Lectures to be held in the morning each day.
Recent developments in the Langlands programme have
relied on an impressive amount of machinery -- the Kisin-Taylor-Wiles
method, cyclic base change, the Fundamental Lemma, the geometry
of unitary Shimura varieties, and the labyrinthian theory of automorphic
forms. One consequence is that non-experts can become needlessly
lost in the early stages of a paper (or during the first five minutes
of a talk) by technical details, even when the key ideas are actually
quite intuitive. The goal of this workshop is to demystify much
of the technical jargon in the subject with an emphasis on examples,
with a special emphasis on comparing the similarities and differences
of the general theory with the special case of modular forms and
modular curves.
Lecturers include Frank Calegari, Ana Caraiani, Florian Herzig,
Keerthi Madapusi Pera, Yiannis Sakellaridis and Chung Pang Mok.
| Monday, March 12 |
| 9:30 - 10: 00 |
Coffee and Welcome |
| 10:00 - 11:00 |
F. Calegari (Northwestern University)
(notes)
Classical Modular Forms |
| 11:00 - 11: 30 |
Break |
| 11:30 - 12:30 |
F. Herzig (University of Toronto) (notes)
Hecke Operators |
| 12:30 - 2:15 |
Lunch |
| 2:15 - 3:15 |
K. Madapusi Pera (Harvard University) (notes)
Modular Curves over Q |
| 3:15 - 3:45 |
Break |
| 3:45 - 4:45 |
C. P. Mok (McMaster University) (notes)
Galois Representations for Modular Forms |
| Tuesday, March 13 |
| 9:30 - 10: 00 |
Coffee |
| 10:00 - 11:00 |
Y. Sakellaridis (Rutgers University) (notes)
Representations of GL2(R) |
| 11:00 - 11: 30 |
Break |
| 11:30 - 12:30 |
F. Calegari (Northwestern University) (notes)
Galois Deformations |
| 12:30 - 2:15 |
Lunch |
| 2:15 - 3:15 |
F. Calegari (Northwestern University) (notes)
Galois Deformations II |
| 3:15 - 3:45 |
Break |
| 3:45 - 4:45 |
F. Calegari (Northwestern University) (notes)
Taylor-Wiles |
| Wednesday, March 14 |
| 9:30 - 10: 00 |
Coffee |
| 10:00 - 11:00 |
C. P. Mok (McMaster University) (notes)
GL(2) |
| 11:00 - 11: 30 |
Break |
| 11:30 - 12:30 |
Y. Sakellaridis (Rutgers University) (notes)
Automorphic Forms |
| 12:30 - 2:15 |
Lunch |
| 2:15 - 3:15 |
A. Caraiani (Harvard University) (notes)
Simple Shimura Varieties |
| 3:15 - 4:10 |
Break |
| 4:10 - 5:00 |
P. Scholze (Universität Bonn) (notes)
Colloquium |
| Thursday, March 15 |
| 9:30 - 10: 00 |
Coffee |
| 10:00 - 11:00 |
A. Caraiani (Harvard University) (notes)
Local-Langlands and Local-Global |
| 11:00 - 11: 30 |
Break |
| 11:30 - 12:30 |
K. Madapusi Pera (Harvard University) (notes)
Local Models |
| 12:30 - 2:15 |
Lunch |
| 2:15 - 3:15 |
F. Calegari (Northwestern University) (notes)
GSp(4) |
| 3:15 - 3:45 |
Break |
| 3:45 - 4:45 |
K. Madapusi Pera (Harvard University) (notes)
Local Models II |
| Friday, March 16 |
| 9:30 - 10: 00 |
Coffee |
| 10:00 - 11:00 |
K. Madapusi Pera (Harvard University) (notes)
p-adic Hodge Theory |
| 11:00 - 11: 30 |
Break |
| 11:30 - 12:30 |
F. Calegari (Northwestern University) (notes)
Kisin-Taylor-Wiles |
Topics to be covered include:
Part I: Classical modular forms:
Modular Forms as functions on lattices, as holomorphic functions,
as sections of coherent sheaves, as cohomology of local systems
Hecke operators, admissible representations, Local Langlands for
GL_2 Modular curves over number fields and over rings of integers.
The special fibre of X_0(p), The Eichler-Shimura relation Representations
of GL_2(R)
Part II: Galois Representations for GL(2):
Galois Representations for classical modular forms
Galois Representations locally at p (introduction)
Deformations of Galois Represenations
The idea behind the Taylor-Wiles argument
Part III: Generalizations to other groups
Reductive algebraic groups, the Langlands dual groups, algebraic
automorphic forms Special Cases: Hilbert modular forms, Siegel
modular forms, Inner Forms of GL(2), Jacquet-Langlands Simple
Shimura varieties Local Models The Local Langlands conjecture
+ global reciprocity (statements) Kisin's modification of Taylor-Wiles
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