The stable homotopy groups of topological spaces have long been known to be isomorphic to framed bordism groups, via the Pontryagin-Thom construction. I will describe joint work with Andrew Blumberg, motivated by the desire to build foundations for Floer homotopy, which extends this relationship to the entire stable homotopy category, i.e. describing its objects, morphisms, compositions, etc from the perspective of bordism. The starting point is the problem of providing a Morse theoretic description of bordism groups. While it will be briefly mentioned, knowledge of Floer theory will not be required to understand the lecture.

Bio-Sketch:
Mohammed Abouzaid is a Professor of Mathematics at Stanford University, working in symplectic topology and its connections to algebraic geometry and homotopy theory. After earning his PhD from the University of Chicago in 2007, he was Clay Research Fellow, was a ICM speaker in 2014, received the 2017 New Horizons in Mathematics Prize, and is a fellow of the AMS.