### Lectures & Talks

[PMI Number Theory Seminar] - Numerical Computations with the Selberg trace formula |
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Date: 2017 Apr 10 18:00 - 19:00 |

Speaker: Min Lee (University of Bristol) |

Place: Math. Bldg. 404 |

첨부파일: poster_Min Lee.pdf |

PMI Number Theory seminar Speaker: Dr Min Lee (University of Bristol) Date and Time: April 10 (Monday) 6pm-7pm Math build room 404 Title: Numerical Computations with the Selberg trace formula Abstract: Among the most well-known examples of L-functions are the Riemann zeta function and the L-functions associated to classical modular forms. Less well known, but equally important, are the L-functions associated to Maass forms, which are eigenfunctions of the Laplace-Beltrami operator on a hyperbolic surface. Named after H. Maass, who discovered some examples in the 1940s, Maass forms remain largely mysterious. Fortunately, there are concrete tools to study Maass forms: trace formulas, which relate the spectrum of the Laplace operator on a hyperbolic surface to its geometry. After Selberg introduced his famous trace formula in 1956, his ideas were generalised, and various trace formulas have been constructed and studied. However, there are few numerical results from trace formulas, the main obstacle being their complexity. Various types of trace formulas are investigated, constructed and used to understand automorphic representations and their L-functions from a theoretical point of view, but most are not explicit enough to implement in computer code. Having explicit computations of trace formulas makes many potential applications accessible. In this talk, I will explain the computational aspects of the Selberg trace formula for GL(2) for general levels and applications towards the Selberg eigenvalue conjecture and classification of 2-dimensional Artin representations of small conductor. |