Commutative Algebra, Representation Theory, and Other Interactions

Date: 25 January - 19 February 2027

Location: Simons Laufer Mathematical Sciences Institute

The AxIOM seeks to build on the many interactions between commutative algebra, representation theory and other areas of mathematics. The focus will be new developments in these subjects, many inspired by the 2024 Commutative Algebra program.  Some of the major themes to be covered are linkage theory, syzygies, and new interactions between commutative algebra and algebraic number theory.

AxIOM are month-long research programs designed to accelerate innovation and introduce transformative ideas into the mathematical sciences. These focused programs are meant to create a dynamic environment for intensive collaboration, where researchers converge to push boundaries, explore bold ideas, and catalyze breakthroughs. Each program centers on a timely theme, from foundational mathematical challenges to fast-moving intersections with fields like artificial intelligence, data science, biology, physics, and medicine. Some programs will amplify the momentum of recent “hot topic” workshops, or build on the outcomes of semester-long programs, while others will chart new territory—engaging with emerging technologies or revisiting classical problems through a modern lens. These one-month intensives, taking place throughout Spring, are uniquely structured to ignite progress on cutting-edge problems, foster cross-disciplinary collaboration and knowledge exchange, translate recent mathematical advances into real-world impact, and seed new research directions and long-term collaborations.

Professor Craig Huneke (University of Virginia) has been appointed as a Clay Senior Scholar to participate in this program.

CMI Enhancement and Partnership Program

Image by Herwig Hauser