WEDNESDAY, August 30, 2006, LCB 215
Speaker:
Krzysztof Klosin
,
University of Utah
Title:L-functions and Selmer groups - Introduction
Abstract:
This will be an elementary introduction to the circle of
ideas inspired by the 1976 paper of Ribet in which the
author uses congruences between modular forms to relate
special value of an L-function to the size of the class
group of a cyclotomic field.
WEDNESDAY, September 6
Speaker:
Krzysztof Klosin
, University of Utah
Title: L-functions and Selmer groups
Abstract: TBA
WEDNESDAY, September 13:
Speaker:
Krzysztof Klosin
, University of Utah
Title: Modular forms on U(2,2) and the Bloch-Kato
conjecture
Abstract: TBA
WEDNESDAY, September 20:
Speaker:
Gordan Savin
, University of Utah
Title: Some examples of modular forms on compact
groups
Abstract: TBA
WEDNESDAY, September 27:
Speaker:
Not meeting this week
Title: TBA
Abstract: TBA
WEDNESDAY, October 4:
Speaker:
Michael Larsen
,
Indiana University
Title: A Mordell-Weil theorem for fields of division
points
Abstract: TBA
WEDNESDAY, October 11:
Speaker:
TBA
,
Title: TBA
Abstract: TBA
WEDNESDAY, October 18:
Speaker:
TBA
,
Title: TBA
Abstract: TBA
FRIDAY, October 27: (Not Wednesday!)
Speaker:
Michael Harris
, Universite Paris
Title: Automorphic Galois representations and the
Sato-Tate Conjecture
Abstract: I will report on my recent proof with Taylor,
Clozel,
and Shepherd-Barron of the Sato-Tate Conjecture
for elliptic curves over Q with non-integral j-invariant.
The theorem is a consequence of the proof of
potential automorphy of even-dimensional symmetric
powers of the Tate module of such an elliptic curve.
This work will be presented in the context of the
conjectured Langlands correspondence between
Galois representations and automorphic representations.
WEDNESDAY, November 1:
Speaker:
Not meeting this week
Title: TBA
Abstract: TBA
WEDNESDAY, November 8:
Speaker:
J-P.
Wintenberger, Universite Louis Pasteur
Title: Lifts of odd 2-dimensional representations of
the Galois group of Q
Abstract: Joint work with C. Khare.
We will try to explain the main ideas of the proofs
of lifting theorems needed in our proof of Serre's conjecture.
For a representation $\overline{\rho }$
of $G_Q$ with values $GL _2 (F)$,
$F$ finite field of characteristic $p$, a lift is a $p$-adic
representation $\rho$ whose reduction is $\overline{\rho }$.
Lifting theorems state :
- if $\overline{\rho}$ is modular and $\rho$ satisfy
suitable hypotheses of ramification, $\rho$ is modular ;
- given $\overline{\rho}$, there exists lifts $\rho$ that satisfy
good
properties of ramification.
We will focus on statements of existence of liftings.
WEDNESDAY, November 15:
Speaker:
TBA
,
Title: TBA
Abstract: TBA
TUESDAY, November 21, 2:00-3:00:
Speaker:
Chandrashekhar
Khare, University of Utah
,
Title: Modularity and motives with good reduction
Note: The seminar will take place in JWB 308
WEDNESDAY, January 22:
Speaker:
Krzysztof Klosin
, University of Utah
Title: P-adic interpolation of modular forms -
Introduction
Abstract: This is the first part of a learning
seminar, where all of us, including the speaker, try to learn some
interesting number theory. Everyone interested, with background in
basic algebraic number theory and modular forms is welcome. Today
we will discuss how one can turn classical modular forms into
p-adic objects.
WEDNESDAY, January 29:
Speaker:
TBA
,
Title: TBA
Abstract: TBA