Sarfraz Ahmad

Combinatorial Commutative Algebra deals with an interaction between Combinatorics, Discrete Geometry and Commutative Algebra. It is driven by the study of simplicial complexes, partially ordered sets and integer polytopes (i.e., polytopes whose vertices have integer coordinates). The combinatorics of these objects is known to encode algebraic invariants of the Stanley-Reisner rings associated to simplicial complex and toric rings associated to integer polytopes. The combinatorial nature of the invariants makes them more easily accessible to beginning graduate students. It allows them to capture the more complicated algebraic invariants through concrete combinatorial examples. I find this area of research very interesting because it turn questions raised in algebra inspire combinatorial problems that are appealing on their own right.