Workshop Proposal: Elliptic Curves over Q(\sqrt{5})

University Of Illinois At Chicago, Chicago IL

Investigators

Abstract

A workshop on elliptic curves over a real quadratic extension of the rational numbers will take place April 27-29, 2012 at the University of Illinois at Chicago. The organizers of this workshop are William Stein (University of Washington at Seattle) and Ramin Takloo-Bighash (University of Illinois at Chicago). The invited speakers are Jennifer Balakrishnan (Harvard), Jonathan Bober (University of Washington at Seattle), John Cremona (Warwick), Lassina Dembele (Warwick), Noam Elkies (Harvard), Edray Goins (Purdue), Matthew Greenberg (Calgary), Richard Pinch, Kenneth Ribet (UC Berkeley), William Stein (UW Seattle), Nike Vatsal (UBC), and John Voight (University of Vermont). This is part of the annual Oliver Atkin Memorial Lecture and Workshop at UIC. The theme of the workshop is the theoretical and computational aspects of elliptic curves over totally real fields, Hilbert modular forms, and the arithmetic of elliptic curves in general. The website of the workshop is http://www.math.uic.edu/~rtakloo/atkin2012.html Elliptic curves are of fundamental interest in number theory. The theory of these objects over the field of rational numbers is starting to look like a coherent theory, but as soon as one steps away from rational numbers our understanding of these objects becomes extremely patchy. This workshop focuses on the theory of elliptic curves on a very simple field different from the field of rational numbers. We hope that bringing together experts working in the area would create an environment in which to exchange ideas and to start new projects which will hopefully lead to a better understanding of these fundamental objects.