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Number Theory Seminar

A Spectral Approach to Counting Problems

Chris Lutsko (Rutgers University)

Location:  Hill Center 425 and zoom
Date & time: Tuesday, 20 September 2022 at 2:00PM - 3:00PM

Abstract:  Since the early 20th century, spectral methods have been used to obtain effective counting theorems for various objects of interest in number theory, geometry and group theory. In this talk I’ll start by introducing two classical problems: the Gauss circle problem, and the Apollonian counting problem. By surveying results on these problems (and some generalizations), I’ll demonstrate how to use spectral methods to obtain effective asymptotics for some very classical problems.

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