Differential Geometry in Geometric and Deformation Quantization - Reading (MTH35X.5))

Venue: Online and H-303 Office Space

Class Timings: Mondays and Fridays from 3:30 to 5:00 PM

First Meeting: 17 August 2026

Course Syllabus: 

    1. Review of manifolds, differential forms, Stokes Theorem, simplicial, singular homology  and deRham cohomology with examples. 
    2. Complex manifolds with examples
    3. Symplectic and Kahler manifolds with examples.
    4. Poisson manifolds with examples. 
    5. Group action on manifolds. 
    6. Vector bundles, especially line bundles, connection and curvature, holonomy
    7. Geometric quantization.
    8. Reproducing Kernel Hilbert spaces and coherent states with example of C^n and CP^n. 
    9. Perelomov and Rawnsley Coherent states.
    10. Berezin quantization and Odzijewicz quantization--outline only.
    Resources:
      Text book:
           1. Nakahara : Geometry, Topology and Physics
           2. Woodhouse: Geometric Quantization
           3. Paulsen and Raghupathi: Introduction to the Theory of Reproducing Kernel Hilbert space
           4. Berezin's and Odzijewicz's papers and some other papers.

Course Outcome:
This course will enable students to  understand and have working knowledge of the  differential geometry required in quantization, so that they are equipped to read the theory behind various quantizations on their own.

Course Evaluation: Assignments 20%, midterm  presentations 40% + final presentation plus exam 40% 

Credit Score: 4