Speaker: Guo Jingwei, Professor, School of Mathematical Sciences, University of Science and Technology of China
Date: Dec. 18, 2017
Time: 10 a.m.—11 a.m.
Location: Room 1044, Block B, Zhixin Building, Central Campus
Sponsor: School of mathematics, SDU
Abstract:
Y. Colin de Verdiere proved in 2011 that the remainder term is of order $O(lambda^{2/3})$ in the two-term Weyl formula for the eigenvalue counting function for the Dirichlet Laplacian associated with the planar disk. In this talk, the speaker would Colin de Verdiere’s result and method, and then explain how to improve his bound by using harmonic analysis and prove a new bound $O(lambda^{2/3-1/495})$. This problem is closely related to the lattice point problem from number theory.
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Edited by: Zhang Kiage and Song Yijun