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With Rosa SenaDias, I'm organizing a special session on Geometric Spectral Theory as
part of the joint meeting of the American, European, and Portuguese
mathematical societies. We've posted information about our session
here.
Publications:

With Eric Bahuaud and Boris Vertman, Mapping properties of the heat
operator on edge manifolds, Mathematische Nachrichten (2014),
DOI 10.1002/mana.201300188. Available on the arXiv.

With Michiel van den Berg and Thomas Kappeler, Isospectrality and heat
content, Bulletin of the London Mathematical Society,
46 (2014), 793808. Available on the arXiv.

With Victor Guillemin and Rosa SenaDias, Equivariant inverse spectral
theory and toric orbifolds, Advances in Mathematics,
231 (2012), 12711290. Available on the arXiv.

With Victor Guillemin and Rosa SenaDias, Equivariant inverse spectral
problems, Spectral Geometry, Proceedings of Symposia in Pure
Mathematics, 84 (2012), 155166.

With Victor Guillemin and Rosa SenaDias, Hearing Delzant polytopes
from the equivariant spectrum, Transactions of the American
Mathematical Society, 364 (2012), 887910. Available on the arXiv.

With Bruno Colbois and Ahmad El Soufi, Bounding the eigenvalues of the LaplaceBeltrami operator on compact submanifolds, Bulletin of the London Mathematical Society, 42 (2010), 96108. Available on the arXiv.

With Alexander Strohmaier,
Huber's theorem for hyperbolic orbisurfaces, Canadian Mathematical Bulletin, 52 (2009), 6671. Available on the arXiv.

With Carolyn S. Gordon, Sarah J. Greenwald and David L. Webb,
Asymptotic expansion of the heat kernel for orbifolds,
Michigan Mathematical Journal, 56 (2008), 205238. Available on the arXiv.

With Miguel Abreu, Pedro Freitas, and Leonor Godinho, Hearing the weights of weighted projective planes, Annals of Global Analysis and Geometry, 33 (2008), 373395. Available
on the arXiv.

With Bruno Colbois and Ahmad El Soufi,
Extremal Ginvariant eigenvalues of the Laplacian of Ginvariant metrics, Mathematische Zeitschrift, 258 (2008), 2941. Available on the arXiv. The original publication is available at www.springerlink.com.

With Charles R. Johnson and Brenda K. Kroschel, Adjacent edge conditions for the totally nonnegative completion
problem, Linear and Multilinear Algebra, 56 (2008), 261277.

With Hugo Parlier,
Collars and partitions of hyperbolic conesurfaces, Geometriae Dedicata, 127 (2007), 139149. Available on the arXiv.

Geometric and Spectral Properties of Compact Riemann Orbisurfaces,
Ph.D. Thesis (pdf), Dartmouth College, 2004.
Preprints:

With Diana Macedo and Rosa SenaDias, Recovering S^{1}invariant
metrics on S^{2} from the equivariant spectrum, 15 pp.

With Victor Guillemin and Rosa SenaDias, Semiclassical weights and
equivariant spectral theory, 35 pp., submitted. Available on the arXiv.
Articles Not Intended for Publication:

With Elizabeth Stanhope, In search of a round football.

Isospectral finiteness of hyperbolic orbisurfaces,
on the arXiv.
Selected Presentations:

"Can you hear the metric on a sphere?" AMS Special Session on Geometry
of Manifolds, Singular Spaces, and Groups, Michigan State
University, 15 March 2015. Slides

"Can you hear the shape of a drum?" Faculty Colloquium, Bucknell University, 19 November 2013.
Video

"Using 'big' spectral data to recover polytopes," Differential
Geometry Seminar, University of Illinois at UrbanaChampaign, 29
October 2013.

"Isospectrality and heat content," AMS Special Session on Geometric
and Spectral Analysis, Temple University, 13 October 2013.

"Beating and heating planar domains," Irish Geometry Conference,
Maynooth, Ireland, 21 June 2013.

"Constructing polytopes from spectral data," Geometric Aspects of
Spectral Theory, Oberwolfach, Germany, 3 July 2012.

"Building polygons from spectral data," MAA Special Session on
Decoding Geometry, Boston, 5 January 2012.
Slides

"Eigenvalue (mis)behavior on manifolds," Mathematics Department Colloquium, Lehigh University, 20 October 2010.
Slides

"Upper bounds for eigenvalues of submanifolds," Topology and Geometric
Group Theory Seminar, Cornell University, 31 August 2010.

