David Hansen

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.

In Summer 2016, Shizhang Li and I are co-organizing an informal learning seminar on rigid analytic geometry.  The website is here.

In Fall 2016, I'm teaching a graduate topics class: p-adic Hodge theory

blog

My Address:
Room 516
Department of Mathematics
Columbia University
2990 Broadway
New York, NY 10027
lastname @ math.columbia.edu


Papers and Preprints

Analytic p-adic L-functions for GL2 (book) (coming soon; here are some notes)
summary

Iwasawa theory of overconvergent modular forms, II: A two-variable main conjecture (coming soon)
summary

Period morphisms and variations of p-adic Hodge structure (pdf )
Preliminary draft (version of 5/6/2016)

Quotients of adic spaces by finite groups ( pdf )
Submitted (version of 3/10/2016)

On the GLn-eigenvariety and a conjecture of Venkatesh ( pdf ), with J. Thorne
Submitted (version of 8/17/2015). A lecture at the IAS.

Overconvergent modular forms and perfectoid Shimura curves (arxiv | pdf ), with P. Chojecki and C. Johansson
Submitted (version of 8/14/2015)

Iwasawa theory of overconvergent modular forms, I: Critical p-adic L-functions ( pdf )
Submitted (version of 6/2/2015)

Universal eigenvarieties, trianguline Galois representations, and p-adic Langlands functoriality (arxiv | pdf | journal )
J. reine angew. Math., to appear.

Minimal modularity lifting for GL2 over an arbitrary number field (arxiv | pdf )
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)

Other writings

Warning: I haven't edited some of these very carefully.

Period maps, variations of p-adic Hodge structure, and Newton stratifications (pdf )
A detailed research announcement.

Notes on diamonds (pdf )
Version of 5/7/2016.

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