Initial Ideals of Toric Ideals: Recent Results and Open Problems
Abstract:Toric ideals provide a useful tool for studying problems in the intersection of convex geometry and commutative algebra. They have important applications to integer programming, computational statistics and hypergeometric differential equations. Many of the properties of toric ideals can be understood from their initial ideals which are simpler in structure and have many special algebraic and topological properties that set them apart from general monomial ideals. However, it remains an open problem to characterize those monomial ideals that appear as toric initial ideals. In this talk I will discuss some of the known results toward such a characterization and present some of the open issues.