45 citations · 146 across the 29 of their papers we have counts for
35 papers
Spectral properties of the Schreier graphs of the basilica group
Kyle Ambrose, Noah Dunham, Michael Morris +2
We study the spectral properties of Laplacians on the Schreier graphs of the basilica group, the iterated monodromy group of the polynomial , which is an important e…
Gaps labeling theorem for the Bubble-diamond self-similar graphs
Elizabeth Melville, Gamal Mograby, Nikhil Nagabandi +2
Motivated by the appearance of fractals in several areas of physics, especially in solid state physics and the physics of aperiodic order, and in other sciences, including the quan…
Spectra of three-peg Hanoi towers graphs
Brett Hungar, Gamal Mograby, Madison Phelps +2
We consider the relationship between the Laplacians on two sequences of planar graphs, one from the theory of self-similar groups and one from analysis on fractals. By establishing…
Resistance Scaling on -Carpets
Claire Canner, Christopher Hayes, Shinyu Huang +2
The carpets are a class of infinitely ramified self-similar fractals with a large group of symmetries. For a -carpet , let be the natural decreasin…
Discretization of the Koch Snowflake Domain with Boundary and Interior Energies
Malcolm Gabbard, Carlos Lima, Gamal Mograby +2
We study the discretization of a Dirichlet form on the Koch snowflake domain and its boundary with the property that both the interior and the boundary can support positive energy.…
Geodesic Interpolation on Sierpinski Gaskets
Caitlin M. Davis, Laura A. LeGare, Cory W. McCartan +1
We study the analogue of a convex interpolant of two sets on Sierpinski gaskets and an associated notion of measure transport. The structure of a natural family of interpolating me…