David Holmes (Leiden)

02/02/2017 - W01 0-012 (Wechloy), 4 pm

Rational torsion points and Gromov-Witten theory

I will try to explain how I started working to understand rational torsion points on abelian varieties, and ended up studying problems related to string theory. The key player in this story is the double ramification cycle (DRC). For a number theorist, the DRC can behave like a generalisation of a modular curve to abelian varieties of higher dimension, and understanding its rational points would give a lot of information about rational torsion points. The DRC is also of interest in enumerative geometry, for example as a prototype for defining Gromov-Witten invariants of Artin stacks. After explaining some of this story, I will describe new results on compactifications and integral models of the DRC.