# David Loeffler: Research

My field of research is number theory. More specifically, I'm interested in the following (closely related) areas:

- P-adic modular forms and automorphic forms
- Locally analytic representation theory of p-adic groups

- p-adic Galois representations and Iwasawa theory

- Computational methods for automorphic forms

See also my **publications** page.

## Galois cohomology study group

In spring 2014, Alex Bartel and I are organising a study group on Galois cohomology; see here.

## Rigid geometry study group

In summer 2011 I am organising a study group on p-adic rigid analytic geometry; see here.

## Notes and other junk

Some of the computer programs I have written can be found here; but newer versions of many of these are incorporated in Sage.

- Computing with algebraic automorphic forms (notes of my lectures at the 2011 Heidelberg summer school)
- Slides for my talk Calculating Automorphic Forms for Unitary Groups Using SAGE at the Sage Days 6 conference, 11/11/2007.
- Notes for my talk Approaches to computing overconvergent
*p*-adic modular forms and the accompanying implementation presentation at the Heilbronn Institute workshop "Computing with automorphic forms", summer 2008 - Slides for my talk Calculating p-adic modular forms at Sage Days 16, 25/6/2009.
- A note on the norm of the U
_{p}operator - A note on the norms of overconvergent eigenfunctions
- Attempts to factorise the U
_{3}operator - Study group talks:
- De Rham cohomology (November 2005)
- The highest weight theorem (October 2006)
- Supercuspidal representations of GL
_{n}(F) (February 2007) - A spectral sequence primer (May 2007)

- Cambridge things:
- Elliptic Curves notes for the Lent 2005 Part III course
- My Part III essay: Congruences between modular forms.
- Spectral Measures, my entry for the 2003 Yeats Mathematical Essay Prize at Trinity College

- General junk:
- A note on topological groups (in which I show that if G is compact and Hausdorff its conjugacy class space is Hausdorff in the quotient topology).
- An introduction to Burnside's algorithm for calculating character tables of finite groups.
- A short note on roots of cubic polynomials (written for Eureka #58, which apparently never appeared), in which I investigate when all of the roots of a complex cubic have the same absolute value. (Although this was motivated by my research on automorphic forms for unitary groups, the actual content is elementary.)