Title: Generalizing the Taylor complex and pruned complexes of monomial ideals in rational normal surfaces

Abstract:  We will first review the Taylor complex for monomial ideals over polynomial rings and how one can use discrete Morse Theory to prune these complexes to obtain free resolutions of monomial ideals in polynomial rings.  We will then discuss how to form a Taylor-like complex for rational normal surfaces and how one can modify these complexes using Discrete Morse Theory.