# Morse Theory and Supersymmetric Quantum Mechanics course

**Instructor**: Vyacheslav Lysov

**Duration**: 13 weeks, 1 hour lectures, twice a week.

**Meeting time**: Tuesday, Thursday, 2-3 pm, L4E01 except the four dates

May 20, Thursday - L4E45

May 25, Tuesday - L4E48

June 17, Thursday - L4E48

July 15, Thursday - L4E48

**Description**: Modern theoretical physics has deep connection with modern mathematics. The foundations of this connection was established by Edward Witten in his works around 80's. We will use Witten`s paper ``Supersymmetry and Morse theory" as prime reference for the course. It is a scientific paper, so it assumes some background knowledge of both supersymmetry and Morse theory, which we will cover in the first part of the course. The second part of the course will be focused on two different approach to the Morse theory: the standard mathematical one, based on differential geometry and topology and the physical one using the supersymmetric quantum mechanics. The goal of this course is to demonstrate the close relation between the modern physics in mathematics using the simplest possible example.

**Background**: Some knowledge of quantum mechanics and differential geometry.

**Grading**: There will be biweekly home assignments.

**References: **E.Witten, "Supersymmetry and Morse theory" J. Diff. Geom. **17** (1982) no.4, 661-692

Hori, K., Thomas, R., Katz, S., Vafa, C., Pandharipande, R., Klemm, A., Vakil, R. and Zaslow, E., 2003. "Mirror symmetry (Vol. 1)" American Mathematical Soc..

**Announcement: **The problems on HW 2 turns out to be harder than intended, so the subnission deadline is extened for 1 week (Jul 6 in new deadline).