Event time:

Tuesday, October 3, 2023 - 4:15pm

Location:

KT 219

Speaker:

Gal Yehuda

Speaker affiliation:

Yale University

Event description:

We prove that the set of growth-rates of subgroups of a rank 2 free group is dense in [1,3]. Our main tool is the probabilistic method: we prove that for any \alpha \in [1,3], there exists a sequence of distributions {P_N} where P_N is a distribution over graphs with N vertices such that

1. For any N and any graph G in the support of P_N, every node in G has either degree 2 or 4, and

2. Pr[gr(G) = \alpha + o(N)] >= 1-o(N), where gr(G) is the growth rate of the universal cover of G.

This is a joint work with Mixalis Louvaris and Daniel Wise.