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Serendipitous decompositions of higher-dimensional continued fractions. (with J. Vandehey). Submitted.

Publications (cf. journal rankings)

Convergence of improper Iwasawa Continued Fractions (with J. Vandehey). To appear in International Journal of Number Theory.

Projection theorems for linear-fractional families of projections (with A. Iseli). Math. Proc. Cambridge Philosophical Soc. 175, no. 3 (2023): 625-647.

Probabilistic motion planning for non-Euclidean and multi-vehicle problems. (with D. Soudbakhsh). Robotics and Autonomous Systems 168 (2023): Article 104487.

Ergodicity of Iwasawa continued fractions via markable hyperbolic geodesics (with J. Vandehey). Ergodic Theory and Dynamical Systems 43, no. 5 (2023): 1666-1711.

Optimal Localized Trajectory Planning of Multiple Non-holonomic Vehicles. Authors (non-alphabetic): A. Lukyanenko, D. Soudbakhsh, H. Camphire, and S. Schmidgall. Proceedings of the 2021 5th IEEE Conference on Control Technology and Applications.

Intrinsic Diophantine approximation in Carnot groups and in the Siegel model of the Heisenberg group (with J. Vandehey). Monatshefte fur Mathematik, 192 (2020), no. 3, 651-676.

Heisenberg quasiregular ellipticity (with K. Fassler and J. Tyson). Rev. Mat. Iberoam. 35 (2019), no. 2, 471–520.

Geometry Labs United: An Invitation (with Jayadev Athreya, David Dumas, William Goldman, Sergey Grigorian, Rosemary Guzman, Philipp Hieronymi, Sean Lawton, Jeremy Tyson, and Aaron Wilson). Notices of the AMS 65 (2018), no. 9.

Quasiconvexity in the Heisenberg group (with D. Herron and J. Tyson). Geom. Dedicata 192 (2018), Issue 1, 157-170.

Separated nets in nilpotent groups (with T. Dymarz, S. Li, and M. Kelly). Indiana Univ. Math. J. 67 (2018), no. 3, 1143–1183.

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, presentations, and translations

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.

Hard-to-find papers

Иванъ Владиславовичъ Слешинскiй, Дополнение къ заметке о сходимости непрерывныхъ дробей, Математический сборник 14 (1889), no. 3, 436–438 (Sleszynski. Supplement to the Note on the Convergence of Continued Fractions.)

Mathematica notebooks

Fractal Snowballs, 2017.

Horisontal Curves, Hopf Fibration, and Lens Spaces, 2010.