Algebraic structures in symplectic geometry I

Speaker:

Nate Bottman

Affiliation:

MPIM

Date:

Mon, 22/05/2023 - 12:15 - 13:45

Location:

MPIM Lecture Hall [2]

Parent event:

IMPRS Minicourse [3]

Contact: Christian Kaiser

Ever since seminal work of Gromov, Floer, Donaldson, and Fukaya in the late 80s and early 90s, a major theme in symplectic geometry has been the construction of invariants defined in terms of moduli spaces of J-holomorphic curves. In this minicourse, I will explain some of these invariants, and describe how creative use of auxiliary moduli spaces of J-curves can equip these invariants with extra structure. The main reference will be my survey article with Abouzaid, https://arxiv.org/abs/2210.11159 [4] . I will not assume any prior knowledge of symplectic geometry.

lecture 1: Lagrangian Floer cohomology, the Fukaya category, associahedra and their operadic structure

lecture 2: J-holomorphic quilts, functors between Fukaya categories, witch balls, the symplectic (A-infinity,2)-category