Higher-Order Stability Through the Regularity Lens

The proposed project sits at the interface of combinatorics and model theory, two branches of pure mathematics that can be said to have their common origin in Ramsey's theorem dating back to the 1930s.

In recent years, a powerful connection has emerged between regularity lemmas, a key tool in extremal and arithmetic combinatorics with far-reaching applications, and stability, a notion of tameness that has been central to model theory since the 1960s.

The present project aims to fully explore and capitalise on the intricate relationship between higher-order generalisations of both regularity and stability, initiated in recent joint work of the applicant.