Commutative Algebra and Algebraic Geometry: The Fellowship of the Ring: Algebraic Aspects of Lattice Polytopes
Seminar | October 3 | 3:45-4:45 p.m. | 939 Evans Hall
Benjamin Braun, University of Kentucky
To a lattice polytope P one can associate a graded semigroup algebra K[P]. A well-known theorem due to Hochster implies that K[P] is Cohen-Macaulay, and since the 1970's there has been a fruitful interaction between combinatorics and commutative algebra using this construction. In this talk I will discuss (1) several open problems regarding the Hilbert series of K[P] (often referred to as the Ehrhart series of P) and (2) recent joint work with my student Brian Davis regarding free resolutions of K over K[P] and rationality of the associated Poincare series for a specific family of lattice polytopes.