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
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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.
