## Speaker:

John Cullinan

## Speaker Link:

## Institution:

Bard College

## Time:

Thursday, January 27, 2022 - 10:00am to 11:00am

## Location:

Zoom: https://uci.zoom.us/j/94794065234

Let G be a finite group. A representation V of G is said to be unisingular if det(1-g) = 0 for all g in G. Unisingular representations arise naturally in arithmetic via point counts on curves over finite fields and l-adic representations on abelian varieties.

In this talk we will survey recent work on properties of elliptic curves and higher dimensional abelian varieties with unisingular l-adic representations with an emphasis on explicit calculation and construction. Some of this work is joint with John Voight, Jeff Yelton, and Meagan Kenney.