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https://sites.google.com/view/kutraceformula1
제목: Lecture series on Selberg trace formula for SL_2(R)
장소: 고려대학교 아산이학관 526호
연사: 이민 Min Lee (University of Bristol)
일정:
8월 20일 4시 – 5시 15분(강연 1)
8월 21일 4시 – 5시 15분(강연 2)
8월 22일 10시 30분 – 11시 45분(강연 3), 1시 30분 – 2시 45분(강연 4)
8월 23일 10시 30분 – 11시 45분(강연 5), 1시 30분 – 2시 45분(강연 6)
내용:
The spectral theory of non-holomorphic automorphic forms began with H. Maass in the 1940s. A Maass form is a function on a hyperbolic surface which is also an eigenfunction of the Laplace-Beltrami operator. Although Maass discovered some examples by using Hecke L-functions, in general, the construction of explicit examples of Maass forms remains mysterious. Even the existence of such functions (except the examples discovered by Maass) was not clear.
In 1956, A. Selberg introduced his famous trace formula, now called the Selberg trace formula, which relates the spectrum of the Laplace operator on a hyperbolic surface to its geometry. By using his trace formula, Selberg obtained Weyl’s law, which gives an asymptotic count for the number of Maass forms with Laplacian eigenvalues up to a given bound.
Let \mathbb{H} be the Poincar\’e upper half plane and \Gamma be a congruence subgroup of $SL_2(\mathbb{Z}). The aim of this short course is to develop Selberg’s trace formulas for \Gamma \backslash \mathbb{H} and study their applications.
