I’m a graduate student at the Harvard math department. You can email me at .

I’m interested in homotopy theory, higher category theory, derived algebraic geometry and combinatorics.

Something to read right here in the browser:

Iteration of rational maps, also available in PDF. This is my

*minor thesis*^{1}, it includes fairly complete proofs of Sullivan’s No Wandering Domains theorem and the classification of the periodic Fatou components and is, I hope, fairly light reading.

Expository papers (PDFs):

In the spring of 2012, I taught a tutorial about the fundamental groupoid called Groupoids in Topology.

For a combined precalculus/calculus course called Math Ma, I wrote a couple of interactive webpages using the brilliant JXSGraph library:

Bottle calibrator. You can draw the profile of a flask by dragging or adding points on a curve and see in real-time the graph of the height reached by some liquid poured in the flask as a function its volume.

Secant line animation. Yet another version of the classical secant line animation. You can specify your own function.

*Nilspaces, nilmanifolds and their morphisms*with Balazs Szegedy. [show abstract]*Positive graphs*with Endre Csóka, Tamás Hubai, Gábor Lippner, László Lovász. [show abstract]*Computing arithmetic invariants for hyperbolic reflection groups*with Gregory R. Maloney and Roland K. W. Roeder. [show abstract]*Corrigendum to “Groupoids, the Phragmen-Brouwer Property, and the Jordan Curve Theorem”, J. Homotopy and Related Structures 1 (2006) 175-183*with Ronald Brown. [show abstract]

Topologists, category theorists and derived algebraic geometers^{2}: David Ayala, John Baez, Clark Barwick, David Ben-Zvi, Dan Dugger, John Francis, Dennis Gaitsgory, Moritz Groth, André Joyal, William Lawvere, Tom Leinster, Jacob Lurie, Peter May, Ieke Moerdijk, David Nadler, Charles Rezk, Emily Riehl, Chris Schommer-Pries, Urs Schreiber, Michael Shulman, Carlos Simpson, David Spivak, Ross Street, Bertrand Toën.

You can find some of these people at the nLab or the n-Category Café.

(Limits of combinatorial structures)-ists^{3}^{,} ^{4}: Tim Austin, Christian Borgs, Jennifer Chayes, Persi Diaconis, Gábor Elek, Tim Gowers, Ben Green, Svante Janson, Yoshiharu Kohayakawa, László Lovász, Jaroslav Nešetřil, Patrice Ossona de Mendez, Alexander Schrijver, Vera Sós, Bálazs Szegedy, Terence Tao, Katalin Vesztergombi.

Top of the line lecture notes on various topics: Akhil Mathew, Anton Geraschenko, Chris Schommer-Pries, Chao Li

This an excellent program requirement: a chance to make a fool of yourself in writing by producing an exposition of a topic outside your field of expertise in a limited amount of time. I loved it! All math departments should have this.↩

Separating them into the three topics named is left as an exercise for the reader.↩

Possibly not the standard name for workers in this field.↩

The people on this list do

*lots*of other stuff too.↩