Szego Seminar: "Spectral Combinatorics"

Abstract: In singularity theory, the spectrum serves as a powerful invariant for understanding the underlying mixed Hodge structure associated to the cohomology of the Milnor fiber of the singularity. Rather than understand the underlying structure, we will view spectra simply as combinatorial objects, namely objects in the free abelian group generated by rational numbers. We show several combinatorial approaches for calculating the spectra of a particular set of isolated singularities, and will show how these are used to bound the number and type of isolated singularities which may be present on any projective hypersurface. We end with a conjecture, based solely around combinatorial arithmetic that two methods of bounding are equivalent.

Host: Nathan Wagner