Let G and H be two finite groups. Does there exist a 3-manifold whose fundamental group admits G as a quotient but not H? We prove a theorem that determines the answers to questions of this type. The proof, when we need to show that a 3-manifold with certain properties exists, relies on a probabilistic argument - we estimate the probability that a random 3-manifold (according to a distribution defined by Dunfield and Thurston) has those properties. Our methods thus mix topology, group theory, and probability, and they were inspired by work in number theory. This talk will discuss the connections to those fields. This is joint work with Melanie Wood.

https://umich.zoom.us/j/97472072420?pwd=T0w3MHpEd2NRMlQ4WjFpdUdnN3BGUT09

Meeting ID: 974 7207 2420
Passcode: UMColloq
Speaker(s): Will Sawin (Columbia University)