PhD Thesis Defense: "Bounding projective hypersurface singularities"

Abstract: We first provide background necessary for understanding monodromy and spectra. We then compare several different methods involving Hodge-theoretic spectra of singularities which produce constraints on the number and type of isolated singularities on a projective hypersurface of fixed degree.  In particular, we introduce a method based on the spectrum of the nonisolated singularity at the origin of the affine cone on such a hypersurface, and relate the resulting explicit formula to Varchenko's bound. We then provide a purely combinatorial interpretation of our theorems and our conjecture.

Host: Matt Kerr