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Texas A&M Number Theory Seminar

Department of Mathematics
Blocker 220
Wednesdays, 1:45–2:45 PM

Junehyuk Jung

Texas A&M University

Wednesday, October 18, 2017

Blocker 220, 1:45PM

Title: Counting immersed totally geodesic surfaces via arithmetic means

Abstract: The prime geodesic theorem allows one to count the number of closed geodesics having length less than X in a given hyperbolic manifold. As a naive generalization of the prime geodesic theorem, we are interested in the the number of immersed totally geodesic surfaces in a given hyperbolic manifold. I am going to talk about this question when the underlying hyperbolic manifold is an arithmetic hyperbolic $3$-manifold corresponding to a Bianchi group SL(2,O_{-d}), where O_{-d} is the ring of integers of Q[sqrt{-d}] for some positive integer d.