# Nicole Looper (UIC)

Date

Friday February 16, 20242:30 pm - 3:30 pm

Location

Jeffery Hall, Room 234## Math & Stats Department Colloquium

**Friday, February 16th, 2023**

**Time:** 2:30 p.m. **Place: **Jeffery Hall, Room 234

**Speaker:** Nicole Looper (UIC)

**Title:** Arakelov–Green’s functions in dynamics and number theory

**Abstract:** This talk will discuss how Green's functions, as well as their dynamical adaptation by Baker and Rumely, have been leveraged in studying arithmetic dynamical systems. Key to the utility of these functions is their connection to the equidistribution of points of small canonical height, along with the fact that Elkies-type lower bounds on their averages may be proven in a way that is nicely uniform across the spaces and dynamical systems in question. After sketching the background, I will talk about recent progress in adapting these ideas to the higher-dimensional setting, which has been far less explored up to this point. As time allows, I will close with natural questions for further exploration and an application to the Lehmer conjecture for abelian varieties.

**Bio:** Prof. Nicole Looper received her PhD from Northwestern University. She then held post-doctoral positions at Cambridge and Brown University before joining the University of Illinois Chicago as an assistant professor. Prof. Looper received the 2020 AWM Dissertation Prize for her thesis work, the 2022 Brin Dynamical Systems Prize for Young Mathematicians and a Sloan fellowship in 2023. Her research lies at the intersection of number theory and dynamical systems.