Conference: Workshop in Commutative Algebra

Purdue University, West Lafayette IN

Investigators

Abstract

This grant provides funding for US-based researchers to participate in a two-week long scientific school and workshop that will take place May 2-12, 2023 at the International Centre for Theoretical Physics (ICTP) in Trieste, Italy. The focus of the meeting will be commutative algebra and algebraic geometry in prime characteristic and mixed characteristic, an area of pure mathematics that has seen fantastic advances in recent years. The ICTP is focused on supporting advanced studies and scientific research in developing countries. Support from this grant will give scientists from the US the opportunity to participate in the meeting and to interact and collaborate with a cohort of researchers from the developing world, as well as other leading international experts in the field. In more detail, with the inception of tight closure theory in the 1980s, commutative algebra and algebraic geometry in prime characteristic has become an important and vibrant field of mathematics. It has lead to vast improvements and simpler proofs of many results. It has also provided notions of singularities that are defined purely algebraically but correspond, somewhat mysteriously, to types of singularities that appear in birational geometry over the field of complex numbers. Commutative algebra in mixed characteristic, the study of rings that do not contain any field, has seen the introduction of new methods and spectacular advances through the recent solution of the celebrated homological conjectures. The scientific school and workshop at ICTP will give students early-career mathematicians an opportunity to get involved in these fast moving areas, and more experienced researchers will have a chance to initiate new trans-national collaborations. The website for the scientific school is https://indico.ictp.it/event/10200. The website for the workshop is https://indico.ictp.it/event/10276. 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.