My main research involves Geometric Group Theory, a field in the intersection of topology and algebra. I am most interested in mapping class groups, the Torelli Group, and the hyperelliptic Torelli Group.
Student Research Projects
I directed undergraduate research projects on chromatic numbers of graphs, hyperbolic geometry and crochet, using tangent circles to define hyperbolas and ellipses, constructible numbers using a rusty compass, and braid groups with applications to cryptography. I have also directed two masters projects, one on Taxicab Geometry and the other on Billiards.
Publications and Preprints
“Cohomology of the hyperelliptic Torelli group” (pdf)
with Tara Brendle and Dan Margalit
Israel Journal of Mathematics, pages 1–18. 10.1007 s11856-012-0075-3
“Simply intersecting pair maps in the mapping class group” (pdf)
Journal of Knot Theory and Its Ramifications, 21(11), 2012
“Subgroups of the Torelli group” (pdf)
Ph.D. Thesis, Louisiana State University, 2010.
“The automorphism group of the hyperelliptic Torelli group” (preprint)
“Surfaces and their symmetries: An introduction to mapping class groups”
with Tara Brendle--to be a chapter in Office Hours with a Geometric
Group Theorist, edited by M. Clay and D. Margalit
“On periodic bounce sequences for billiard tables” with Kariane Calta
For the academic year 2012-2013, I am teaching Calculus 1, Discrete Structures, Basic Concepts of Geometry, Mathematical Software for Teachers, and Knot Theory. At PSU I have also taught Elementary Statistics, Geometric Group Theory, and Advanced Geometry. At LSU I taught Calculus 1, College Algebra, Math for Elementary Education, and ran Trigonometry recitation classes.