For you Simpsons fans out there, I like to think of myself as a hyperbolic topologist. The terminology comes from the following Professor Frink quote: "Well, it should be obvious to even the most dimwitted individual who holds an advanced degree in hyperbolic topology, that Homer Simpson has stumbled into... the third dimension!"
Research Interests
 lowdimensional topology
 mapping class groups; geometric and topological group theory
 curve graphs; combinatorics
 hyperbolic geometry; identities on hyperbolic manifolds
 Riemann surfaces; Teichmüller theory (both finite and infinitedimensional)
 convex real projective structures; Hitchin representations
Preprints
 Thurston norms of tunnel numberone manifolds (arXiv)
Joint with Natalia PachecoTallaj^{†} and Kevin Schreve.
 The first integral cohomology of pure mapping class groups (arXiv  pdf*)
Joint with Javier Aramayona and Priyam Patel.
^{†}Denotes an undergraduate author.
*A pdf link for a preprint indicates that there is a new version available that is not currently posted on the arXiv.
Publications
 Algebraic and topological properties of big mapping class groups (arXiv)
Joint with Priyam Patel.
Algebr. Geom. Topol., to appear.
 Coloring Curves on Surfaces (journal  arXiv)
Joint with Jonah Gaster and Josh Greene.
Forum Math. Sigma 6 (2018), e17.
 Graphs of curves on infinitetype surfaces with mapping class group actions (arXiv)
Joint with Matthew Durham and Federica Fanoni.
Ann. Inst. Fourier (Grenoble), to appear.
 The BridgemanKahn identity for hyperbolic manifolds with cusped boundary (journal  arXiv)
Joint with Andrew Yarmola.
Geom. Dedicata 194 (2018), 8197.
 Automorphisms of the compression body graph (journal  arXiv)
Joint with Ian Biringer.
J. London Math. Soc. (2) 95 (2017), no. 1, 94114.
 Basmajian identities in higher TeichmüllerThurston theory (journal  arXiv)
Joint with Andrew Yarmola.
J. Topology 10 (2017), no. 3, 744764.
 Moments of a length function on the boundary of a hyperbolic manifold (journal  arXiv)
Algebr. Geom. Topol. 15 (2015), no. 4, 19091929.
 Quasiconformal homogeneity and subgroups of the mapping class group (journal  arXiv)
Michigan Math. J. 64 (2015), no. 1, 5375.
(You can also see a list of all my publications/preprints on the arXiv here.)
Recorded Talks
My talk "Algebraic and topological properties of big mapping class groups" at the Groups, Geometry, and Dynamics seminar at UIUC was recorded and can be found here (the link will take you to YouTube).
