During the Spring term 2019 we will learn the basics of Lagrangian Floer Homology and Fukaya categories. This seminar is organised by Ricky Wedeen and Riccardo Pedrotti.

Meeting:

We will meet on Fridays 11am - 12pm in RLM 10.176

References:

We will follow these references:

• [P] J. Pascaleff's notes on Lagrangian Floer Homology
• [A] D. Auroux introduction to Fukaya categories
• [S] P. Seidel's Fukaya categories and Picard-Lefschetz theory
• [S2] P. Seidel Graded Lagrangian Submanifolds

Schedule:

Planning meeting and overview

Riccardo, Ricky - January 23

Overview of the construction and Elliptic theory: [A] par 1.2, [P] chapters 9,10

Rok, Ricky - February 1

Fredholm theory and transversality: [A] par 1.4, [P] chapters 11, 12 (as far as you can get)

Cameron - February 8

Maslov index: [A] par 1.3, [P] chapters 12 (remaining), 13

Kenny - February 15

Gromov compactness of Moduli spaces: [A] par 1.4, [P] chapter 14

Riccardo - February 22

HF and the Arnold's conjecture: [A] par 1.5, 1.6, [P] chapters 9,16

Kai - March 1

Product operations: [A] par 2.1, [S], [P] chapter 20

Sebastian - March 8

A ∞ categories and derived categories part 1: [A] par 2.2, [S]

Cameron - March 15

A ∞ categories and derived categories part 2: [A] par 2.2, [S]

Leon - March 29

Absolute grading of the Floer Complex: [S2]

Riccardo - April 5

Exact Triangle and twisted complexes: [A] par 3.1,3.2

Charlie, Cameron - April 12

Exact Triangle in the Fukaya category: [A] par 3.3

Cameron - April 19

Generators and the Yoneda embedding: [A] par 3.4

Ricky - April 26

TBD

Leon - May 3

HMS

Cameron - May 10