Master Course 'Modular Forms'
(Landelijk Mastercollege Modulaire Vormen)
This course intends to give an introduction to the area of
modular forms.
Modular forms occurs every where in mathematics,
in algebraic geometry, in number theory and even in
string theory. They play a very important role, for
example they were pivotal for the proof of Wiles
of Fermats Last Theorem.
Prerequisites are a (modest) knowledge of
algebra and function theory. Some knowledge of algebraic
geometry and number theory will be helpful, but is not absolutely necessary.
Topics treated are: modular forms on SL(2,Z), Hecke operators,
modular symbols, Atkin-Lehner theory, periods, Dirichlet series,
modular curves, Eichler-Shimura, Galois representations
Siegel modular forms.
Literature:
F. Diamond, J. Shurman: A first course in modular forms.
Graduate Texts in Math 228, Springer Verlag 2005.
W. Stein: Modular Forms, a computational approach. Graduate Studies
in Math. AMS 2007.
G. Shimura: Introduction to the arithmetic theory of automorphic
functions. Princeton University Press.
More references to the literature will be given during the course.
The course starts in week 6 of 2009.
Time: Wednesday 10:15-13:00
Location: REC-D 028, Gebouw D, Nieuwe Achtergracht 129, Amsterdam
Click here
for the exercises.
Click here for a list of
topics treated and to be treated.
Planned course dates:
March 25, April 1, April 8, April 22, May 20.
But please check here for updates!