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math.SP2025
On the hot spots conjecture in higher dimensions
James B. Kennedy, Jonathan Rohleder
We prove a strong form of the hot spots conjecture for a class of domains in which are a natural generalization of the lip domains of Atar and Burdzy [J. Amer. Math.…
math.SP2025
Positivity properties of the Dirichlet-to-Neumann operator on graphs
Daniel Daners, Jochen Glück, James B. Kennedy
We explore positivity properties of the semigroup generated by the negative of the Dirichlet-to-Neumann operator with real potential , defined on a subset of the vertices of a…
math.SP2024
Geometric spectral theory of quantum graphs
James Kennedy
These are lecture notes from a course given at the summer school "Heat kernels and spectral geometry: from manifolds to graphs" in Bregenz, Austria, 2022. They are designed to be a…