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With Rosa Sena-Dias, 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:
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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.
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With Michiel van den Berg and Thomas Kappeler, Isospectrality and heat
content, Bulletin of the London Mathematical Society,
46 (2014), 793-808. Available on the arXiv.
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With Victor Guillemin and Rosa Sena-Dias, Equivariant inverse spectral
theory and toric orbifolds, Advances in Mathematics,
231 (2012), 1271-1290. Available on the arXiv.
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With Victor Guillemin and Rosa Sena-Dias, Equivariant inverse spectral
problems, Spectral Geometry, Proceedings of Symposia in Pure
Mathematics, 84 (2012), 155-166.
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With Victor Guillemin and Rosa Sena-Dias, Hearing Delzant polytopes
from the equivariant spectrum, Transactions of the American
Mathematical Society, 364 (2012), 887-910. Available on the arXiv.
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With Bruno Colbois and Ahmad El Soufi, Bounding the eigenvalues of the Laplace-Beltrami operator on compact submanifolds, Bulletin of the London Mathematical Society, 42 (2010), 96-108. Available on the arXiv.
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With Alexander Strohmaier,
Huber's theorem for hyperbolic orbisurfaces, Canadian Mathematical Bulletin, 52 (2009), 66-71. Available on the arXiv.
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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.
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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.
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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.
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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.
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With Hugo Parlier,
Collars and partitions of hyperbolic cone-surfaces, Geometriae Dedicata, 127 (2007), 139-149. Available on the arXiv.
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Geometric and Spectral Properties of Compact Riemann Orbisurfaces,
Ph.D. Thesis (pdf), Dartmouth College, 2004.
Preprints:
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With Diana Macedo and Rosa Sena-Dias, Recovering S1-invariant
metrics on S2 from the equivariant spectrum, 15 pp.
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With Victor Guillemin and Rosa Sena-Dias, Semi-classical weights and
equivariant spectral theory, 35 pp., submitted. Available on the arXiv.
Articles Not Intended for Publication:
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With Elizabeth Stanhope, In search of a round football.
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Isospectral finiteness of hyperbolic orbisurfaces,
on the arXiv.
Selected Presentations:
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"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
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"Can you hear the shape of a drum?" Faculty Colloquium, Bucknell University, 19 November 2013.
Video
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"Using 'big' spectral data to recover polytopes," Differential
Geometry Seminar, University of Illinois at Urbana-Champaign, 29
October 2013.
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"Isospectrality and heat content," AMS Special Session on Geometric
and Spectral Analysis, Temple University, 13 October 2013.
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"Beating and heating planar domains," Irish Geometry Conference,
Maynooth, Ireland, 21 June 2013.
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"Constructing polytopes from spectral data," Geometric Aspects of
Spectral Theory, Oberwolfach, Germany, 3 July 2012.
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"Building polygons from spectral data," MAA Special Session on
Decoding Geometry, Boston, 5 January 2012.
Slides
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"Eigenvalue (mis)behavior on manifolds," Mathematics Department Colloquium, Lehigh University, 20 October 2010.
Slides
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"Upper bounds for eigenvalues of submanifolds," Topology and Geometric
Group Theory Seminar, Cornell University, 31 August 2010.
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"Are right spherical triangles wrong?" Mathematics Department
Colloquium, Bowdoin College, 13 April 2010.
Slides
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"Upper bounds on eigenvalues of the Laplacian: surfaces and beyond," Texas Geometry and Topology Conference, Texas Christian University, 27 February 2010.
Slides
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"Hearing Delzant polygons from the equivariant spectrum," AMS-AWM Special Session on Spectral Problems on Compact Riemannian Manifolds, San Francisco, 15 January 2010.
Slides
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"Upper bounds for eigenvalues of submanifolds," AMS Special Session on Microlocal Analysis and Spectral Theory on Singular Spaces, University Park, Pennsylvania, 25 October 2009.
