MATH 7670: Monomial Resolutions (spring 2009)

Instructor: Irena Peeva

In the early 1960's, Kaplansky posed the problem of finding a minimal free resolution of a monomial ideal over a polynomial ring. Despite the helpful combinatorial structures in monomial ideals, this problem turned out to be very difficult. The study of monomial resolutions is at the interface of commutative algebra, topological combinatorics, and computational algebra; it relies on reach and beautiful interplay between these fields. We will cover several topics: the Stanley-Reisner correspondence, Alexander duality, least common multiple lattices, cellular resolutions, linear resolutions, generic resolutions, lex ideals, edge ideals, and Hilbert functions.