I will discuss recent work with Farsi and Seaton in which we introduce the -extension of the spectrum of the Laplacian of a Riemannian orbifold, where is a finitely generated discrete group.This extension, called the -spectrum, is the union of the Laplace spectra of the -sectors of the orbifold, and hence constitutes a Riemannian invariant that is directly related to the singular set of the orbifold. In our work, we compare the -spectra of known examples of isospectral pairs and families of orbifolds and demonstrate that in many cases, isospectral orbifolds need not be -isospectral. We additionally prove a version of Sunada's theorem that allows us to construct pairs of orbifolds that are -isospectral for any choice of .
-extensions of the spectrum of an orbifold Sponsored by the Meyer Fund
Apr. 09, 2015 3pm (Webber 20…
Algebraic Geometry
Csar Lozano Huerta (Harvard)
X
In this talk, I will focus on compactifying the family of smooth quadric hypersurfaces in projective space using tools from the Minimal Model Program. I will also discuss work in progress on the Hilbert scheme of curves in projective 3-space which borrows ideas and properties from the quadric hypersurface case.