Geometry in the Presence of Symmetries
My research interests lie in Riemannian geometry and geometric spectral theory where I typically explore questions related to symmetry and rigidity. Recently, I have been particularly interested in studying the nodal sets and nodal domains of (Laplace) eigenfunctions in the presence of symmetry.
Articles
- Geometric structures and the Laplace spectrum, Part I , with S. Lin & B. Schmidt, Ann. Inst. Fourier (Grenoble), 74 (2024), no. 2, 867 - 914.
- Spectral multiplicity and nodal sets of generic torus-invariant metrics, with D. Cianci, C. Judge & S. Lin, Int. Math. Res. Not. IMRN (2024), no. 3, 2192 - 2218.
- Geometric structures and the Laplace spectrum, Part II , with S. Lin & B. Schmidt, Trans. Amer. Math. Soc., 374 (2021), no. 12, 8483-8530.
- Spectral geometry in the presence of symmetry , Notices Amer. Math. Soc., 68 (2021), no. 6, 869-883.
- On the Poisson relation for compact Lie groups, Ann. Global Anal. Geom. 57 (2020), 537 - 589.
- Detecting the moments of inertia of a molecule via its rotational spectrum II, with B. Schmidt, Unpublished (2014). Material incorporated into "Geometric structures and the Laplace spectrum II" (above).
- Detecting the moments of inertia of a molecule via its rotational spectrum I, Unpublished (2013). Material incorporated into "On the Poisson relation for compact Lie groups" (above).
- Constructing metrics with a partially prescribed stable norm, with E. Makover & H. Parlier, Manuscripta Math. 139 (2012), no. 3-4, 515-534.
- Isospectral surfaces with distinct covering spectra via Cayley graphs, with B. de Smit & R. Gornet, Geom. Dedicata 153 (2012), no. 1, 343-352.
- Two remarks on the length spectrum of a Riemannian manifold, with B. Schmidt, Proc. Amer. Math. Soc. 139 (2011), 4113-4119.
- Sunada’s method and the covering spectrum, with B. de Smit & R. Gornet, J. Differential Geom., 86 (2010), no. 3, 501-537.
- Spectral isolation of bi-invariant metrics on compact Lie groups, with C. Gordon & D. Schueth, Ann. Inst. Fourier (Grenoble) 60 (2010), 1617-1628.
- Spectral isolation of naturally reductive metrics on simple Lie groups, with C. Gordon, Math. Z. 266 (2010), 979-995.
- Equivariant isospectrality and Sunada's method, Arch. Math. 95 (2010), 75-85.
- Measures invariant under the geodesic flow and their projections, Proc. Amer. Math. Soc. 131 (2003), 2933-2936.
- Isospectral simply-connected homogeneous spaces and the spectral rigidity of group actions, Comment. Math. Helv. 77 (2002), 701-717.
Thesis
- Applications of representation theory to dynamics and spectral geometry, Ph. D. Thesis, University of Michigan, Ann Arbor, MI USA 48104, 2001. (Advisor: Ralf Spatzier )