Geometry in the Presence of Symmetries
My research interests lie in Riemannian geometry with an emphasis on spectral geometry and homogeneous spaces.
Articles
Geometric structures and the Laplace spectrum, Part II
with S. Lin & B. Schmidt, preprint (2019).
Geometric structures and the Laplace spectrum, Part I
with S. Lin & B. Schmidt, preprint (2019).
On the Poisson relation for compact Lie groups,
41 pages.
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with B. Schmidt, Unpublished (2014).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Unpublished (2013).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
)