Lecturer: Vyacheslav Lysov
Course Description: The course is the second part of the “Morse Theory and Supersymmetric Quantum Mechanics” I taught in the spring of 2024. I will provide detailed lecture notes on part 1. We will start with a detailed discussion of the Morse theory from a mathematics perspective, and introduce the notions of gradient trajectory, moduli space of trajectories, Morse differential, Morse-Witten complex, and Morse cell decomposition. I will provide concrete examples in dimensions 2 and 3. Then, we will discuss the Morse theory from a physics perspective and introduce the notions of the supersymmetric sigma model, superpotential, ground states, tunneling, and instantons. In the remaining lectures, we will discuss more advanced topics such as Morse-Bott theory, Morse-Novikov theory, and Index theorems.
Number of Sessions: 2 classes (45 min with a 10 min break) per week
Time and Location:
- 9:30-11:00, Monday, Room 1410
English 
简体中文