Speaker
Ryoki Endo
(Niigata)
Description
A conjecture of Laugesen and Siudeja asserts that the second Dirichlet eigenvalue of the Laplacian is simple for every non-equilateral triangle. This talk presents a computer-assisted proof of this conjecture. The argument combines rigorous numerical eigenvalue bounds with two methods for singular regimes in the space of triangles: a difference quotient approach for nearly equilateral triangles, where the relevant eigenvalues form a tight cluster, and an asymptotic analysis for collapsing triangles, where the eigenvalues diverge.