A working seminar on homological (quasi-) hamiltonian reduction

This is the website for a working seminar on homological hamiltonian reduction (a.k.a. classical BRST cohomology) and its generalisations.

Hamiltonian reduction (understood very broadly) is a very powerful tool. It is particularly useful in the context of gauge theory. In some cases (e.g., Poisson reduction) it admits a homological reformulation (which, ironically, was first discovered in perturbative quantum field theory) which goes by the name of classical BRST cohomology and which plays a very important rôle in gauge theory, string theory, conformal field theory, integrable systems,... The aim of the seminar is to explore the possibility of extending this homological reformulation beyond the Poisson case. A particularly intersting case is that of quasi-hamiltonian reduction. A possible common language in which to rephrase hamiltonian reduction is that of Lie algebroids and part of the seminar will be devoted to that.

Schedule of seminars

1. Friday, 25 September 2015
   2-4pm in JCMB 4325A
   José Figueroa-O'Farrill
   Classical BRST cohomology
   I will present the standard homological approach to the symplectic quotient in the case of a hamiltonian group action and, more generally, of coisotropic reduction.
2. Friday, 2 October 2015
   1:30-3:30pm in JCMB 6206
   David Jordan + Tim Weelinck
   Quasihamiltonian Reduction (I)
3. Friday, 23 October 2015
   2-4pm in JCMB 4325B
   David Jordan + Tim Weelinck
   Quasihamiltonian Reduction (II)
4. Thursday, 29 October 2015
   1-3pm in JCMB 5326
   Carlos Zapata-Carratalá
   Groupoids and algebroids
5. Friday, 6 November 2015
   9-11am in JCMB 6311
   Ana Rovi
   Lie-Rinehart algebras
6. Friday, 13 November 2015
   3-4pm in JCMB 4325B
   José Figueroa-O'Farrill
   Contact reduction
7. Friday, 20 November 2015
   2-4pm in JCMB 6206
   TBA
   TBA
8. Friday, 27 November 2015
   2-4pm in JCMB 6206
   TBA
   TBA

References

• Lie group valued moment maps
  Anton Alekseev, Anton Malkin, and Eckhard Meinrenken
• Lectures on Calogero-Moser systems
  Pavel Etingof
• Quasi-Hamiltonian reduction via classical Chern-Simons theory
  Pavel Safronov
• Quasi-Poisson manifolds
  Anton Alekseev, Yvette Kosmann-Schwarzbach, and Eckhard Meinrenken
• Generalized complex geometry
  Marco Gualtieri
• Reduction of Courant algebroids and generalized complex structures
  Henrique Bursztyn, Gil Cavalcanti and Marco Gualtieri