two upcoming number theory seminar talks
William Stein
Can you post the following two upcoming number theory seminar talks?
1) http://wiki.wstein.org/seminar/nt/20110513
SPEAKER: A. Deines
TITLE: Dembele's Algorithm for Modular Elliptic Curves Over Real
Quadratic Fields
DATE: May 13, 2011 in Padelford C401 at 3:30pm
ABSTRACT: From the Eichler-Shimura construction we know that for each
newform $f$ of weight 2 and level $n$ with rational Fourier
coefficients,
there exists an elliptic curve $E_f$ over ${\mathbf Q}$ attached to $f$.
We can instead work over $F$, a real quadratic number field with
narrow class number one, instead of over $\mathbf{Q}$.
Let $f$ be a Hilbert newform of weight 2 and level $I$ with rational
Fourier coefficients,
where $I$ is an integral ideal of $F$.
It is a conjecture that for every $f$ there is an elliptic curve $E_f$
over $F$ attached to $f$.
Recently Dembele has developed an algorithm which computes the
(candidate) elliptic curve $E_f$ under the assumption that the
Eichler-Shimura conjecture is true.
I will discuss Dembele's algorithm, give an example, and discuss the
status of implementing this algorithm in Sage.
2) http://wiki.wstein.org/seminar/nt/20110520
TITLE: Shafarevich-Tate Groups of Elliptic Curves of Rank at Least Two
SPEAKER: W. Stein
DATE: May 20, 2011 in Padelford C401 at 3:30pm
ABSTRACT: Consider the set X of pairs (E,p), where E is an elliptic
curve of rank at least 2 and p is a prime such that the p-primary part
of the Shafarevich-Tate group of E is finite. It is an open problem to
prove that X is infinite! I will talk about various approaches to this
extremely difficult unsolved problem.
--
William Stein
Professor of Mathematics
University of Washington
http://wstein.org