Title: Bounding Projective Hypersurface Singularities
Speaker: Ben Castor (Washington University in St. Louis)
Speaker's URL: https://math.wustl.edu/people/ben-castor
Abstract: In this talk, I will discuss methods for studying singularities on projective hypersurfaces. 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.
URL associated with Seminar: https://research.math.osu.edu/agseminar/