Conference: Homological Commutative Algebra And Related Topics

This award supports participation in an international conference on homological commutative algebra and related topics at Georgia Southern University, Armstrong Campus in Savannah in summer of 2025. This goals of this conference are: (1) to support research in algebra and related topics in our region; (2) to promote excellence in research and scholarship among faculty from a diverse mathematical background related to commutative algebra at the institutions in the Southeast of the United States; (3) to encourage students to attend a world class conference in order to become acquainted with experts and build a successful career; (4) to bring together speakers from diverse mathematical fields that are connected through homological commutative algebra; and (5) to promote diversity and inclusion by working to ensure significant participation of researchers from underrepresented groups.

The conference will consist of a series of talks given by senior faculty, junior faculty, postdoctoral researchers, and students.

Algebraic geometry, number theory, and invariant theory are the primary fields of applications of commutative algebra. In its modern shape, commutative algebra originated in the works of several well-known mathematicians, especially Dedekind, Hilbert, Kronecker, Krull, Kummer, and Noether, during the nineteenth century and was vastly developed later in the outstanding work of Grothendieck on modern algebraic geometry and algebraic topology.

In the 1950's, homological algebra (that originates from algebraic topology) made its way into the commutative algebra toolbox in the works of Auslander-Buchbaum and Serre to help with solving open problems in commutative algebra. Connections between commutative algebra, representation theory, combinatorics, and deformation theory appeared in the past century in numerous places as well.

This conference focuses on topics in the above-mentioned fields that are tightly connected (and can be applied) to fundamental problems in homological commutative algebra such as problems related to the betti numbers and minimal free resolutions, relative homological algebra, properties of subcategories of the module category, and vanishing of homology and cohomology modules. The URL of the event is under construction. However, a primary version of it can be found at

https://sites.google.com/georgiasouthern.edu/commutative-algebra-2025?usp=sharing

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.