MATH 480/595/693/740: Hyperbolic Geometry and
Automorphic Forms. Winter 2013
This is an undergraduate/graduate course, and mini-seminar, on
hyperbolic geometry and automorphic forms. Students are expected
to give many lectures in the course.
The two basic references for the course will be Svetlana Katok's
book Fuchsian groups, and Peter Sarnak's book Some applications
of modular forms. We shall discuss selected topics from both books.
Additional references will be added.
Dynamics and Quantum Chaos on hyperbolic surfaces by Alex Gorodnik
The students registered for the course will be expected to make
two oral presentations (between 30-50 minutes) on one of the topics
suggested by the instructors. Graduate students will also be expected
to write a short paper on a topic related to the course material.
The grades will be based on the presentations and the paper.
Homework problems: your grade will not depend on them,
but we suggest that you should do a few problems to better understand
Topics for presentation (references to be added):
Closed geodesics, continued fractions, etc: papers by S. Katok:
Automorphic forms, Quantum chaos etc: papers by P. Sarnak:
McGill University values academic integrity. Therefore, all
students must understand the meaning and consequences of
cheating, plagiarism and other academic offences under the Code
of Student Conduct and Disciplinary Procedures (see McGill web page
on Academic Integrity
for more information).
NOTICE: In accord with McGill University's Charter of Student
Rights, students in this course have the right to submit in English or
in French any work that is to be graded.
NOTICE: In the event of extraordinary circumstances beyond the
University's control, the content and/or evaluation scheme in this
course is subject to change