## General information

I am an Assistant Professor of Mathematics at Stanford University. In Spring 2018 I am teaching Math 120, and in Winter 2018 I taught Math Discovery Lab.

My research is in topology, especially low-dimensional topology, and representation theory. I am especially interested in moduli spaces, broadly defined. I was honored to receive the 2015 Kamil Duszenko Prize.

My CV is available.

I've just posted notes from a undergraduate reading course on differential topology.

**New papers posted:**

*Which groups are amenable to proving exponent two for matrix multiplication?*, with Blasiak, Cohn, Grochow, and Umans (posted **December 2017**)

*On finite generation of the Johnson filtrations*, with Ershov and Putman (posted **November 2017**)

*Linear and quadratic ranges in representation stability*, with Miller, Nagpal, and Reinhold (posted **June 2017**)

*Bounding the homology of FI-modules* (posted December 2016)

*On cap sets and the group-theoretic approach to matrix multiplication*, with Blasiak, Cohn, Grochow, Naslund, Sawin, and Umans (major update August 2016)

*The codimension-one cohomology of SL*_{n}**Z**, with Putman (July 2016, final version)

*Homology of FI-modules*, with Ellenberg (major rewrite September 2016, final version)

*Integrality in the Steinberg module and the top-dimensional cohomology of GL*_{n}*O*_{K}, with Farb and Putman (revised August 2016)