Instanton moduli spaces and W-algebras

• Time : Sep. 29(Mon.), 30(Tue.), Oct. 1(Wed.) 10:30-12:30, 14:30-17:00
• Place : Univ. of Tokyo, Department of Mathematical Sciences
• Aim of lectures : I would like to explain details of Maulik-Okounkov's paper and our paper.
• Prerequisite
  1. Basics on quiver varieties and Hilbert/Gieseker schemes, i.e., definition (Chapter 2 of Maulik-Okounkov) and Heisenberg action on equivariant cohomology groups (http://arxiv.org/abs/1401.6782)
  2. Equivariant derived category, such as Bernstein-Lunts LNM 1578
  3. Vertex algebras and W-algebras, e.g., Arakawa's paper on representation of W-algebras, Invent. Math. 2007
  4. We omit the physical motivation, i.e., the AGT conjecture. It is not required, but better to know physical motivation, e.g., http://arxiv.org/abs/1108.5632
• Syllabus
  1. We review Maulik-Okounkov's paper, especially stable envelop, R-matrices, definition of Yangian, and toroidal gl(1) as an example from quiver varieties for the Jordan quiver. (Here only 1 is required.)
  2. We review the hyperbolic restriction functor and its applications, such as the definition, the use in geometric Satake (see Mirkovic-Vilonen, Ann. of Math. 2007), and its relation to stable envelop (http://arxiv.org/abs/1207.0529). (Only 1 and 2 are required.)
  3. We then explain our paper, starting from equivariant sheaves on Uhlenbeck spaces.