Lassina Dembele's Course

MSRI 2006 Summer Graduate Workshop in Computational Number Theory

This is what I intend to cover in my lecture.

  1. Hilbert modular forms (HMF) and Hilbert modular varities (HMVs): the analytic theory.
  2. The arithmetic compactification of HMVs.
  3. Oda conjecture: this is a conjectural generalization of the Eichler-Shimura construction to HMFs.
  4. Computation of HMFs using the theory of Brandt modules. I will mainly focus on real quadratic fields.
  5. An algorithm for modular abelian surfaces defined on real quadratic fields based on Oda conjecture.

    If time permit, there will be an additional section:
  6. Computations of automorphic forms on the unitary groups in three variables and Hilbert-Siegel modular forms of genus 2.
I know David said he was interested in these topics. Paul G., I am sorry but I hope I am not overlaping on some of the things you want to cover. In any case, you use modular symbols, not Brandt modules. My main references are: I will also make available some of my papers that I will be following, very shortly. I am currently finishing the final corrections. I will arrive on July 28th and will be there for all the duration of the program. I will probably stay on campus (this for Gabor who asked me).

My Papers