Lenny Fukshansky's Abstract

 

Claremont Mathematics Weekend

 

Sponsored by Claremont Colleges

 

January 30 - 31, 2016

 

Speaker: Lenny Fukshansky
Title: Arithmetic Lattices and Elliptic Curves
Abstract:

We will review the classical construction of elliptic curves from lattices in the plane, focusing specifically on the important class of arithmetic lattices. To this end, we will discuss the connection between certain properties of elliptic curves and their corresponding lattices, as well as provide counting estimates for planar arithmetic lattices, up to a certain natural equivalence. Bridging arithmetic geometry and analytic number theory, this talk will feature group actions, fundamental domains, the modular j-invariant, and height functions. This is joint work with Pavel Guerzhoy (Hawaii) and Florian Luca (Wits, South Africa).