Uniform simplicity, group actions on the circle, and Ulam width (Yash Lodha, University of Hawaii at Manoa)

18.03.2025 10:30

A fundamental notion in group theory, which originates in an article of Ulam and von Neumann from 1947 is uniform simplicity.
A group is uniformly simple if there is a natural number n such that for each pair of nontrivial elements f,g, the element f can be expressed as a product of at most n conjugates of g, g^{-1}. The smallest such n is called the Ulam width.
In this talk, I will describe this notion and describe for each natural number n, a construction of a group of homeomorphisms of the circle that is finitely presented, infinite and simple, whose Ulam width is larger than n.

Lieu

Bâtiment: Conseil Général 7-9

Room 1-05, Tuesday 18.03.2025, Séminaire "Groupes et géométrie"

entrée libre