Cornell Math - MATH 735, Spring 2007

MATH 735: Hilbert Functions, and Resolving Monomial and Toric Ideals (Spring 2007)

Instructor: Irena Peeva

Meeting Time & Room

The lectures will focus on two topics: Hilbert functions, and resolutions of Monomial and Toric Ideals.

Tentative list of topics on Hilbert Functions: Hilbert functions of graded ideals in a polynomial ring; Lexicographic ideals, Compression, Macaulay's Theorem, Gotzmann's Persistence Theorem, Green's Theorem, Maximal Betti numbers of lex ideals, Hilbert functions over exterior algebras and Kruskal-Katona's Theorem, Quotient rings and Clements-Lindstrom's Theorem, Open problems and Conjectures.