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 dim-witted individual who holds an advanced degree in hyperbolic topology, that Homer Simpson has stumbled into... the third dimension!"

Research Interests

  • low-dimensional topology
  • (big) mapping class groups
  • curve graphs; combinatorics
  • hyperbolic geometry; identities on hyperbolic manifolds
  • Riemann surfaces; Teichmüller theory (both finite- and infinite-dimensional)
  • convex real projective structures; Hitchin representations

In Preparation*

*A paper is considered in preparation if either it is currently being written or there are main theorems forming the core of an article with (drafts of) proofs written.  Titles of articles in preparation are working titles.

Preprints

Publications

  • The Bridgeman-Kahn identity for hyperbolic manifolds with cusped boundary (journalarXiv)
    Joint with Andrew Yarmola.
    Geom. Dedicata (2017). doi:10.1007/s10711-017-0267-4
  • Automorphisms of the compression body graph (journalarXiv)
    Joint with Ian Biringer.
    J. London Math. Soc. (2) 95 (2017) 94-114.
  • Basmajian identities in higher Teichmüller-Thurston theory (journalarXiv)
    Joint with Andrew Yarmola.
    J. Topology 10 (2017), no. 3, 744-764.
  • Moments of a length function on the boundary of a hyperbolic manifold (journalarXiv
    Algebr. Geom. Topol. 15 (2015), no. 4, 1909-1929.
  • Quasiconformal homogeneity and subgroups of the mapping class group (journal | arXiv)
    Michigan Math. J. 64 (2015), no. 1, 53-75.
(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).