Upcoming Events

Logic Colloquium

November 13, 2026, 4:10 PM

Evans 1015

Alex Kruckman
Wesleyan University

Structural Ramsey theory via ultrafilters on presheaves

Structural Ramsey theory starts with the observation that the classical finite Ramsey theorem can be phrased as a fact about finite linear orders and embeddings between them. We can then ask whether the theorem holds if we replace the finite linear orders with other finite structures or, more generally, with the objects of some category. In this talk, I will explain what it means for a general category to be Ramsey, and (under a very mild hypothesis on C), I will prove that the Ramsey property has a natural categorical equivalent: every presheaf on C with full support admits a “global ultrafilter”. An equivalent formulation is that every contravariant functor from C to the category of non-empty compact Hausdorff spaces has a global element (a kind of fixed-point). As applications, I obtain new proofs of (1) Scow’s theorem on finding generalized indiscernibles in model theory, and (2) the Kechris-Pestov-Todorčević theorem characterizing extreme amenability of automorphism groups of countable structures. All the necessary concepts from Ramsey theory and category theory will be explained from scratch in the talk.

Logic Colloquium

December 04, 2026, 4:10 PM

Evans 1015

Artem Chernikov
University of Maryland

TBA