Publications:

• With Alexander Strohmaier, Huber's theorem for hyperbolic orbisurfaces, Canadian Mathematical Bulletin, 52 (2009), 66-71. 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), 205-238. 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), 373-395. Available on the arXiv.

• With Bruno Colbois and Ahmad El Soufi, Extremal G-invariant eigenvalues of the Laplacian of G-invariant metrics, Mathematische Zeitschrift, 258 (2008), 29-41. 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), 261-277.

• With Hugo Parlier, Collars and partitions of hyperbolic cone-surfaces, Geometriae Dedicata, 127 (2007), 139-149. Available on the arXiv.

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

  Preprints:

• With Elizabeth Stanhope, In search of a round football, submitted.

• With Bruno Colbois and Ahmad El Soufi, Bounding the eigenvalues of the Laplace-Beltrami operator on compact submanifolds, submitted.

• With Victor Guillemin and Rosa Sena-Dias, Hearing Delzant polytopes from the equivariant spectrum, submitted. Available on the arXiv.

• Isospectral finiteness of hyperbolic orbisurfaces, on the arXiv.

  Selected Presentations:

• "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 Física-Matemática, 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 Cone-Surfaces," 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 Cone-Surfaces," 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 Two-Dimensional 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.