I'm a Ritt assistant professor here at Columbia. I like algebra and number theory, especially p-adic Hodge theory and p-adic aspects of the Langlands program. Previously I was a postdoc at l'Institut de Mathematiques de Jussieu. During 2010-2013 I was a Ph.D. student at Boston College, where my advisor was Avner Ash. I graduated from Brown University in May 2010 with a B.A. in mathematics. Here's my CV.
This semester I'm teaching Honors Math A and Number Theory and Cryptography.
Department of Mathematics
New York, NY 10027
lastname @ math.columbia.edu
Want me to referee something? Read this first.
Papers and Preprints
Vanishing and comparison theorems in rigid analytic geometry ( pdf )
Preprint (version of 2/6/2018)
A primer on reflexive sheaves, an appendix to On the Kottwitz conjecture for local Shimura varieties ( pdf | arxiv ) by T. Kaletha and J. Weinstein
Preprint (version of 9/19/2017)
On p-adic L-functions for Hilbert modular forms ( pdf | arxiv ), with J. Bergdall
Preprint (version of 10/15/2017)
Line bundles on rigid varieties and Hodge symmetry ( pdf | arxiv ), with S. Li
Preprint (version of 8/3/2017)
Degenerating vector bundles in p-adic Hodge theory ( pdf )
Preprint (version of 7/3/2017)
Extensions of vector bundles on the Fargues-Fontaine curve ( pdf | arxiv ), with C. Birkbeck, T. Feng, S. Hong, Q. Li, A. Wang and L. Ye
Preprint (version of 6/14/2017)
Moduli of local shtukas and Harris's conjecture, I ( pdf )
Preprint (version of 8/3/2016)
Period morphisms and variations of p-adic Hodge structure ( pdf )
Preliminary draft (version of 5/6/2016). The next version will be rather seriously revised - in the meantime, here's an Oberwolfach report.
Quotients of adic spaces by finite groups ( pdf )
Math. Res. Letters, to appear.
On the GLn-eigenvariety and a conjecture of Venkatesh ( pdf | journal ), with J. Thorne
Selecta Math., Vol. 23 Issue 2, pp. 1205-1234. A lecture at the IAS.
Overconvergent modular forms and perfectoid Shimura curves ( pdf | arxiv | journal ), with P. Chojecki and C. Johansson
Documenta Math., Vol. 22, pp. 191-262.
Iwasawa theory of overconvergent modular forms, I: Critical-slope p-adic L-functions ( pdf | arxiv )
Preprint (version of 6/15/2016)
Universal eigenvarieties, trianguline Galois representations, and p-adic Langlands functoriality ( pdf | arxiv | journal )
J. reine angew. Math., Vol. 2017 Issue 730, pp. 1-64.
Minimal modularity lifting for GL2 over an arbitrary number field ( pdf | arxiv )
Math. Res. Letters, to appear.
Shimura lifts of half-integral weight modular forms arising from theta functions ( pdf ), with Y. Naqvi
The Ramanujan Journal, Vol. 17 No. 3 (2008)
Warning: I haven't edited some of these very carefully. Also, some of these have been cannibalized by "official" papers above.
Artin vanishing in rigid analytic geometry ( pdf )
Obsolete shorter version of the paper "Vanishing and comparison..." above. Version of 8/24/2017
Some remarks on Banach-Colmez spaces and related diamonds (pdf )
The ideas sketched here are fully developed in the paper "Extensions..." above. Version of 3/3/2017.
p-adic Hodge theory (pdf )
Notes from a graduate topics class I taught at Columbia in Fall 2016. Unedited; use at your own risk!
Smoothness of Bunn for dinguses (pdf )
A letter to Jared Weinstein. Version of 12/25/2016.
Notes on shtukas and Harris's conjecture (pdf )
A letter to Jared Weinstein. Version of 5/24/2016.
Period maps, variations of p-adic Hodge structure, and Newton stratifications (pdf )
An announcement (?) of some results in the paper "Period morphisms..." above.
Notes on diamonds (pdf )
Version of 8/25/2016. Now with stacks!
Motivic cohomology actions and the geometry of eigenvarieties (pdf )
Notes on my paper with Jack.
A canonical two-variable p-adic L-function over the eigencurve (pdf )
Some version of this material will appear in "Iwasawa theory of overconvergent modular forms, II".
p-adic geometry, d'apres Peter Scholze (pdf )
Notes from an informal lecture series I gave at Columbia in Spring 2015, on Scholze's Berkeley course and related material. Most everything of interest here is redone more carefully and correctly in the "Notes on diamonds" above.
Overconvergent cohomology: theory and applications (pdf )
My PhD thesis; everything here has been incorporated into "Universal eigenvarieties..."
The Petersson norm of the Jacobi theta function (pdf )
What is a spectral sequence? (pdf )
Pairings on modules of analytic distributions (pdf )
The Gross-Zagier formula: a brief introduction (pdf )
Notes for a talk in the Harvard graduate student number theory seminar, March 2011.
Mordell-Weil growth for GL2-type abelian varieties over Hilbert class fields of CM fields (arxiv | pdf )
This is an extract from my Brown senior thesis.
The arithmetic of elliptic curves (pdf )
Notes for a talk I gave to some undergraduates at Williams College, November 2008.
Some German bicycles