[Turkmath:7775] Talk(s) by Karl Rubin on June 21st

[Kazim Buyukboduk]

Dear All,

Prof. Karl Rubin will give two talks on June 21st (Tuesday) starting
at 14:00, at the Sabanci University Karakoy Iletisim Merkezi; see
below for a link to a map. All are cordially invited to attend.

Karl Rubin (http://en.wikipedia.org/wiki/Karl_Rubin) is a leading
expert in the study of elliptic curves and he has obtained some of the
most spectacular results towards the resolution of the Birch and
Swinnerton-Dyer Conjecture -- one of the Clay Millenium Problems. The
details of his talks may be found below.

Best Wishes,

Kazim Buyukboduk

PS: Karl Rubin's visit is partially supported by grants
TUBITAK-107T897 and Marie Curie FP7-IRG 230668.

Speaker: Prof. Karl Rubin
Date: June 21st, 2011 (Tuesday)
Time: 14:00-15:00 (General Talk); 15:00-15:30 (Break); 15:30-16:30
(Less General Talk)
Location: Sabanci University Karakoy Iletisim Merkezi
(http://www.sabanciuniv.edu/tr/?kampus_hayati/hizmet_ve_olanaklar/karakoy_iletisim_merkezi_adres_ve_ulasim_krokisi.html)

Title (General talk):  Ranks of elliptic curves

Abstract: The rank of an elliptic curve is a measure of the size of
the set of rational points on the curve.  In recent years there has
been spectacular progress in the theory of elliptic curves, but the
rank remains very mysterious.  Even basic questions such as how to
compute the rank, or whether the rank can be arbitrarily large, are
not settled.  In this lecture we will introduce elliptic curves and
discuss what is known, as well as what is conjectured but not known,
about ranks.


-----------------------------

Title (Less general talk):  Ranks of elliptic curves in families of
quadratic twists.

Abstract: In this talk I will discuss some current joint work with
Klagsbrun and Mazur on the distribution of 2-Selmer ranks in families
of quadratic twists of elliptic curves.  We study the density of
twists with a given 2-Selmer rank, and obtain some surprising results
on the fraction of twists with 2-Selmer rank of given parity.  Since
the 2-Selmer rank is an upper bound for the Mordell-Weil rank, this
work has consequences for Mordell-Weil ranks in families of quadratic
twists.