The Bellairs Workshop in Number Theory
The Bellairs Institute, McGill University, Barbados, 2014
of arithmetic groups and the Langlands
May 2-9, 2014
Frank Calegari (Northwestern University
The workshop is dedicated to cohomology of arithmetic groups with a view to applications to the Langlands program. A series of lectures will be given by Frank Calegari on this topic, supplemented by lectures from attending experts, for a total of 20 hours and many more hours of stimulating exchanges. The intention of the workshop is to provide an access point to the field, assuming at least a background comparable to advanced graduate students. Participation is by invitation only; Those interested in participation should contact the organizers to inquire about space availabilities and to make arrangements.
The general schedule is morning lectures by
Calegari followed by after-lunch and
after-dinner lectures by participating experts.
The program is designed to encourage discussion
and new research initiatives by allowing enough
free time and having all the participants in the
An important milestone towards proving Langlands's reciprocity conjecture was the work of Wiles (and others) showing that any elliptic curve E over Q is modular (equivalently, automorphic). Despite the immense progress in the field over the past twenty years, the class of natural algebraic varieties that we know to be modular is still extremely limited. For example, consider the problem of proving modularity of a general elliptic curve E over an imaginary quadratic number field F. In this instance, the associated locally symmetric spaces are hyperbolic manifolds of real dimension three and thus are not amenable to the usual techniques of algebraic geometry. Moreover, the relevant cohomology classes of these manifolds are no longer concentrated in a single degree. All previous generalizations of the Taylor-Wiles method are restricted to contexts in which neither of these difficulties occurs.
of the main goals of these lectures is to
outline a viable strategy to overcome these
issues, with an emphasis on explaining the
various outstanding problems and conjectures
which still need to be resolved. An overarching
theme of our approach is the study of torsion
classes in cohomology --- both in the Betti
cohomology of arithmetic groups and the coherent
cohomology of Shimura varieties --- and their
conjectural relationship with the Langlands
|Friday (2 May)
9:00-11:30 Frank Calegari: Selmer groups, the Greenberg-Wiles formula, and the Taylor-Wiles method.
19:30-20:30 Jared Weinstein: The geometry of modular curves.
20:00-21:30 Peter Scholze: The geometry of Shimura varieties.
9:00-11:30 Frank Calegari: Local-global compatibility for torsion representations in weight one; the doubling method.
15:00-16:30 Peter Scholze: An approach to the vanishing of non-Eisenstein cohomology of Shimura varieties outside the middle degree.
19:00-21:00 Toby Gee: An overview of local-global compatibility.
9:00-11:30 Frank Calegari: A modification of the Taylor-Wiles method when l_0 > 0.
14:30-16:00 Jack Thorne: Ordinary minimal modularity lifting for GL(n) and Leopoldt's conjecture.
19:00-21:30 Jack Thorne: Taylor-Wiles primes.
9:00-11:15 Frank Calegari: Minimal modularity lifting for low weight Siegel modular forms.
14:30-16:00 David Geraghty: The Kisin modification of Taylor-Wiles.
19:00-22:30 Sug Woo: Automorphic forms and cohomology.
9:00-11:00 Frank Calegari: Non-minimal modularity lifting in weight one.
14:30-16:00 George Boxer: Mod p^n coherent cohomology of automorphic vector bundles on Shimura varieties.
19:00-21:00 Ila Varma: Local-global compatibility for l=/=p non-self-dual Galois representations.
21:00-22:15 David Geraghty: Vexing primes.
9:00-11:00 Frank Calegari: The stable cohomology of congruence subgroups and algebraic K-theory.
|Friday (9 May)
Sug Woo Shin
Naser Talebi Zadeh
Bellairs Research Institute
Here is a link to the Institute's website. It is located in St. James, which is just to the north of Holetown. The exact location is
13.192104, -59.640130 (I think... you can plug these coordinates in http://maps.google.ca)
Getting to Bellairs
Here you can find maps of Barbados, as well as much information about tourism. The local airport is in