, and plays a central role in the emerging field of Floer homotopy. I will explain how it is related to the notion of "homotopical bordism" due to tom Dieck in the 1970's, and formulate some conjectures about its structure in the complex oriented case.