Student Harmonic Analysis and PDE Seminar (HADES): Self-adjoint extensions of Laplace operators on singular geometry

Seminar | April 30 | 3:40-5 p.m. | 740 Evans Hall

 Xuwen Zhu, UC Berkeley

 Department of Mathematics

Spectral geometry aims at understanding how geometry influences the spectrum of geometrically related operators such as the Laplace operator. I will first talk about Von Neumann theory on classification of self-adjoint extensions of symmetric operators, and in particular focus on the Laplace operator on metrics with conical singularities. Then I will give a survey on how geometry (e.g. curvature and monodromy) and choice of self-adjoint extensions influence the spectrum, and discuss some results related to translation surfaces and spherical conical metrics.