Instructor: Prof. Eyal Goren

Ofiice: 1108

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.)

The theory of algebraic groups is important 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. Reprint of the 1998 second 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.

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 information).

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 to change.