Reading Seminar in Algebraic Geometry
Fall 2012
This is a reading seminar that we run together with Hristo Iliev.
Logistics : Friday 24 pm, IMI, room 578. (Notice room change!)
Nov 23 Some G_{2} geometry (cancelled)
Nov 16 The Hitchin system, spectral covers  2
Nov 8 (Thursday!) The Hitchin system, spectral covers 1
Nov 2 Global properties of Bun_{G}.
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 G_{2} 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 pullpush formulas, relative duality and GRR
· Remarks on the duality for SL(2)/PGL(2): see HauselThaddeus and 1102.1717
· The duality in the G_{2} case, following Hitchin
· Special Kähler geometry and the DonagiMarkman cubic
· Tentatively: Comparison with the
KatzarkovPantev
description of the moduli space and the general Langlands duality for Hitchin systems
Summer 2012
June 12 – July 31: Intersection Theory (Hristo Iliev)
