Title: Profinite rigidity
Speaker: Alan Reid (Rice University)
Abstract: It is an old and natural idea to distinguish finitely presented groups via their finite quotients. For instance, one might prove that a group presentation does not represent the trivial group by exhibiting a map onto a non-trivial finite group. A natural way to organise finite quotients of a finitely generated group G is via its profinite completion $\widehat{G}$. Say that a finitely generated residually finite group is profinitely rigid if whenever $H$ is another such group and $\widehat{H}\cong \widehat{G}$ then $H\cong G$. This talk will survey recent work on profinite rigidity in both positive and negative directions through the lens of low-dimensional topology (so the groups in question are free groups, surface groups and 3-manifold groups).
Bio: Alan Reid received his Ph.D. at the University of Aberdeen in 1988. He held several academic positions, including Instructor at Ohio State and Royal Society University Research Fellow at Cambridge, before becoming Assistant Professor at The University of Texas in 1998 and gaining the title Pennzoil Company Regents Professor in 2005. He was elected Fellow of the AMS in 2012 and recently became Edgar Odell Lovett Professor of Mathematics at Rice University. His research on hyperbolic manifolds, discrete groups and low-dimensional topology has earned him numerous accolades, including an invitation to speak at the 2018 I.C.M. in Rio de Janeiro.
Colloquium URL: https://web.math.osu.edu/colloquium/
