Combinatorics Seminar - Soohyun Park
Speaker: Soohyun Park
Title: Anti-Ramsey theory, lattice points on polytopes, and Hodge structures on toric hypersurfaces
Abstract: The relation between the topics in the title is obtained by combining combinatorial interpretations of the simplicial chromatic polynomial. A reinterpretation of the definition yields the connection to edge colorings of graphs avoiding monochromatic colorings of specified subgraphs. As for lattice point counts on polytopes and Hodge structures on toric hypersurfaces, we specialize an expression of the polynomial in terms of the h-vector of an auxiliary simplicial complex.