Joint Colloquium PMath+CO - Nick Olson-Harris

Title: On the Theory of the Analytical Forms called Trees

Abstract:

Trees are among the most fundamental of combinatorial structures. Nowadays they appear all over mathematics and computer science, but this has not always been the case. Trees were first introduced, at least under that name, in an 1857 paper of Cayley by the same title as this talk. While the main result of the paper was combinatorial in nature, his motivation was quite different: he was interested in expressions for compositions of differential operators. In this talk I will explain how trees appear in this context from a modern perspective. The key is the connection between trees and pre-Lie algebras. (No prior knowledge of the latter topic will be expected.)