Ahlfors Lecture Series: Mohammed Abouzaid

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Join us for a reception following the September 16th lecture from 5:15 p.m. to 7 p.m. in the The Austine & Chilton McDonnell Common Room on the fourth floor of the Science Center.

• September 16:
• Framed bordism and nearby Lagrangians

The problem of understanding Lagrangian embeddings in symplectic manifolds remains a mystery. The simplest class of symplectic manifolds are the cotangent bundles of smooth manifolds, which is the setting for the most prominent open problem in the subject: Arnold’s nearby Lagrangian conjecture which asserts the connectedness of the space of Lagrangians for which the relative class of the symplectic form vanishes. In particular, the conjecture asserts that all such submanifolds are diffeomorphic. In view of recent work with Alvarez-Gavela, Courte, and Kragh, as well as work of Procelli and Smith, I will use the question as a motivation for joint work with Andrew Blumberg on a bordism-theoretic approach to define bordism-valued refinements of Floer homology.

• September 17:
• Complex bordism and Hamiltonian fibrations

As a consequence of his theory of weights, Deligne proved that smooth complex projective varieties, carrying a smooth morphism to the projective line, have rational cohomology groups that are isomorphic to the tensor product of the cohomology of the fibre with that of the base. In joint work with McLean and Smith, we should that the result not only holds for symplectic manifolds, but is in fact a consequence of an analogous result that holds for complex cobordism. The proof identifies bordism of “stably complex derived orbifolds” as the correct framework in which to formulate these results, and I will discuss joint work with Shaoyun Bai to understand these bordism groups.

Speaker Bio: Mohammed Abouzaid is a Professor of Mathematics at Stanford University. He completed his Ph.D. 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).

About the Ahlfors Lecture Series: The Ahlfors Lecture Series is presented by the Harvard University Math Department in memory of our distinguished colleague, Professor Lars Ahlfors.