Geometry in the Presence of Symmetries

My research interests lie in Riemannian geometry with an emphasis on spectral geometry and homogeneous spaces.

Articles

with S. Lin & B. Schmidt, preprint (2019).*Geometric structures and the Laplace spectrum, Part II*with S. Lin & B. Schmidt, preprint (2019).*Geometric structures and the Laplace spectrum, Part I*41 pages.*On the Poisson relation for compact Lie groups,*with B. Schmidt, Unpublished (2014).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and the Laplace spectrum II" (above).*Detecting the moments of inertia of a molecule via its rotational spectrum II,*Unpublished (2013). Material incorporated into "On the Poisson relation for compact Lie groups" (above).*Detecting the moments of inertia of a molecule via its rotational spectrum I,*with E. Makover & H. Parlier, Manuscripta Math. 139 (2012), no. 3-4, 515-534.*Constructing metrics with a partially prescribed stable norm,*with B. de Smit & R. Gornet, Geom. Dedicata 153 (2012), no. 1, 343-352.*Isospectral surfaces with distinct covering spectra via Cayley graphs,***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 )