"Are right spherical triangles wrong?" Mathematics Department
Colloquium, Bowdoin College, 13 April 2010.
Slides

"Upper bounds on eigenvalues of the Laplacian: surfaces and beyond," Texas Geometry and Topology Conference, Texas Christian University, 27 February 2010.
Slides

"Hearing Delzant polygons from the equivariant spectrum," AMSAWM Special Session on Spectral Problems on Compact Riemannian Manifolds, San Francisco, 15 January 2010.
Slides

"Upper bounds for eigenvalues of submanifolds," AMS Special Session on Microlocal Analysis and Spectral Theory on Singular Spaces, University Park, Pennsylvania, 25 October 2009.

"Orbifolds and isometries," Mellon 23 Workshop on Global Riemannian Geometry, Orbifolds, and Related Topics, Middlebury College, 10 October 2009.
Slides

"The equivariant heat trace and isospectrality," Spring Meeting of the Swiss Mathematical Society 2009: Geometric Spectral Theory, Neuchâtel, 10 June 2009.

"Eigenvalue (mis)behavior on manifolds," Mathematics Department Colloquium, Dartmouth College, 7 May 2009.
Slides

"Hearing Delzant polygons," Spectral Geometry Seminar, Dartmouth College, 7 May 2009.

"Hearing the geometry of orbifolds," Mathematics Department Colloquium, San Francisco State University, 5 November 2008.
Slides

"The asymptotic expansion of the heat kernel for orbifolds," MSRI Postdoctoral Seminar, 24 October 2008.

"Hearing the geometry of orbifolds," Mathematics Department Colloquium, UC Santa Cruz, 7 October 2008.
Slides

"Listening to orbifolds: What does the Laplace spectrum tell us?" Interdisciplinary Seminar on PDEs and their Applications, Penn State Altoona, 9 May 2008.
Slides

"Extremal invariant eigenvalues of the Laplacian of invariant metrics," AMS Special Session on Inverse Problems in Geometry, San Diego, 8 January 2008.
Slides

"Bagels, beach balls and the Poincaré Conjecture," Mathematics Department Colloquium, Susquehanna University, 18 October 2007.
Slides

"Hearing the weights of weighted projective planes," AMS Special Session on Orbifolds, Symplectic Reduction and Quantization, Oxford, Ohio, 17 March 2007.
Slides

"Using heat invariants to hear the geometry of orbifolds," Geometria em Lisboa,
CAMGSD/Instituto Superior Técnico, 7 March 2006.
Slides

"Upper bounds for invariant eigenvalues of the Laplacian," Seminário
de FísicaMatemática, Universidade de Lisboa, 10 February 2006.
Slides

"The Laplace spectrum reveals (some of) its secrets," Research Seminar,
Centre Interfacultaire Bernoulli, Lausanne, Switzerland, 31 August 2005.

"Can one hear the shape of a ...?" Mathematics Department Colloquium,
Scripps College, 16 February 2005.
Slides

"Triangles, Tilings, and Tori," Mathematics Department Colloquium,
Middlebury College, 8 February 2005.

"Listening to Orbifolds: What does the Laplace spectrum tell us?"
Mathematics Department Colloquium, Bucknell University, 1 February 2005.
Slides

"Inverse Spectral Problems on Hyperbolic Orbisurfaces," Analysis Seminar,
McGill University, 28 January 2005.

"Collars and Partitions of Hyperbolic ConeSurfaces," AMS Special Session on
Inverse Spectral Geometry, Atlanta, 8 January 2005.
Slides

"Isospectrality of Compact Riemann Orbisurfaces," Recent developments in
spectral geometry, Blossin, Germany, 2 November 2004.
Slides

"Geodesic Behavior on Hyperbolic ConeSurfaces," Séminaire CIRGET,
Université du Québec à Montréal, 10 September 2004.

"Geometric and Spectral Properties of Compact Riemann Orbisurfaces," Thesis
Defense, Dartmouth College, 13 May 2004.
Slides

"Bounding the Size of Isospectral Sets of Orbifolds,"
Analysis Seminar,
McGill University, 27 February 2004.
Slides

"Isospectrality of TwoDimensional Riemannian Orbifolds,"
Workshop on Inverse Spectral Problems,
Dartmouth College, 21 November 2003.
Slides

"Inverse Spectral Problems on Riemannian Orbifolds,"
Union College Mathematics Conference,
Differential Geometry Session, 8 November 2003.
Slides

"Isospectrality of Orbifolds,"
École Polytechnique Fédérale de Lausanne, Switzerland,
Geometry Seminar, 25 June 2003.
