Unlikely intersection and the eigenvalue multiplicity of discrete tori

Speaker: 赵永强 教授，四川大学

Inviter: 周喆

Title: Unlikely intersection and the eigenvalue multiplicity of discrete tori

Language: Chinese

Time & Venue: 2026.10.23 13:00-13:50 #腾讯会议：145-307-270

Abstract: It is well known that the standard flat torus T^2=R^2/Z^2 has arbitrarily large Laplacian-eigenvalue multiplicities. We prove, however, that 24 is the optimal upper bound for the multiplicities of the nonzero eigenvalues of a 2-dimensional discrete torus. For general higher dimension discrete tori, we characterize the eigenvalues with large multiplicities. As consequences, we get uniform boundedness results of the multiplicity for a long range and an optimal global bound for the multiplicity.