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.