Seminar:
Analysis
Event time:
Thursday, March 30, 2023 - 4:00pm
Location:
LOM 205
Speaker:
Xuwen Zhu
Speaker affiliation:
Northeastern University
Event description:
The study of “small” eigenvalues of the Laplacian on hyperbolic surfaces has a long history and has recently seen many developments. In this talk I will focus on the recent work (joint with Yunhui Wu and Haohao Zhang) on the higher spectral gaps, where we study the differences of consecutive eigenvalues up to λ2g−2 for genus g hyperbolic surfaces. We show that the supremum of such spectral gaps over the moduli space has infimum limit at least 1/4 as genus goes to infinity. The analysis relies on previous joint works with Richard Melrose on degenerating hyperbolic surfaces