I use the algebraic geometry of formal groups and p-divisible groups to study chromatic stable homotopy theory. I'm particularly interested in transchromatic questions: what happens when formal groups change height, and what this tells us about chromatic localizations. I'm also interested in using the analytic geometry of Lubin-Tate space to study the action of the Morava stabilizer group.

Introduction to infinity-categories, a student seminar, October 2016.

Stable infinity-categories, Northwestern pre-Talbot seminar, February 2016.

The Steenrod algebra, a student algebraic topology seminar, January 2016.

Stable homotopy theory and geometry, Northwestern graduate student seminar, October 2014.

K3 cohomology theories, K3 seminar, September 2014.

Talk for number theorists on TMF, Northwestern number theory day, September 2014.

The Kervaire invariant, more focused on geometric topology aspects (and the construction of the Kervaire manifold) than stable homotopy theory, Kan seminar, May 2014.

Representability of algebraic K-theory by a motivic spectrum, Talbot, March 2014.

p-divisible groups, topological automorphic forms seminar, October 2013.

Kuhn's proof of the splitting of Goodwillie towers after finite *K(n)*-localization, summer Goodwillie calculus seminar, August 2013.

The construction of the A-hat genus, viewed as a height-1 analogue of the Ando-Hopkins-Rezk string orientation of tmf, reading course on Thom spectra, May 2013.

Introduction to spectra and Bousfield localization, Northwestern pre-Talbot seminar, January 2013.

Unfinished notes on topological automorphic forms, April 2014.

Notes for Paul Goerss's fall 2014 class on the Sullivan conjecture.

Notes and references for the fall 2013 topological automorphic forms seminar.

Talbots: structured ring spectra 2017, motivic homotopy theory 2014, chromatic homotopy theory 2013 (for which I typed up a whole lot of notes).

Advice on being a graduate student, from Terry Tao and Ravi Vakil.

On being a mathematician in the world: C. P. Snow's 'The Two Cultures'. Paul Lockhart's lament. A little parable.

A few philosophy papers: Carnap on language and ontology, Benacerraf on mathematical truth and knowledge, Benacerraf again on structuralism, Maddy on the axioms of set theory.