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K-State Today

February 4, 2016

Mathematics Colloquium lecture Feb. 4

By Reta McDermott

Lino Amorim, University of Oxford, will present "Symplectic Categories" as part of the Mathematics Department Colloquium Lecture series at 2:30 p.m. Thursday, Feb. 4, in 122 Cardwell Hall.

The abstract for the lecture — Amorim will begin by describing Weinstein's idea that the category of symplectic manifolds should have Lagrangian correspondences as its morphisms. Amorim will review the difficulties in constructing this and making symplectic invariants, such as the Donaldson-Fukaya category, functorial.

Amorim will then explain how tools from derived algebraic geometry can be used to implement these ideas in the case of algebraic, or holomorphic, symplectic manifolds, or even stacks. In particular we will see how to redefine the Donaldson-Fukaya category, starting from a "quantization" of (-1)-shifted symplectic derived stacks. This quantization assigns a perverse sheaf to each (-1)-shifted symplectic derived stack — this was proved by Joyce and his collaborators — and a map of perverse sheaves to each (-1)-shifted Lagrangian correspondence (still conjectural).