Speaker: Max Neunhöffer

Title: Algorithmic Generalisations of Small Cancellation Theory

Abstract: In this talk I will report on joint work in progress with Stephen Linton, Richard Parker and Colva Roney-Dougal. We want to generalise classical small cancellation theory (SCT) in an algorithmic direction.

SCT used to be a fixed set of conditions to test on a finite presentation of a group. If these conditions are fulfilled, SCT proves that the group is infinite, word-hyperbolic and provides a solution to the word problem.

I will describe our ideas to generalise this beyond recognition. In the end, the computer will analyse a finite presentation of a group or other algebraic structure and come up with a SCT-like proof showing that the algebraic structure is infinite and providing a solution to the word problem.