Research

My interests lie in low-dimensional topology and geometry, and particularly deformations of geometric structures on 3-manifolds and their character varieties.

My Ph.D. advisor was Steven Kerckhoff. My thesis was Singular hyperbolic structures on pseudo-Anosov mapping tori. Chapter 4 has been superseded by the similarly titled paper below. Chapter 5 has some results on veering triangulations which may be of interest.

Papers

Deformations of reducible SL(n,C) representations of fibered 3-manifold groups (Preprint)

with Erica Flapan. Linking number and writhe in random linear embeddings of graphs (Preprint; accepted by J. Math. Chem.).

Hyperbolic structures from Sol on pseudo-Anosov mapping tori (Preprint; to appear in Geom. Topol.).

with Jason Bustamante, Jared Federman, Joel Foisy, Kevin Matthews, Kristen McNamara, Emily Stark and Kirsten Trickey. Intrinsically linked graphs in projective space, Algebr. Geom. Topol. 9 (2009), 1255-1274 (Print version).

Science(-ish) papers

with L. G. de Pillis, K. Renee Fister, W. Gu, Tiffany Head, Kenny Maples, Todd Neal, Anand Murugan. Optimal Control of Mixed Immunotherapy and Chemotherapy of Tumors, J. Biol. Syst. 16 (2008), 51-80 (Print version).

with J. B. Nowak, J. A. Neuman, L.G. Huey, D. J. Tanner, J. S. Holloway, T. B. Ryerson, G. J. Frost, S. A. McKeen, F. C. Fehsenfeld. A chemical ionization mass spectrometry technique for airborne measurements of ammonia, J. Geophys. Res. 112 (2007), D10S02 (Print version).

with L. G. de Pillis, W. Gu, K. R. Fister, T. Head, K. Maples, T. Neal, A. Murugan. Chemotherapy for Tumors: An Analysis of the Dynamics and a Study of Quadratic and Linear Optimal Controls, Math. Biosci. 209 (2007), 292-315 (Print version).