Prof. Mark Sapir, Vanderbuilt University

Title: Residual finiteness of 1-related groups

Abstract: This is a joint work with A. Borisov and I. Kozakova. We prove that with probability tending to 1, a 1-relator group with at least 3 generators and the relator of length n is residually finite, virtually residually (finite p)-group for all sufficiently large p, and coherent. The proof uses both combinatorial group theory, non-trivial results about Brownian motions, and non-trivial algebraic geometry (and Galois theory).