Speaker: Yongqiang ZHAO (West Lake University)

Time： May 25, 16:00-17:00

Place： 5406

Title： Eigenvalue mutiplicities and vanishing sums of roots of unity

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.