Conference: Algebra and Arithmetic from Model Theory

This project supports the participation of US-based researchers in the conference A85: algebra and arithmetic from model theory to be held at the International Centre for the Mathematical Sciences in Edinburgh, Scotland from May 11th to May 15 of 2026. The conference will bring together specialists from the algebraic, arithmetic and the pure model theory communities to exposit the latest results on the connections between model theory, arithmetic, and algebra. Participation by American researchers and scientists is essential for maintaining our leading position within the field of model theory and its applications to other parts of mathematics through the knowledge to be acquired, potential new collaborations, and the education and training afforded to doctoral students and early career researchers.

More technically, the conference and attendant discussions focus on the following intertwined aspects of model theory and its applications: Algebra from classification theory, Measurable structures, Fields with operators, Definability in natural rings and fields, O-minimality and Ax-Schanuel-type problems, Peano arithmetic, and Model theory and categorical logic. For example, it has been known since the early 1970s that classification theoretic hypotheses such as superstability have strong consequences on the structure of groups and fields. Contemporary research extends the classification theoretic tameness / algebraic simplicity correspondence to much more sophisticated classes. In another direction, functional transcendence theorems in the style of Ax's Schanuel conjecture have been proven using methods from the model theory of differential fields and from o-minimality.
The workshop website is at https://icms.ac.uk/activities/workshop/a85/

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.

Award Number: 2619243
Principal Investigator: Thomas Scanlon
Funds Obligated: $36,376
State: CA