Tertiary navigation


Intrinsic Diophantine approximation in Carnot groups and in the Siegel model of the Heisenberg group (with J. Vandehey). Submitted.


Quasiconvexity in the Heisenberg group (with D. Herron and J. Tyson). To appear in Geometriae Dedicata.

Heisenberg quasiregular ellipticity (with K. Fassler and J. Tyson). To appear in Revista Matematica Iberoamericana.

Separated nets in nilpotent groups (with T. Dymarz, S. Li, and M. Kelly). To appear in Indiana Math J.

Quasiregular mappings on sub-Riemannian manifolds (with K. Fassler and K. Peltonen). J. Geom. Anal. 26 (2016), no. 3, 1754-1794.

Continued fractions on the Heisenberg Group (with J. Vandehey). Acta Arithmetica 167 (2015), 19-42.

On the lack of density of Lipschitz mappings in Sobolev spaces with Heisenberg target (with N. DeJarnette, P. Hajlasz, and J. Tyson). Conform. Geom. Dyn. (2014), 119-156.

Bi-Lipschitz extension from boundaries of certain hyperbolic spaces. Geom. Dedicata 164 (2013), Issue 1, 47-71.

Quasi-isometric co-Hopficity of non-uniform lattices in rank-one semi-simple Lie groups (with I. Kapovich). Conform. Geom. Dyn. 16 (2012), 269-282.


Geometric mapping theory of the Heisenberg group, sub-Riemannian manifolds, and hyperbolic spaces. Ph.D. thesis, University of Illinois at Urbana-Champaign, 2014.

Projective deformations of triangle tilings. Master's thesis, University of Maryland, College Park, 2008.

Notes and presentations (caveat emptor!)

Continued fractions on the Heisenberg group. Short lecture at the 2013 IPAM workshop "Dynamics of Groups and Rational Maps".

Bi-Lipschitz extension from boundaries of certain hyperbolic spaces. Lecture at the 2012 joint math meetings.

Image inpainting and a geometric model of the visual cortex. Lecture at the visual cognition and heierarchical perception brownbag, December 2011.

Fillings in nilpotent groups. Notes for a lecture at the summer school on filling invariants and asymptotic geometry, 2011.

Tangent approximations to sub-Riemannian manifolds. Notes for a talk at the working seminar in geometry and analysis, October 2009.

Translation of Guichard's "Sur la regularitet Holder des convexes divisibles". Not guaranteed to be a good translation, but at least it's in English.