This will be an introduction to the basics of modular forms, with talks
given by students. I plan to start with the hyperbolic and complex
geometry of the upper half plane, and move on to some examples (theta
functions, Eisenstein series) and fundamental theorems. Depending on
pace, we may consider some more advanced topics, such as positive
characteristic questions, modular jacobians and representations of
SL_{2}(**R**).

(4/14) The schedule of final talks is up. I will put up some notes on what I expect from a final paper.

(3/2) The definition of the lattice II_{p,q} given in class was
incorrect (and it was entirely my fault), so here is the correct
definition. The lattice vectors have
the form x_{1},...,x_{p},y_{1},...,y_{q},
where the sum of coordinates is even, and either all x_{i} and
y_{j} are integers or all are integers plus 1/2. Norms are given
by
x_{1}^{2}+...+x_{p}^{2}-y_{1}^{2}-...-y_{q}^{2}.
When p is congruent to q mod 8, the resulting lattice is even and
unimodular.