28 citations · 59 across the 10 of their papers we have counts for
12 papers
Measurable Riemannian structure on higher dimensional harmonic Sierpinski gaskets
Sara Chari, Joshua Frisch, Daniel J. Kelleher +1
We prove existence of a measurable Riemannian structure on higher-dimensional harmonic Sierpinski gasket fractals and deduce Gaussian heat kernel bounds in the geodesic metric. Our…
Differential forms for fractal subspaces and finite energy coordinates
Daniel J. Kelleher
This paper introduces a notion of differential forms on closed, potentially fractal, subsets of Euclidean space by defining pointwise cotangent spaces using the restriction of $C^1…
Magnetic Laplacians of locally exact forms on the Sierpinski Gasket
Jessica Hyde, Daniel J. Kelleher, Jesse Moeller +2
We give a mathematically rigorous construction of a magnetic Schrödinger operator corresponding to a field with flux through finitely many holes of the Sierpinski Gasket. The opera…
Differential forms on Dirichlet spaces and Bakry-Émery estimates on metric graphs
Fabrice Baudoin, Daniel J. Kelleher
We develop a general framework on Dirichlet spaces to prove a weak form of the Bakry-Émery estimate and study its consequences. This estimate may be satisfied in situations, like m…
Dual graphs and modified Barlow--Bass resistance estimates for repeated barycentric subdivisions
Daniel J. Kelleher, Antoni Brzoska, Hugo Panzo +1
We prove Barlow--Bass type resistance estimates for two random walks associated with repeated barycentric subdivisions of a triangle. If the random walk jumps between the centers o…
Energy and Laplacian on Hanoi-type fractal quantum graphs
Patricia Alonso Ruiz, Daniel J. Kelleher, Alexander Teplyaev
This article studies potential theory and spectral analysis on compact metric spaces, which we refer to as fractal quantum graphs. These spaces can be represented as a (possibly in…
Gaps in the spectrum of the Laplacian on -Gaskets
Daniel Kelleher, Nikhar Gupta, Maxwell Margenot +3
This article develops analysis on fractal -gaskets, a class of post-critically finite fractals which include the Sierpinski triangle for , specifically properties of the L…
Metrics and spectral triples for Dirichlet and resistance forms
Michael Hinz, Daniel J. Kelleher, Alexander Teplyaev
The article deals with intrinsic metrics, Dirac operators and spectral triples induced by regular Dirichlet and resistance forms. We show, in particular, that if a local resistance…
Measures and Dirichlet forms under the Gelfand transform
Michael Hinz, Daniel Kelleher, Alexander Teplyaev
Using the standard tools of Daniell-Stone integrals, Stone-Čech compactification and Gelfand transform, we discuss how any Dirichlet form defined on a measurable space can be trans…
Analysing properties of the C. Elegans neural network: mathematically modeling a biological system
Daniel J. Kelleher, Tyler M. Reese, Dylan T. Yott +1
The brain is one of the most studied and highly complex systems in the biological world. It is the information center behind all vertebrate and most invertebrate life, and thus has…
Random walks on barycentric subdivisions and the Strichartz hexacarpet
Matthew Begue, Daniel J. Kelleher, Aaron Nelson +3
We investigate the relation between simple random walks on repeated barycentric subdivisions of a triangle and a self-similar fractal, Strichartz hexacarpet, which we introduce. We…
From Self-Similar Structures to Self-Similar Groups
Daniel J. Kelleher, Benjamin A. Steinhurst, Chuen-Ming M. Wong
We explore the relationship between limit spaces of contracting self-similar groups and self-similar structures. We give the condition on a contracting group such that its limit sp…