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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.