*Instructor:* Dr. Peter MAGA

*Course description:* our ultimate goal is to give a (partly) explicit bound on Hecke-Maass cusp
forms of PGL(n,Z)\PGL(n,R)/PO(n,R) in terms of their Laplace eigenvalue. Spectral analysis and the amplification
technique reduce the original problem to a (more or less) elementary matrix-counting one which can be analyzed using
algebraic (Galois theory and classical linear algebra) and combinatorial tools.
In the course, we try to work out the already existing method in explicit terms and potentially improve on that.