Duntroon workshop on Hitchin fibration and the fundamental Lemma

Aug 23 - 27, Duntroon Ontario

Organizers: Joel Kamnitzer, Carl Mautner

Main speaker: David Nadler

This will be a learning workshop on Ngo's work on the Hitchin fibration and the proof of the fundamental Lemma.

The workshop will be held at Highlands Nordic in Duntroon, Ontario, a 1.5 hour drive northwest of Toronto.

Photos:

everyone and the pigs.

Schedule and Speakers (pdf version):

M. Arithmetic motivation.

  • M1. (Masoud Kamgarpour) Statement of Fundamental lemma.
  • M2. (Yiannis Sakellaridis) Role of Fundamental Lemma in trace formula.

    • T. Lie theory and bundles on curves.

  • T1. (Brad Hannigan-Daley) Adjoint quotient, characteristic polynomial, Kostant slice, regular centralizers.
  • T2. (Sabin Cautis) Higgs fields, Hitchin fibration, symmetries of Hitchin fibration.
  • T3. (Mike Skirvin) Language of spectral curves.
  • T4. (David Jordan) Distinguished subsets of Hitchin base.
  • T5. (David Nadler) Stratification of Hitchin base.

    • W. Global vs local geometry of bundles.

  • W1. (Stephen Morgan) Uniformization of bundles, affine Grassmannian.
  • W2. (Bruce Fontaine) Affine Springer fibers, general properties and symmetries.
  • W3. (Travis Schedler) Examples of affine Springer fibers, regular characteristic polynomials.
  • W4. (Joel Kamnitzer) Factorization of affine Grassmannian, Hitchin fibration.
  • W5. (Sam Gunningham) Explanation of problem: Decomposition Theorem and characters applied to Hitchin fibration.

    • Th. Cohomology of Hitchin fibration.

  • Th1. (Geo Tam) Langlands duality and endoscopic groups from a geometric perspective.
  • Th2. (Carl Mautner) Abelian fibrations and Ngo's support theorem.
  • Th3. (Sarah Kitchen) Cohomology of Hitchin fibration and affine Springer fibers.
  • Th4. (David Nadler) Examples.
  • Th5. (Xinwen Zhu) Interpretation in terms of counting points.

    • F. Further directions: traces in geometry.

  • (David Nadler)

    • References:

  • Ngo: Fundamental Lemma.
  • Dat-Ngo: A survey of Ngo's proof.
  • Ngo: On abelian fibrations.
  • Ngo: Madrid ICM talk.
  • Ngo: Lecture notes.
  • Drinfeld's notes: Kostant's Theorem, the Hitchin fibration, regular centralizers, and SL_n.
  • Beilinson-Drinfeld, Quantization preprint: 1-100, 101-200, 201-300, 301-384.
  • Donagi: Spectral curves.
  • Sorger: Lectures on G-bundles.
  • Goresky-Kottwitz-MacPherson: On affine Springer fibers.
  • Paris book project.
  • David Ben-Zvi GRASP lecture on the fundamental lemma.