| DATE |
SPEAKER |
TOPIC |
| Sep 17 |
Benedict Gross
Harvard University |
Integral zeta values and the number of automorphic representations
Abstract
|
| Sep 24 |
David Donoho
Stanford University |
Counting Faces of
Randomly-Projected Polytopes,
with applications to Compressed Sensing, Error-Correcting
Codes, and Statistical Data Mining.
Abstract
|
| Oct 1 |
Alan Reid
University of Texas |
The geometry and topology of
arithmetic hyperbolic 3-manifolds
This talk will discuss recent
advances in regards to some
of the main open problems about hyperbolic 3-manifolds in the context
of arithmetic hyperbolic 3-manifolds.
|
| Oct 8 |
No colloquium
|
Yom Kippur
|
| Oct 15 |
David Vogan
MIT |
Unitary representations of simple Lie groups
By 1950, work of Gelfand and others had led to a general program for
"non-commutative harmonic analysis": understanding very general
mathematical problems (particularly of geometry or analysis) in the
presence of a (non-commutative) symmetry group G. A first step in
that program is classification of unitary representations - that is,
the realizations of G as automorphisms of a Hilbert space. Despite
tremendous advances from the work of Harish-Chandra, Langlands, and
others, completing this first step is still some distance away.
Since functional analysis is not as fashionable now as it was in 1950,
I'll explain some of the ways that Gelfand's problem can be related to
algebraic geometry (particularly to equivariant K-theory). I'll also
discuss the (closely related) question of whether computers may be
able to help solve these problems.
|
| Oct 22 |
Frans Oort
Utrecht and Columbia |
Three conjectures in arithmetic
geometry
We discuss the Manin-Mumford conjecture (about the closure of any set of
torsion points in an abelian variety),
the Andr\'e-Oort conjecure (about the closure of any set of CM-points in a
moduli space)
and the Hecke Orbit Conjecture (about the closure of the Hecke orbit of a
moduli point). These conjectures,
on the borderline of geometry and arithmetic, seem to be (have been)
solved. We explain the similarities.
We will discuss the motivation for these conjectures, and in some cases we
will say something about methods of proofs.
|
| Oct 29 |
No colloquium
|
Fall break
|
| Nov 5 |
János Kollár
Princeton University |
Cremona transformations and
homeomorphisms of topological surfaces
Abstract
|
| Nov 12 |
Bao Châu Ngô
IAS |
|
| Nov 19 |
Valery Alexeev
University of Georgia |
|
| Nov 26 |
No colloquium
|
Thanksgiving
|
| Dec 3 |
Bruce Kleiner
Yale University |
|
| Dec 10 |
Kai Behrend
University of British Columbia |
|