Intercity Seminar Algebraic Geometry 2008/9
The topic of the Intercity seminar Autumn 2008 is the proof by
Ngô, Bao Châu of the fundamental lemma. The fundamental lemma
is a conjecture about 'orbital integrals' --in essence of
combinatorial nature-- and has its origins in the Langlands program
where one tries to compare automorphic forms on different groups.
Ngo has recently proposed a new approach to proving the fundamental
lemma based on the Hitchin fibration. Ngô and Laumon have used this
to prove the fundamental lemma for unitary groups and very recently
Ngo has put a
manuscript on math arXiv with a proof of the fundamental
lemma in the general case. One of the attractive features of this
approach is the role that geometry (the Hitchin fibration) plays
in this proof.
Program
- Friday September 19, 2008, UvA, Euclides, Plantage Muidergracht 24,
Room P 018
11:00-13:00 Gerard van der Geer: What is the Fundamental Lemma?
14:00-16:00 Jochen Heinloth: The Hitchin fibration and the endoscopic
structure of the trace formula
- Friday October 17, 2008, UL,
Room 403 Snellius Building
11:00-12:00 Jonas Bergstroem: Regular centralizer and Kostant section
12:00-13:00 Wilberd van der Kallen: Affine Springer fibres
14:00-15:00 Wilberd van der Kallen: Affine Springer models
15:00-16:00 Bas Edixhoven: Neron models
- Friday November 7, 2008, UU, Room BBL 430
11:00-13:00 Eduard Looijenga: The Hitchin fibration
(the notes of the lecture)
14:00-16:00 Robin de Jong: Hitchin fibration and Neron models
- Friday November 21, 2008, UvA, Room J/K 3.85, the room is in the physics department, next to the mathematics department see map
11:00-13:00 Gerard van der Geer: Stratification ([Ngo] Sec. 5)
14:00-16:00 Franziska Heinloth: Perverse sheaves and the decomposition theorem.
- Friday November 28, 2008, UvA, Euclides, Room P 015a (morning),
Room P 018 (afternoon)
11:00-13:00 Jochen Heinloth: Cohomology over the anisotropic part. ([Ngo] Sec. 6)
14:00-16:00 Ben Moonen: The support theorem. ([Ngo] Sec. 7)
- > Friday April 3, 2009, UvA, Room P014
15:00-17:30 G. Laumon (Universite Paris-Sud) : The weighted
fundamental lemma. Click here for the
notes.
Literature and Links
Ngô, Bao Châu: Le Lemme Fundamental pour les algebres de Lie.
arXiv: 0801.0446v3 [math.AG] cited [Ngo]
Thomas C. Hales: A statement of the fundamental lemma.
arXiv: 0312227v2 [math.RT]
Ngô, Bao Châu: Fibration de Hitchin et structure endoscopique de la
formule de traces. Fibration de Hitchin et structure endoscopique de la
formule des traces. (French) [Hitchin fibration and endoscopic
structure of the trace formula] International Congress of
Mathematicians. Vol. II, 1213--1225, Eur. Math. Soc., Zürich, 2006.
Ngô, Bao Châu: Fibration de Hitchin et endoscopie. (French)
[Hitchin fibration and endoscopy] Invent. Math. 164 (2006), no. 2,
399--453.
A useful link is the webpage of Drinfeld on geometric Langlands.
Further information can be obtained from
Jochen Heinloth and Gerard van der Geer.