Contents
Quaternionic Modular Forms
Hermitian Modular Forms
Hilbert Siegel Modular Forms
Hilbert Jacobi Forms
Modular Forms over Function Fields
Cohomology of Arithmetic Groups
To do:
- Give definitions. Relation between cohomology of group and cohomology of locally symmetric space.
- Give examples. Relation to other topics in this section (e.g. Siegel, Hilbert).
- Explain relationship between cohomology of arithmetic groups and automorphic forms (Borel conjecture/Franke's Theorem). Cuspidal cohomology and Eisenstein cohomology.
- Hecke operators and how they act on the cohomology.
- Topological models used to compute cohomology.
Results; examples of cuspidal cohomology (SL_3(\mathbf{Z}), SL_4(\mathbf{Z})). Examples of boundary cohomology.