# Lassina Dembele's Course

## This is what I intend to cover in my lecture.

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

**If time permit, there will be an additional section:**
- 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