Mathematics
Noncommutative geometry, special functions, and number theory.
Education
Ph.D. in Mathematics, Minor in Physics
Georgia Institute of Technology, 2008
Dissertation: The Noncommutative Geometry of Ultrametric Cantor Sets
Advisor: Jean Bellissard
Best Ph.D. Thesis Award, School of Mathematics
B.A. in Mathematics
Dartmouth College, 2002
Research Areas
Noncommutative Geometry
Algebraic and geometric structures arising from quantum groups and operator algebras. The doctoral work developed a noncommutative Riemannian geometry for ultrametric Cantor sets — spaces that appear naturally in number theory, dynamical systems, and solid-state physics — and constructed Laplacians and diffusion processes on these spaces using spectral triples.
Gamma Function Geometry
Geometric properties of the gamma function and related special functions. This work connects classical identities — Viete's formula, Knar's formula — to the geometry of the gamma function, revealing structure that had been hiding in plain sight for centuries.
Generalized Pythagorean Nonexistence Conjecture
Current focus. Extending classical Pythagorean equation results to higher-dimensional number theory — investigating when and why certain Diophantine equations fail to have solutions in higher dimensions.
Publications
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Viete's Formula, Knar's Formula, and the Geometry of the Gamma Function
American Mathematical Monthly, vol. 125, no. 8, 2018, pp. 704–714.
Connects two classical infinite-product identities to the geometric structure of the gamma function.
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Noncommutative Riemannian Geometry and Diffusion on Ultrametric Cantor Sets
Journal of Noncommutative Geometry, vol. 3, no. 3, 2009, pp. 447–480.
Develops a Riemannian geometry and Laplacian theory for ultrametric Cantor sets via spectral triples. Joint work with Jean Bellissard.
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The Noncommutative Geometry of Ultrametric Cantor Sets
Ph.D. Thesis, Georgia Institute of Technology, 2008.
Awarded Best Ph.D. Thesis by the School of Mathematics.