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"Orbifolds and isometries," Mellon 23 Workshop on Global Riemannian Geometry, Orbifolds, and Related Topics, Middlebury College, 10 October 2009.
Slides
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"The equivariant heat trace and isospectrality," Spring Meeting of the Swiss Mathematical Society 2009: Geometric Spectral Theory, Neuchâtel, 10 June 2009.
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"Eigenvalue (mis)behavior on manifolds," Mathematics Department Colloquium, Dartmouth College, 7 May 2009.
Slides
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"Hearing Delzant polygons," Spectral Geometry Seminar, Dartmouth College, 7 May 2009.
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"Hearing the geometry of orbifolds," Mathematics Department Colloquium, San Francisco State University, 5 November 2008.
Slides
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"The asymptotic expansion of the heat kernel for orbifolds," MSRI Postdoctoral Seminar, 24 October 2008.
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"Hearing the geometry of orbifolds," Mathematics Department Colloquium, UC Santa Cruz, 7 October 2008.
Slides
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"Listening to orbifolds: What does the Laplace spectrum tell us?" Interdisciplinary Seminar on PDEs and their Applications, Penn State Altoona, 9 May 2008.
Slides
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"Extremal invariant eigenvalues of the Laplacian of invariant metrics," AMS Special Session on Inverse Problems in Geometry, San Diego, 8 January 2008.
Slides
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"Bagels, beach balls and the Poincaré Conjecture," Mathematics Department Colloquium, Susquehanna University, 18 October 2007.
Slides
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"Hearing the weights of weighted projective planes," AMS Special Session on Orbifolds, Symplectic Reduction and Quantization, Oxford, Ohio, 17 March 2007.
Slides
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"Using heat invariants to hear the geometry of orbifolds," Geometria em Lisboa,
CAMGSD/Instituto Superior Técnico, 7 March 2006.
Slides
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"Upper bounds for invariant eigenvalues of the Laplacian," Seminário
de Física-Matemática, Universidade de Lisboa, 10 February 2006.
Slides
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"The Laplace spectrum reveals (some of) its secrets," Research Seminar,
Centre Interfacultaire Bernoulli, Lausanne, Switzerland, 31 August 2005.
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"Can one hear the shape of a ...?" Mathematics Department Colloquium,
Scripps College, 16 February 2005.
Slides
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"Triangles, Tilings, and Tori," Mathematics Department Colloquium,
Middlebury College, 8 February 2005.
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"Listening to Orbifolds: What does the Laplace spectrum tell us?"
Mathematics Department Colloquium, Bucknell University, 1 February 2005.
Slides
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"Inverse Spectral Problems on Hyperbolic Orbisurfaces," Analysis Seminar,
McGill University, 28 January 2005.
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"Collars and Partitions of Hyperbolic Cone-Surfaces," AMS Special Session on
Inverse Spectral Geometry, Atlanta, 8 January 2005.
Slides
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"Isospectrality of Compact Riemann Orbisurfaces," Recent developments in
spectral geometry, Blossin, Germany, 2 November 2004.
Slides
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"Geodesic Behavior on Hyperbolic Cone-Surfaces," Séminaire CIRGET,
Université du Québec à Montréal, 10 September 2004.
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"Geometric and Spectral Properties of Compact Riemann Orbisurfaces," Thesis
Defense, Dartmouth College, 13 May 2004.
Slides
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"Bounding the Size of Isospectral Sets of Orbifolds,"
Analysis Seminar,
McGill University, 27 February 2004.
Slides
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"Isospectrality of Two-Dimensional Riemannian Orbifolds,"
Workshop on Inverse Spectral Problems,
Dartmouth College, 21 November 2003.
Slides
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"Inverse Spectral Problems on Riemannian Orbifolds,"
Union College Mathematics Conference,
Differential Geometry Session, 8 November 2003.
Slides
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"Isospectrality of Orbifolds,"
École Polytechnique Fédérale de Lausanne, Switzerland,
Geometry Seminar, 25 June 2003.
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