### Hyperbolic lattice point counting in unbounded rank

Ergodic Theory and Dynamical Systems Seminar

18th April 2024, 3:30 pm – 4:30 pm

Fry Building, 2.04

Counting lattice points in balls is a classical problem which goes back to Gauss in the Euclidean setting. In the hyperbolic setting this corresponds to counting matrices of norm T in \SL_n(\Z). For n=2 the record belongs to Selberg in the early 1980s. In a recent paper with Valentin Blomer we extend Selberg's method to higher rank (n > 2) and thus improve on the best known bounds for the hyperbolic lattice point counting problem in higher rank. In the first half of this talk I will introduce the problem, summarize the history, and give a sketch of Selberg's method. Then in whatever time remains, I will give a sketch of the proof of Blomer and myself.

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