Professor II

Faculty

Department of Mathematics and Computer Science

**Field of Specialization: Hyperbolic Geometry, Teichmüller Theory, Kleinian Groups, & Algorithms**

## Courses Taught

College Algebra, Trigonometry, Precalculus, Calculus I, II, Honors Calculus I,II, Abstract Algebra I, II, Complex Variables, Calculus I, Topology I, II, Mathematics Seminar, Computers & Programming I, Graduate Differential Geometry, Graduate Topics in Complex Variables, Graduate Topics in Geometry

## Education

Ph.D., Columbia University

## Publications

__Referreed Research Articles__"Canonical Symplectic Representations for Prime Order Conjugacy Classes of the Mapping Class Group,"Journal of Algebra, 318 (2007), 430-455

"The Structure of Two-Parabolic Space: Parabolic Dust and Iteration," Geometriae Dedicata 131 (2008), 27-48

"Prime Order Automorphisms of Riemann surfaces," in Proceedings of the International Workshop on Teichmuller Theory and Moduli Problems, HRI Lecture Notes Series, Ramanujan Mathematical Society, (2009) 21 pages

"Cutting Sequences and Palindromes (with Linda Keen) in geometry of Riemann Surfaces," London Math Soc Lecture Note Series volume 368, (2009) 24 pages

"Discreteness Criteria and the Hyperbolic Geometry of Palindromes," (with Linda Keen), Journal of Conformal Geometry and Dynamics 13 (2009), 76-90

"Enumerating Palindromes and Primitives in Rank Two Free Groups (with Linda Keen), Journal of Algebra, (2011) 1-13

"Lifting free subgroups of PSL(2;R to a rank-two free group" (with Linda Keen), submitted

## Research Initiatives

Kleinian groups, Teichmuller theory, mapping-class groups, hyperbolic geometry including computational aspects, combinatorial group theory and dynamical systems