Logic Seminar
James Freitag
UC Berkeley
Intersections of isogeny classes and varieties
Abstract: Take $ \alpha \in GL_2$ and a complex number $a$. There are at most $36^7$ complex numbers $b$ such that the elliptic curves $E_a$ and $E_b$ are isogenous and $E_ {\alpha (a)}$ and $E_ {\alpha (b)} $ are isogenous. Proving this fact along with an effective form of a special case of the Zilber-Pink conjecture uses input from model theory, differential algebra, and diophantine geometry. We will describe the proof and partial generalizations to various moduli spaces of abelian varieties.
Thursday October 16, 2014 at 1:00 PM in SEO 636