EVENT DETAILS AND ABSTRACT

Title: Sheaf quantizations and the J-homomorphism
Speaker: Xin Jin
Speaker Info: Northwestern University
Brief Description:
Special Note:
Abstract:

I will present a procedure to quantize an exact Lagrangian submanifold $L$ in a cotangent bundle $T^*M$ using microlocal sheaf theory. The quantization is over any (commutative) ring spectrum, and we will see a natural link between the notion of a brane structure on a Lagrangian in symplectic geometry and the J-homomorphism in stable homotopy theory. As an application, I will describe a purely topological realization of the Nadler-Zaslow theorem, which assigns a local system on a Lagrangian brane to a constructible sheaf on $M$ using Floer theory. This is joint work with David Treumann.