Lectures on recent developments in Hamiltonian Floer homology
by Shaoyun Bai (Columbia university)
Abstract: This lecture series will provide an introduction to recent conceptual and technical advances in Hamiltonian Floer theory.
Lecture one (Lundi 11 de 10h00 à 11h30, à Jussieu 15-16-413): In the first lecture, we will discuss how to organize moduli spaces from Floer theory into structures like flow categories (gradient flow lines), flow bimodules (continuation maps), and flow multi-modules (algebraic structures). Then, we will indicate how coherent Kuranishi-type structures can be defined and why they are relevant to defining virtual counts.
Lecture two (Mercredi 13 de 14h30 à 16h00, à jussieu 15-25-502): In the second lecture, we will focus on explaining the construction of global Kuranishi charts of various types of moduli spaces arising in Hamiltonian Floer theory.
Lecture three (jeudi 14 de 15h30 à 17h, à Orsay, salle 2L8): In the final lecture, we will introduce a perturbation scheme, known as the Fukaya-Ono-Parker perturbations, which allows one to define Hamiltonian Floer theory with integer coefficients. The principle will be sketched, emphasizing how to use this theory as a black box.
