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

**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 GL_{2} (book)** (

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** (

Preliminary draft (version of 5/6/2016)

**Quotients of adic spaces by finite groups** (* pdf *)

Submitted (version of 3/10/2016)

**On the GL _{n}-eigenvariety and a conjecture of Venkatesh** (

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** (

Submitted (version of 6/2/2015)

**Universal eigenvarieties, trianguline Galois representations, and p-adic Langlands functoriality** (

**Minimal modularity lifting for GL _{2} over an arbitrary number field** (

**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** (

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** (

Some version of this material will appear in "Iwasawa theory of overconvergent modular forms, II".

** p-adic geometry, d'apres Peter Scholze** (

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.