Bordered Heegaard Floer homology seminar
Fridays 3 PM in MS 5138
List of talks

Date: January 13, 2023
Title: A_infinity structures
Speaker: Advika Rajapakse
Abstract: We will review the definitions of A∞algebras, A∞modules, and tensor products of A∞modules, before reviewing basic properties of A∞ tensor products. We will then define type D structures on graded kmodules and show how type D homomorphisms can be identified with A∞ homomorphisms.
Notes:A_infinity Structures Notes

Date: January 20, 2023
Title: The algebra associated to a pointed mathched circle
Speaker: Colin Ni
Abstract: We will discuss the differential graded algebra A(Z) of a socalled pointed matched circle of a closed oriented 2manifold. In particular, we will carefully compute A(Z) in the case of a torus. Later in this seminar, we will see that the bordered Heegaard Floer invariants CFD and CFA are respectively a left differential module over A(Z) and a right A_infty module over A(Z).
Notes:Matched Circle Notes

Date: January 27, 2023
Title: Bordered Heegaard diagrams
Speaker: Jung Joo Suh
Abstract: In this talk, we explore the connections between bordered 3manifolds, which are compact 3manifolds with boundary with extra data about the their boundaries, and bordered Heegard diagrams, which are compact surfaces with boundary, together with extra information. Specifically, we will show how to construct a bordered 3manifold from a bordered Heegard diagrams, and how they help characterize said bordered 3manifold. In addition, we will discuss some connections to Morse Theory, and describe spin^c structures associated with bordered Heegard diagrams.

Date: February 3, 2023
Title: Moduli spaces
Speaker: Roman Krutowski
Abstract: The key tool for defining algebraic structures in any Floertype theory is the count of certain Jholomorphic curves. In this talk, we will describe the moduli spaces of such curves in a "strip" over a given surface with boundary and compactifications of such spaces given by holomorphic combs. Time permitting, we will discuss some gluing results essential for the Bordered Heegaard Floer homology.

Date: February 10, 2023
Title: Type D modules
Speaker: Yan Tao
Abstract: In this talk, we will define the type D module CFD of a bordered Heegaard diagram. Since it will be convenient to choose certain structures in this definition, we will focus on showing that CFD does not depend on this choice, and moreover that CFD is a bordered 3manifold invariant. Time permitting, we will also give a version of CFD with twisted coefficients.

Date: February 17, 2023
Title: Type A modules
Speaker: Yan Tao
Abstract: In this talk, we will define the type A module CFA of a bordered Heegaard diagram. In contrast to the type D module CFD from last week's talk, we will show that CFA is an Ainfinity module. Similarly to CFD, we will then show that CFA does not depend on the choice of almost complex structure used to define the moduli spaces and that CFA is a bordered 3manifold invariant.

Date: February 24, 2023
Title: Pairing theorem
Speaker: David Popovic
Abstract: In this talk, we will introduce the pairing theorem, connecting CFD and CFA structures with the classical Heegaard Floer homology. We will give an outline of the proof of the pairing theorem and a few example calculations.

Date: March 3, 2023
Title: Immersed curves: setup
Speaker: Eilon ReisinTzur
Abstract: TBD

Date: March 10, 2023
Title: Immersed curves: applications
Speaker: Konstantinos Varvarezos
Abstract: TBD

Date: March 17, 2023
Title: TBD
Speaker: Raphael Rouquier
Abstract: TBD