Introduction
Classical modular forms are functions on the
complex upper half plane which transform in a certain way under the
action of integral Mobius transformations. In spite of their
somewhat pedestrian definition, modular forms may be variously
viewed as:
- functions, and differential forms, on modular curves;
- generating functions which encode combinatorial
identities;
- transcendental functions which occasionally (and predictably) take
algebraic numbers to other algebraic numbers in a meaningful way;
- etc.
Modular forms and their generalizations appear throughout
geometry and number theory.
This course develops the classical theory of complex modular forms and
curves, and selectively visits some of its recent applications.
Logistics
The course meets MWF10-10:50 in Weber 130.
Requirements
For much of the semester, homework will be posted weekly. It is
expected that for each problem set you will at least look at every problem, and hand in
(or be prepared to present) two problems.
Help
Questions directed to
j.achter@colostate.edu
will be answered swiftly. Office hours will be listed here.