Date/Time
Date(s) - 08/10/2024
11:30 am - 12:30 pm

Location: HH – 312 Tuesday, October 8, from 11:30 AM – 12:30 PM.

Title: Arithmetic dynamics in toric geometry.

Speaker: Brett Nasserden

Abstract:The study of the automorphism group of a projective variety provides insight into the geometry of that variety. When we broaden our scope to all surjective endomorphisms of a variety, we uncover an interesting relationship: the existence of a surjective endomorphism that is not an automorphism often implies special geometric characteristics for X.

In this we will illustrate this principle by studying surjective endomorphisms of projectivized toric vector bundles. Specifically we will discuss how to construct surjective maps from the perspective of transition functions, and explain how this may be applied in arithmetic dynamics to prove new instances of the Kawaguchi-Silverman conjecture.