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)
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