PhD Students

Current: Francisco Arana Herrera, co-advised with Steven Kerckhoff, Stanford.

Former: Ben Dozier, co-advised with Maryam Mirzakhani, Stanford, graduated Spring 2018.

Semester Program

From July 1 to December 31, 2018 the Fields Institute in Toronto will host a Thematic Program on Teichmuller Theory and its Connections to Geometry, Topology and Dynamics


Retrospective on Maryam Mirzakhani that I wrote for Science: preprint, published version.

Quanta Magazine article on my joint work: New Shapes Solve Infinite Pool-Table Problem. Accompanying blog post: Why Mathematicians Like to Classify Things.

Not for Publication

Notes on Mirzakhani's work on earthquakes

Notes on Cubic curves

Course notes on Moduli spaces of Riemann surfaces

Illumination and Security (with Kathryn Mann)

Luck's Theorem on growth of Betti numbers

Notes on Filip's proof that orbit closures are algebraic

A brief summary of Otal's proof of marked length spectrum rigidity

Deligne's Theorem on the semisimplicity of variations of Hodge structures

Smillie's Theorem on closed SL_2(R) orbits of quadratic differentials (with Ilya Gekhtman)

Topic Proposal: Translation surfaces and Teichmüller theory

Old Material

Undergraduate Projects

Chicago Informal Dynamics Seminar, 2013-2014

Reading group on the Cremona group, summer 2016