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Finite-volume hyperbolic 3-manifolds are almost determined by their finite quotient groups


In this talk, I will report a recent result of mine showing that the profinite completion of the fundamental group determines finite-volume hyperbolic 3-manifolds up to finitely many possibilities.  I plan to spend most of the time discussing background of that problem, so the talk should be accessible to audience with general math background.

About the speaker

Yi Liu is a professor in mathematics at Peking University.  He completed his PhD degree in 2012 from the University of California, Berkeley, under the supervision of Ian Agol.  He then moved to Caltech and in 2015 he joined the Beijing International Center for Mathematical Research.  His research centers around the fundamental ideas of Thurston on the structure of hyperbolic 3-manifolds, and the geometry and dynamics of their finite coverings.  Yi Liu received the Qiu Shi Outstanding Young Scholar Award in 2017 and the National Science Fund for Distinguished Young Scholars in 2019.