Morse Theory

morse theory & homology (Analysis in dynamics), Fall 2019

Course description

We will be following Chapters 1-4 of Morse Theory and Floer Homology by Audin and Damian. This will cover Part I of the book, which is about Morse theory/homology, but we will not talk about Part II of the book, which is concerned with Hamiltonian Floer homology. (The official title of the course is Analysis in Dynamics.)

Grading

The course grade will be determined by two homework assignments and a short oral exam at the end of the semester. The grade will be calculated as the unweighted average of the three grades: homework 1, homework 2, and exam.

Homework assignments:

The homework assignments will be posted here.

Assignment 1: pdf due on 8 November in class

Assignment 2: pdf due on 13 December in class (the day of the exam)

Schedule (tentative)

The course meets on Fridays 3:30-5:30 in M.G. 015, here is the tentative schedule:

Sept 27: Lecture 1 - Chapter 1
Oct 4: Lecture 2 - Chapter 1
Oct 11: Lecture 3 - Chapter 2
Oct 18: Exercise session 1
Oct 25: Lecture 4 - Chapter 2
Nov 1: no class
Nov 8: Lecture 5 - Chapter 2 and homework 1 due
Nov 15: class canceled
Nov 22: Exercise session 2 (and lecture on singular homology)
Nov 29: Lecture 6 - Chapters 3 & 4
Dec 6: Lecture 7 - Chapter 4 (or class canceled)
Dec 13: Final exam (oral exam) and homework 2 due
Dec 20: class canceled

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