Date: Monday, September 11 (09/11/2023)

Time: 4:00 PM - 5:00 PM

Location: Witmer 309

Title: Some Algebraic Techniques for Ramsey Theory

Speaker: Bryce Christopherson, Assistant Professor of Mathematics, University of North Dakota

Abstract: Ramsey theory addresses the mathematical phenomenon where the local structure of the objects in an ordered collection often becomes more regular beyond a certain bifurcation point, provided there is a suitable degree of global structure in the overall collection. Usually, a Ramsey-theoretic problem asks when this occurs, and the emergent local structure is constant in some sense (for instance, a monochromatic sub-graph). In this talk, we details some algebraic tricks for characterizing classical Ramsey numbers and use this to show that there are interesting non-constant emergent local structures in ordered collections of objects with slightly different global structure requirements.