PASCA 2.0: Pan-American School in Commutative Algebra 2026

A number of significant breakthroughs have occurred in Commutative Algebra in the past couple of years. One revolution in the field is the application of perfectoid spaces to Commutative Algebra which has resolved a number of major open questions about rings of mixed characteristic, e.g., the direct summand conjecture (as solved by André) and uniform comparison of symbolic powers and ordinary powers in regular rings (established by Ma and Schwede). Three major breakthroughs on the structure of free resolutions arrived in the solutions to Stillman’s question (Ananayan and Hochster), a counterexample to the Eisenbud-Goto conjecture (McCullough and Peeva), positive solution to the Buchsbaum-Eisenbud-Horrocks rank conjecture (Walker), and positive solution to Vasconcelos' conjecture (Briggs). Various techniques such as the Frobenius map, differential operators, perfectoid spaces, convex geometry, and representation theory, have found powerful new applications in the study of classical topics in Commutative Algebra such as singularities, symbolic powers, and local cohomology. The basic scientific purpose of this school is to connect students with a range of questions and techniques of current interest in Commutative Algebra.