汇报标题 (Title)：离散环面特点值的多沉性（Eigenvalue mutiplicities of discrete torus）
汇报人 (Speaker)： 赵永强 副教授（西湖大学）
汇报功夫 (Time)：2023年8月29日(周二) 10:00
汇报地址 (Place)：校本部F309
约请人(Inviter)：毛雪峰 教授
主办部门：理学院数学系
汇报提要：Abstract： It is well known that the standard flat torus T^2=R^2/Z^2 has arbitrary large Laplacian-eigenvalue multiplicies. Consider the discrete torus C_N * C_N with the discrete Laplacian operator; we prove, however, its eigenvalue multiplicities are uniformly bounded for any N, except for the eigenvalue one when N is even. Our main tool to prove this result is the beautiful theory of vanishing sums of roots of unity. In this talk, we will give a brief introduction to this theory and outline a proof of the uniformly boundedness multiplicity result. This is a joint work with Bing Xie and Yigeng Zhao.
