News
Organizational Meeting: Monday, October 5, 13h s.t., INF 288 HS 4
Let us know as soon as possible if you were unable to attend this meeting, but are still interested in the seminar!
Meeting time and place: INF 501, Rm 103.
The seminar will meet in INF 501, Rm 103. Our regular meeting time is Wednesday 14 s.t..
The meeting on October 21 has been canceled. The first regular meeting will be on Oct 28. Please contact us if you cannot attend at this time.Instructors
Dr. Richard Eager, eager@mathi.uni-heidelberg.de
Prof. J. Walcher, walcher@uni-heidelberg.de
Description
Supersymmetric quantum mechanics stands at the beginning of much of the interaction between geometry/topology and quantum field/string theory in the past 25 years. It first led to a re-interpretation of classical Morse theory, and later inspired the development of Floer theory and the Fukaya category as prototypes of systems with an infinite number of degrees of freedom. Recent years have seen a resurgence of interest and progress in foundational aspects of the subject, including the calculation of supersymmetric indices by localization, and the complexification of parameter space.
This seminar aims to trace supersymmetric quantum mechanics from its beginnings in papers by E. Witten from the early 1980s to three select cutting edge developments:
- The calculation of the supersymmetric index of gauged linear sigma models by Benini, Eager, Hori, and Tachikawa
- The study of boundary conditions for A-branes in Landau-Ginzburg models and an IR description of the Fukaya-Seidel category by Gaiotto, Moore and Witten
- Witten's paper "A new look at the path integral of quantum mechanics", as an accessible introduction to the complexification of parameter space and to the relation between topological field theories of Chern-Simons and Witten/cohomological type.
In addition to recent excitement, a thorough understanding of supersymmetric quantum mechanics provides an easy gateway to many other contemporary topics in mathematical physics.
Prerequisites: The seminar is aimed at Masters students and advanced Bachelor students of mathematics and physics. The early parts should be accessible with a good knowledge of undergraduate quantum mechanics of finite-dimensional systems and basic notions of differential geometry. The level of the latter parts will be adjusted to the participants' background.
Schedule of Talks
| Date | Speaker | Title | Scribe |
|---|---|---|---|
| Week 1: Oct 28 | Tobias | Supersymmetry in zero dimensions | Menelaos |
| Week 2: Nov 4 | Menelaos | Supersymmetric quantum mechanics | |
| Week 3: Nov 11 | Michael | Landau-Ginzburg models and sigma models in SQM | Michael |
| Week 4: Nov 18 | Lukas | Chern-Gauss-Bonet from SQM | Lukas |
| Week 5: Nov 25 | No Seminar | Thanksgiving | |
| Week 6: Dec 2 | No Seminar | No Seminar | |
| Week 7: Dec 9 | Oskar | Instantons in SQM and the Morse-Smale-Witten complex | |
| Week 8: Dec 16 | Sebastian | Morse homotopy and A-infinity category | |
| Week 9: Dec 17 | Felix | Electron-monopole system (Quantum Hall halo) | |
| Week 9 3/4 | Harry P. | Xmas | |
| Week 10: Jan 13 | Benjamin | Supersymmetric Lattice Models | Sebastian |
| Week 11: Jan 20: | Robert | Lattice Models and Spectral Sequences | |
| Week 12: Jan 27 | Adam | Equivariant Localization | Adam |
| Week 13: Feb 3 | Maximilian | Gauged Linear Sigma Model / Moduli Space of Flat Connections | Maximilian |
| Next Semester | Next Generation | Everything Else |