Talk Announcement: Eyal Goren at MSR on Monday 12/15 13:30

[Dan Shumow]

You are invited to attend...
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WHO: Eyal Goren
AFFILIATION: McGill University
TITLE: Singular Moduli
WHEN: Mon 12/15/2008
WHERE: 99/2535 Research Conference Room
TIME: 1:30PM-3PM
HOST: Kristin Lauter
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ABSTRACT:
The values of the elliptic modular function $j$ at imaginary quadratic
numbers $\tau$ are called singular moduli. They are of fundamental
importance in the study of elliptic curves and in algebraic number
theory, including the study of elliptic curves over finite fields.
The theorem of Gross and Zagier has provided striking congruences
satisfied by these numbers. Various aspects of this theorem were
generalized in recent years by Jan Bruinier and Tonghai Yang and by
Kristin Lauter and the speaker. These may be viewed as concerning the
theory of curves of genus 2 and their singular moduli that are
obtained by evaluating the Igusa invariants at certain 2x2 complex
matrices $\tau$. I will describe some of the recent ideas introduced
in this area and, time allowing, describe some current projects.

BIO:
Eyal Goren is an associate professor of mathematics at McGill
University. His area of expertise is arithmetic geometry and in
particular modular forms and moduli spaces of abelian varieties and
their various applications to class field theory, p-adic modular
forms, Galois representations and expander graphs. See
http://www.math.mcgill.ca/goren/ for publications, students and other
information.