My research is in dynamics--the mathematical study of systems that change over time. I am also interested in differential geometry and topology, and especially in how dynamics are generated or restricted by the underlying geometry or topology of a space. Two dynamical systems that I have spent a lot of time thinking about are geodesic flows and convex billiards.
Publications
Explorations in analysis, topology, and dynamics: an introduction to abstract mathematics (textbook).
[preface | toc | preview | buy]
(with A. Uribe)
AMS Pure and Applied Undergraduate Texts 44 (2020), 180 pages.
Measuring mathematics engagement anxiety: new dimensions of math anxiety in an RMARS-addendum.
[pdf | journal]
(with N. White)
International Journal of Research in Undergraduate Mathematics Education, 6 (2020), 113-144.
A new proof of the existence of embedded surfaces with Anosov geodesic flow.
[pdf | arXiv | journal]
(with V. Donnay)
Regular and Chaotic Dynamics,
23(6)
(2018), 685-694.
Equilibrium measures for certain isometric extensions of Anosov systems.
[pdf | arXiv | journal]
(with R. Spatzier)
Ergodic Theory & Dynamical Systems,
38(3)
(2018), 1154-67.
A Franks' lemma for convex planar billiards.
[pdf | journal]
Dynamical Systems: An International Journal,
30(3)
(2015), 333-340.
A new proof of Franks' lemma for geodesic flows.
[pdf | arXiv | journal]
Discrete and Continuous Dynamical Systems-Series A,
34(11)
(2014), 4875-4895.
A Case Study of Student and Instructor Reactions to a Calculus E-Book.
[pdf | journal]
(with M. Bode and M. Khorami)
PRIMUS,
24(2)
(2014), 160-174.
Minimal free resolutions of complete bipartite graph ideals.
[pdf | journal]
Communications in Algebra,
34(10)
(2006), 3761-66.