Time: MW 10:15-11:30 am

Dates: Wednesday September 16 to Wednesday October 14

Location: **online** on Zoom; enter meeting ID **920 4953 2379**

Instructor: Lenny Ng

**The minicourse is now finished. Thanks everyone who attended!
Lecture notes and password-protected lecture recordings are
available below.**

The Zoom meeting ID above will work for each meeting of the minicourse.

Here are the lecture notes (in the form of a PDF of the screens that I share during the class) and links to the Zoom recordings of the classes. Please note that the password for the Zoom recordings is the password for the minicourse, but with the five characters 2020! added to the end.

- Lecture notes part 1 (9/16 through 9/28)
- Lecture notes part 2 (9/30 through 10/5)
- Lecture notes part 3 (10/7 through 10/14)
- 9/16 lecture
- 9/21 lecture
- 9/23 lecture
- 9/28 lecture
- 9/30 lecture
- 10/5 lecture
- 10/7 lecture
- 10/12 lecture
- 10/14 lecture

Here are links to notes from two of my previous minicourses. I will be following the notes from the Fukaya category minicourse fairly carefully in the present minicourse, so it may be helpful to have that handy to follow along during lectures.

- A-infinity categories and Fukaya categories (spring 2017)
- Morse theory and Floer homology (spring 2015): see this for background on Morse homology.

My plan for this minicourse is to present a rather nontechnical
introduction to Lagrangian
intersection Floer theory, which underlies many recent developments in
symplectic topology as well as low-dimensional topology (e.g. through
Heegaard Floer theory). This includes a very quick overview/review of
Morse homology building to a geometry-flavored overview of Lagrangian
Floer theory; an introduction to associated algebraic structures such as
A-infinity algebras and Fukaya categories; and probably some cursory
discussion of analytical issues involved in all of these constructions.

My intention is to make this minicourse as accessible as possible. I
will assume familiarity with smooth manifolds at the level of Math
620, and algebraic topology at the level of Math 611. It will also be
helpful (but not absolutely necessary) to know something about Morse
homology. I will not assume familiarity with symplectic geometry.

I taught a variant
of this minicourse in Spring 2017.
The outline that I posted for that minicourse is also a good outline for
the
present one:

- Morse homology (the basic setup)
- background in symplectic geometry: symplectic forms, Lagrangian submanifolds, Hamiltonian diffeomorphisms
- Lagrangian intersection Floer homology
- A-infinity algebras and A-infinity categories
- Fukaya categories.