M 392C Morse Theory (54490)

Dr. Dan Freed

W 4 – 7pm

RLM 9.166

 

Course Description:

 

The critical points of a smooth function on a smooth manifold encode information about its topology, and conversely the topology constrains the structure of critical points. This idea was exploited by Marston Morse, especially in the infinite dimensional example of the loop space of a smooth manifold. An important variation in infinite dimensions was introduced by Floer, which has led to many striking applications. The course will begin with the basic theory, following the classic text by Milnor. In the second half of the course we will treat some of the modern topics, depending on the interest of students. Some of that material will be from a text by Nicolescu. I will lecture half of the time and students in the course, working in pairs, will lecture the other half. I will provide additional materials and coaching to help students with their lectures. Basic knowledge of manifold theory (at the level of the differential topology prelim class) is necessary, and some Riemannian geometry wouldn't hurt either. I will review some necessary background; summer reading is recommended!