# Talk by Wesley Jones

On March 12th, 2021, Wesley Jones (Emory University) gave a talk about "**Sharp diameter bound on the spectral gap of quantum graphs**" as part of the research seminar Analysis of the FernUniversität in Hagen. This lecture is partially supported by the COST action Mathematical models for interacting dynamics on networks.

## Abstract

This seminar will investigate a new bound for the heat kernel on an arbitrary quantum graph. Using a representation of the heat kernel as a sum of gaussians, we created an upper bound for the heat kernel along an edge of a quantum graph by the Neumann interval with the same length as the edge. The bound uses a technique for partitioning the paths along a quantum graph that we believe could be applied to other areas of quantum graph research.