# Discrete Mathematics Seminar

This seminar is held on Thursdays at 11am in 105 Fenton.

### Winter Quarter, 2020

- March 4,
**Dev Sinha** (UO)

**Special Time:** 4pm in 119 Fenton

A pairing between graphs and trees
**Abstract**: Given a graph with vertex set S and a planar rooted trivalent tree with leaves labeled by S, one can define a map from edges of the graph to internal vertices of the tree. Namely, if an edge has vertices v, w, send that edge to the greatest lower bound of the leaves labeled by v and w. This gives rise to a pairing between the graph and tree whose value is plus or minus one if this map is a bijection or zero if not.

This pairing arises in the study of Lie algebras, configuration spaces, lower central series, and Hopf invariants, among other topics. In this accessible talk I’ll develop the basics and touch on some of these applications, hoping that combinatorially minded folks might see ways to carry things further.