Conference: Horizons in Descriptive Set Theory

This award supports participants of conference "Horizons in Descriptive Set Theory" that will take place at Cornell University from October 10-12, 2026. Descriptive set theory is a branch of mathematics which develops tools for understanding and manipulating infinite sets, particularly in settings where other mathematical structure, such as algebra or geometry, is either not present or minimized. These methods have nevertheless proved very fruitful in yielding new insight into other areas of mathematics such as algebra, geometry, dynamics, and probability. The conference will provide opportunities for researchers to network, for fields outside of set theory to learn of new developments in descriptive set theory, and for set theorists to explore new opportunities for applications for their methods, as well to learn techniques from other fields of mathematics. Descriptive Set Theory has long been at the forefront of applications of set theory to other fields of mathematics. This has been especially true of Ergodic Theory, Topological Dynamics, and Combinatorics. Historically this interaction has been fruitful in both directions, with each field learning techniques from the other and with the applications of descriptive set theory to other fields shaping its own future directions. The conference Horizons in Descriptive Set Theory will showcase the state of the art in applications of descriptive set theory with an eye for future directions in the field. It with bring together senior leaders and rising stars working in descriptive set theory and in fields with which it interacts. The conference will feature 16 invited speakers--7 of which have given invited talks at the International Congress of Mathematicians. The speakers include both people working primarily within Descriptive Set Theory, as well as those working in Ergodic Theory, Topological Dynamics and Combinatorics. Topics covered include classical ergodic theory, orbit equivalence relations of group actions, the dynamics of automorphism groups of countable structures and other transformation groups, structural Ramsey theory, and constraint satisfaction problems. Some of these connections are emerging, while others are well studied but remain fertile. More information about the meeting can be found on the conference website https://math.cornell.edu/horizons-descriptive-set-theory . 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.