Joshua Eike

I am in my seventh year, studying geometric group theory with Ruth Charney. Group actions on metric spaces are traditionally used to study the geometric properties of the metric space. More recently, geometric group theorists have found ways to deduce properties of the group from the geometry of the spaces it acts on. These spaces are quite beautiful because they are so rich in symmetries. Imagine a labyrinth with passages corresponding to moves on a Rubik's cube; then extend it out infinitely (and make the triangles skinny). That is the sort of geometry I like to study.

My office is Goldsmith 104 and my email is jeike@brandeis.edu