My research interests are in geometric topology, mapping class groups, Teichmüller theory, and geometric group theory.

Previously I was a graduate student at the University of Chicago, where I received my PhD under the direction of Benson Farb.

Department of Mathematics

1409 W Green Street

Urbana, IL 61801

**Hyperbolic extensions of free groups**(pdf) (arXiv)

(with Samuel J. Taylor)

**Unbounded asymmetry of stretch factors**(pdf) (arXiv)

(with Ilya Kapovich and Christopher J. Leininger)

**McMullen polynomials and Lipschitz flows for free-by-cyclic groups**(pdf) (arXiv)

(with Ilya Kapovich and Christopher J. Leininger)

**Dynamics on free-by-cyclic groups**(pdf) (arXiv)

(with Ilya Kapovich and Christopher J. Leininger)

**Pseudo-Anosov subgroups of fibered 3–manifold groups**(pdf) (arXiv)

(with Richard P. Kent IV and Christopher J. Leininger)

to appear in*Groups, Geometry, and Dynamics*

**Spheres in the curve complex**(pdf) (arXiv)

(with Moon Duchin and Howard Masur)

*Contemporary Mathematics*, vol. 590, Amer. Math. Soc., Providence, RI, 2013, pp.1-8. (journal link)

**Statistical hyperbolicity in Teichmüller space**(pdf) (arXiv)

(with Moon Duchin and Howard Masur)

*Geom. Funct. Anal.*Vol. 24 (2014) 748-795. (journal link)

**Dilatation versus self-intersection number for point-pushing pseudo-Anosov homeomorphisms**(pdf) (arXiv)

*Journal of Topology*4 (2011) no. 4: 942-984. (journal link)

This material is based upon work supported by the National Science Foundation under Award No. 1204814.

Spring 2014: Not teaching this semester.

Spring 2013: Math 231 (Calculus II), Lectures CL1 and DL1

Spring 2012: Math 402 (Non-Euclidean Geometry), sections C13 and D13

Fall 2011: Math 402 (Non-Euclidean Geometry), section C13

(at the University of Chicago):

Autumn 2010: Math 112 (Studies in Mathematics), section 40

Winter 2010: Math 153 (Calculus 3), section 24

Autumn 2009: Math 152 (Calculus 2), section 24

Spring 2009: Math 133 (Calculus 3), section 22

Winter 2009: Math 132 (Calculus 2), section 22

Autumn 2008: Math 131 (Calculus 1), section 22