Class Timings: Tuesday and Thursday from 11:30 am - 01:00 pm
Venue: Feynman Lecture Hall
First Meeting: 10 August 2023
1. Real and complex manifolds with examples
2. Differential forms, vector bundles, fiber bundle, connection, curvature and other basic topics
3. Symplectic and Kahler geometry with examples
4. Group action on manifolds, especially adjoint and coadjoint action of Lie groups
5. Coherent states from many angles
6. Geometric quantization and Berezin quantization
7. Connections to other areas of mathematics like harmonic analysis and non-commmutative geometry (if time permits)
References: Nakahara (geometry, topology and physics), Lee (Smooth manifolds), Perelomov (Generalized coherent states and their application), Sakurai (Quantum mechanics), Woodhouse (Geometric quantization), R.O. Wells, Griffiths and Harris, some papers (Radcliffe, Berezin etc).
Course Evaluation: 20% assignments, 40% presentations (taken throughout the course) and 40% final exam.
Prerequisites: Basic knowledge of topology and complex analysis
- Teacher: Rukmini Dey