Peter Dalakov

Reading Seminar in Algebraic Geometry
Fall 2012

This is a reading seminar that we run together with Hristo Iliev.

Logistics : Friday 2-4 pm, IMI, room 578. (Notice room change!)

  • Nov 23 Some G2 geometry (cancelled)
  • Nov 16 The Hitchin system, spectral covers - 2
  • Nov 8 (Thursday!) The Hitchin system, spectral covers -1
  • Nov 2 Global properties of BunG.
  • Oct 23, Tuesday (!): Stability of bundles (5): Rank two, genus two case (Example, cont'd).
  • Oct 19 Stability of bundles (4): Rank two, genus two case (Example, cont'd).
  • Oct 12 Stability of bundles (3): Rank two bundles on a genus two curve (Example)
  • Oct 5 Stability of bundles (2) : properties and reformulations. Rank two, genus two -1
  • Sep 28: Stability; moduli of bundles - 1
  • Sep 20: Plan and overview

    In a series of talks I will try to understand and discuss some details about the Langlands duality for G2 Higgs bundles.
    Here is an optimistic list of topics:

  • · Introduction: plan and overview
  • · Basic properties of moduli of (Higgs) bundles. Example: genus two, rank two.
  • · Spectral and cameral covers. Possible digression on pull-push formulas, relative duality and GRR
  • · Remarks on the duality for SL(2)/PGL(2): see Hausel-Thaddeus and 1102.1717
  • · The duality in the G2 case, following Hitchin
  • · Special Kähler geometry and the Donagi-Markman cubic
  • · Tentatively: Comparison with the Katzarkov-Pantev description of the moduli space and the general Langlands duality for Hitchin systems

    Summer 2012

    June 12 – July 31: Intersection Theory (Hristo Iliev)

    " ...and signs and the signs of signs are used only when we are lacking things ", William of Baskerville