Instructor: Prof. Eyal Goren
Office hours: TBA
Lectures: BURN 1214, MWF 11:35
- 12:25 (I wish to change it to MW 11:00 - 12:30, or 11:30 - 13:00. It
will be discussed in the first meeting on Wednesday, January 4.)
to many subjects of mathematics,
physics and other branches of science and engineering. We shall pay
special attention to considering algebraic groups over any field, and
not just over the complex numbers. Thus, our perspective is influenced
by the role algebraic groups play in number theory, although such
considerations are often relevant in algebraic geometry, differential
geometry and representation theory.
Text Book: Springer, T.
A.: Linear algebraic groups.
edition. Modern Birkhäuser Classics.
Birkhäuser Boston, Inc., Boston, MA, 2009.
Syllabus: This is an introductory
course about linear algebraic groups. While we
shall assume familiarity with basic algebraic geometry (the material
covered in a typical one semester course on algebraic geometry, and, in
particular, the material in Chapter one of Springer's book), we shall
not assume any familiarity with the theory of algebraic groups itself.
We shall, to a large extent, follow T. A. Springer's book "Linear
algebraic groups", which will serve as the official text book for this
course. To the extent time permits, we shall supplement Springer's book
with the study of representations of algebraic groups, where the book
by Fulton and Harris "Representation theory, a first course", GTM, will
be our main reference. For a more detail overview of the course simply
refer to the table of contents in Springer's book. We shall cover as
much of it as time permits (and in the same order), altough the
material will be "sprinkled" with examples and applications going
beyond the material in the book.
Method of Evaluation: 50%
take-home final, 30% midterm (in class), 20% assignments.
Notes: 1 2 3 4 5
(The notes may still contain mistakes. Please bring those to my
attention at eyal dot goren "at" mcgill "dot" ca)
Academic integrity: 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 www.mcgill.ca/integrity for more
Submitting work: In accord with
McGill University’s Charter of Students’ Rights, students in this
course have the right to submit in English or in French any written
work that is to be graded.
Syllabus and Grade Calculation:
In the event of extraordinary circumstances beyond the University’s
control, the content and/or evaluation scheme in this course is subject