Fall 2016: Berstein seminar on Sheaves on Manifolds

Mondays and Wednesdays, 8:40-9:55 in Malott 205.
Some days will be missed, with warnings placed here.

Our main source will be Kashiwara and Schapira, Sheaves on Manifolds, downloadable there from Cornell machines (or use Passkey from off-campus).

Notes so far, updated 8/31

Some goals, and papers we might read:

  • understand D-modules well enough to prove Beilinson-Bernstein, as here
  • understand perverse sheaves well enough to define the maps in the Riemann-Hilbert correspondence, and the quivers in
  • Perverse sheaves on Grassmannians, Tom Braden
  • Perverse sheaves on rank stratifications, Tom Braden and Mikhail Grinberg
  • understand when Lagrangians are smooth enough to define maps on what sort of homology, e.g. the Springer representations
  • Euler obstructions and the correspondence between constructible functions and Lagrangian cycles
  • functorial operations on the derived category of perverse sheaves, and how they decategorify to operations on functions
  • dream: connect the theory of CSM classes with that of Deligne's weight filtration on H^*, maybe via Sch\"urmann, as (on smooth manifolds) both derive from the log tangent bundle
  • understand the appearance of CSM classes in maximum likelihood
  • mixed Hodge modules
  • microlocal sheaves:
  • Microlocal Perverse Sheaves, S. Gelfand, R. MacPherson, K. Vilonen
  • Microlocal sheaves and quiver varieties, Roman Bezrukavnikov, Mikhail Kapranov
  • Cluster varieties from Legendrian knots, Vivek Shende, David Treumann, Harold Williams, Eric Zaslow
  • Ind-Sheaves, distributions, and microlocalization, Masaki Kashiwara, Pierre Schapira
  • Microlocal Category, Dmitry Tamarkin (152 pp!)
  • Categories of (co)isotropic linear relations, Alan Weinstein