[Reading group on spectral geometry] On the distribution of eigenvalues of the Laplacian on a compact surface

Conference room, 1st floor!

In this talk, we will discuss some results on the distribution of eigenvalues of the Laplacian on a compact Riemann surface. In particular, we will study how many eigenvalues can lie in the interval [0, 1/4], and whether such eigenvalues can occur at all. The proofs rely on Cheeger’s inequality and the minimax principles introduced in the previous talk, as well as on some facts about pair-of-pants decompositions of surfaces.