Speaker: Richard Parker

Title: The Algebra of Curvature

Abstract: This talk follows on from Max's. By putting elements of some set on the face corners, to define valid vertices and making certain natural finiteness and uniqueness assumptions we are led "immediately" to an algebraic structure (pongo) that seems to be new.

The pongo axioms can be investigated and it is not too hard to classify pongos of small order. Each of these yield a small cancellation theory, and a method (soon to be a computer program) for solving some sort of word problem. Many of these problems have been identified - for example word problems in groups, rewrite systems, semigroups or (I think) cancellative monoids. Others seem to answer questions that mathematicians have not yet asked.