Research

• Manifold Submetries from Compact Homogeneous Spaces
  (with Ricardo Mendes and Marco Radeschi), arxiv

• A Weyl's Law for Singular Riemannian Foliations with Applications to Invariant Theory,
  (with Ricardo Mendes and Marco Radeschi)
  to appear in Geometry and Topology, arxiv

• Spectral Multiplicity and Nodal Sets for Generic Torus-Invariant Metrics,
  (with Donato Cianci, Chris Judge, and Craig Sutton)
  International Mathematics Research Notices (2024), no. 3, 2192–2218 article

• Geometric Structures and the Laplace Spectrum, Part II,
  (with Benjamin Schmidt and Craig Sutton)
  Transactions of American Mathematical Society, 374 (2021), 8483-8530, article

• Geometric Structures and the Laplace Spectrum,
  (with Benjamin Schmidt and Craig Sutton)
  Annales de l'Institute Fourier, 74(2024) no. 2 pp.867-914,  article

• Curvature Free Rigidity for Higher Rank Three-manifolds,
  Indiana University Mathematics Journal, 67, (2018), no.6, 1597-1623, article

• Manifolds With Many Hyperbolic Planes,
  (with Benjamin Schmidt)
  Differential Geometry and its Applications, 52 (2017), 121-126, article

• Real Projective Space with All Geodesics Closed,
  (with Benjamin Schmidt)
  Geometric and Functional Analysis, 27, (2017), no. 3, 631-636, article

• Isometric Torus Actions and the Eigenfunctions of the Dirichlet-to-Neumann Operator, with Chris Judge and Craig Sutton.

• Generic Irreducibility of Eigenspaces for Non-free Torus Actions, with Chris Judge and Craig Sutton.

Here are some videos of the talks I gave online:

• Spectral Multiplicity and Nodal Domains of Torus-invariant Metrics (November 2023, Spectral Geometry in the Clouds) YouTube Video

• Geometric Structures and the Laplace Spectrum (January 2021, Virtual Seminars on Geometry with Symmetries) YouTube Video