Crypto/Number Theory Talks at Microsoft Research: Ken Ribet / Adi Shamir

[Dan Shumow]

On behalf of Kristin Lauter I would like to pass along this invitation
to anyone at the UW who might be interested in coming.

In the next month MSR has two talks by visiting researchers that may
be of interest:

Kenneth A. Ribet - 8/13 3:30pm
Adi Shamir - 8/27 1:30pm

Ribet's abstract is at the end of this e-mail. We do not have one for
Shamir yet, but his talks are always very interesting and
entertaining. When we have one, I will send an update.

For anyone who is interested in attending, please contact me directly
by a day or so in advance, so we can coordinate.


You are invited to attend… please pass on to internal MS employees who
may be interested.
*****************************************************************************************************
WHO: Kenneth A. Ribet
AFFILIATION: UC Berkeley
TITLE: Two-dimensional mod p Galois representations
attached to modular forms
WHEN: Wed 8/13/2008
WHERE: 99/1919 Research Lecture Room C
TIME: 3:30PM-5PM
HOST: Kristin Lauter
******************************************************************************************************
ABSTRACT:
Classical newforms are cusp forms on congruence subgroups of SL(2,Z)
that are eigenvectors for the Hecke operators. These modular forms
give rise to two-dimensional representations of the absolute Galois
group of the rational field. Conversely, if one starts with a
semisimple two-dimensional representation of this Galois group over a
finite field, the representation should arise from a newform if a mild
necessary condition (involving complex
conjugation) is satisfied. When the representation is irreducible,
Serre's conjecture (which is essentially a theorem) predicts the
modularity and specifies that possible weights and levels of newforms
that give rise to the representation. When the representation is
reducible, the set of weights and levels that give rise to it is
apparently more complicated to describe. I will discuss the simplest
possible examples of this phenomenon, where the representation is
about as uncomplicated as possible, the weight is 2 and the level is
either a prime number or the product of two distinct primes.