Commutative algebra, the study of commutative rings and their modules, is a central field in mathematics. It plays a fundamental role in linking together algebra, geometry, and combinatorics. Commutative algebra provides the algebraic language used within algebraic geometry, and via the

Stanley-Reisner correspondence, commutative algebraic techniques can be brought to bear upon problems in combinatorics. Number theory also has a long history with commutative algebra, where important notions like an ideal first arose out of Kummer and Dedekind’s work on factorization. Buchberger’s work in the 1960s on Gröbner bases, which relies heavily on commutative algebra, has become an integral tool within the community (and is commonly taught at the undergraduate level). In particular, the implementation of Buchberger’s work on Gröbner bases and modern computing power has enabled the commutative algebra community to experiment and generate examples and conjectures that would have been unattainable to founders of the field, like Hilbert and Noether. In recent years, commutative algebra has also found numerous applications beyond pure mathematics, to areas such as algebraic statistics, computer vision, cryptography, and coding theory. In light of all of these connections, commutative algebra is an important and active area of research.