Geometric quantization, moduli spaces and TQFT


When and where:



Course Plan:




References:



Non of the above are complete now, but they will be modified as the course progresses. I very much hope we can announce lectures by some of the participants here too. - So please have a look at the references, select one and get started.
Suggestions as to how we can develop and extend this page further are encouraged.

Course Calender:


WeekDescription
Sep 3. -- 7. Wednesday: Introduction. Deformation quantization and geometric quantization.
Thursday: Introduction. Witten's quantum Chern-Simons theory.
Sep 9. -- 13. Wednesday: Symplectic vector spaces and manifolds, Darboux' Theorem and the Poisson bracket (W. Ch. I.).
Thursday: Canceled.
Sep 16. -- 20. Wednesday: Michael Hansen: Lagrangian and Hamiltonian mechaniques (W. Ch. II.)
Thursday: Derivation of the Euler-Lagrange equations, Integrability of Distibutions and the space of motion (W. Ch. I.)
Sep 23. -- 27. Wednesday: Presymplectic manifolds, reduction, constraints and time dependent Lagragian/Hamiltonians (W. Ch. II.)
Thursday: Christian Zickert: Proof of Darboux' theorem
Sep 30. -- Oct 4. Wednesday: Symmetry and moment maps (W. Ch. 3)
Thursday: John Olsen: Pseudoriemannsk geometri og generel relativitetsteori
Oct 7. -- Oct 11. Wednesday: Symmetry and moment maps (W. Ch. 3)
Thursday: Symmetry and moment maps (W. Ch. 3)
As a supplement to Woodhouse on quotients, the following note by Emiko Dupont is highly recommended: Quotient manifolds by group actions
Oct 14. -- Oct 18. Monday: Symmetry and moment maps (W. Ch. 3)
Wednesday: Real polarizations (W. Ch. 4)
Thursday: Erik Olsen: The Kepler system
Oct 21. -- Oct 25. Wednesday: Real polarizations (W. Ch. 4)
Thursday: Real polarizations (W. Ch. 4)
Friday: Simon Willerton: A Gerbe-like view of the Wess-Zumino-Witten and Chern-Simons Terms
Oct 28. -- Nov 1. Wednesday: Real polarizations (W. Ch. 4)
Thursday: Anders Skovborg: Convexity and commuting Hamiltonians (following Atiyah)
Nov 4. -- Nov 8. Wednesday: Real polarizations (W. Ch. 4)
Thursday: Real polarizations (W. Ch. 4)
Nov 11. -- Nov 15. Wednesday: Søren Galadius: Chern Classes.
Nov 18. -- Nov 22. Midterm recess/Classification of compact symplectic manifolds with reducible real polarizations.
Nov 25. -- Nov 29. Wednesday: Complex polarizations (W. Ch. 5)
Thursday: Gregor Masbaum: TQFT from skein theory
Dec 2. -- Dec 6. Tuesday: Gregor Masbaum: TQFT from skein theory
Wednesday: Gregor Masbaum: TQFT from skein theory
Thursday: Gregor Masbaum: TQFT from skein theory
Dec 9. -- Dec 13. Wednesday: Complex polarizations (W. Ch. 5)
Thursday: Complex polarizations (W. Ch. 5)
Dec 16. -- Dec 20. Wednesday: Prequantization (W. Ch. 7)
Thursday: Quantization (W. Ch. 8)




Last updated. The 9. of December 2002.
Jørgen Ellegard Andersen, andersen@imf.au.dk