24 citations · 45 across the 15 of their papers we have counts for
19 papers
Affine mappings of translation surfaces: shrinking targets and Diophantine properties
Chris Judge, Josh Southerland
Let be a translation surface whose Veech group is a lattice. We prove that the generic orbit of the group of affine homeomorphisms of can be used to approximate…
Generic simplicity of ellipses
Luc Hillairet, Chris M. Judge
We prove that the Laplace spectrum of the generic ellipse is simple, both with Neumann and Dirichlet boundary condition. We rely on the known multiplicities in the spectrum of the…
Spectral multiplicity and nodal sets for generic torus-invariant metrics
Donato Cianci, Chris Judge, Samuel Lin +1
Let a torus act freely on a closed manifold of dimension at least two. We demonstrate that, for a generic -invariant Riemannian metric on , each real -eigens…
Some remarks on critical sets of Laplace eigenfunctions
Chris Judge, Sugata Mondal
We study the set of critical points of a solution to and in particular components of the critical set that have codimension 1. We show, for example, that if a secon…
Critical points of Laplace eigenfunctions on polygons
Chris Judge, Sugata Mondal
We study the critical points of Laplace eigenfunctions on polygonal domains with a focus on the second Neumann eigenfunction. We show that if each convex quadrilaterals has no seco…
Haupt's theorem for strata of abelian differentials
Matt Bainbridge, Chris Johnson, Chris Judge +1
Let S be a closed topological surface. Haupt's theorem provides necessary and sufficient conditions for a complex-valued character of the first integer homology group of S to be re…