Biography
I am interested in low dimensional topology and geometric group theory. In particular, I study mapping class groups. It is a beautiful area that combines geometry, topology, algebra, and combinatorics. I focus on the subgroups of mapping class groups that relate to (branched) covering spaces of surfaces.
Recently I've been working on applying topological techniques to complex dynamical problems. Specifically, I've been looking at recognizing topological polynomials.
Papers
"Twisting cubic rabbits" with Lanier.
"A solution to the degree-d twisted problem" with Mukundan.
"Pseudo-Anosov homeomorphisms of punctured non-orientable surfaces with small stretch factor" with Khan and Partin. To appear in Algebraic Geometry and Topology.
"Recognizing topological polynomials by lifting trees" with Belk, Lanier, and Margalit. To appear in Duke Mathematical Journal
"Big Torelli Groups: Generation and Commensuration" with Aramayona, Ghaswala, Kent, McLeay, and Tao. Geometry, Groups, and Dynamics.
"Using strong branching to find automorphisms of n-gonal surfaces" with Broughton, Camacho, Paulhus, and Wootton. In memory of Kay Magaard. Albanian Journal of Mathematics. Volume 12 (2018), no. 1, pg 89–129
"Birman--Hilden theory" (expository) with Dan Margalit.
"Lifting homeomorphisms and cyclic branched covers of the sphere" with Tyrone Ghaswala. Michigan Math Journal. Volume 66 (2017), no.4, pg 885-890
"The liftable mapping class group of superelliptic covers" with Tyrone Ghaswala. New York Journal of Mathematics.
"Symmetry, isotopy, and irregular covers" Geometria Dedicata.