Cornell Math - MATH 731, Fall 2004

MATH 731: Seminar in Noncommutative Algebra and Geometry II (Fall 2004)

Instructor: Yuri Berest

Meeting Time & Room

NOTE: The first lecture will be on Wednesday, September 1.

This is a continuation of our seminar on noncommutative algebra and geometry started in Fall 2003. The purpose of the seminar to study a variety of topics from homological algebra and algebraic geometry which find applications in modern mathematical physics. In particular, we plan to give a (more or less) faithful introduction to A_{\infinity}-structures (including A_{\infinity}-categories which are at the heart of a homological approach to Kontsevich's mirror symmetry conjecture) as well as to the theory of triangulated (derived) categories and derived equivalences.

We will try to make the discussion understandable for graduate students with various backgrounds and will not assume the knowledge of the material
discussed in the first part of the seminar.

Some references:

1. M.Kontsevich, "Triangulated Categories and Geometry", lecture notes, IHES, 1998

2. B.Keller, "Introduction to $A$-infinity algebras and modules. Homology Homotopy Appl. 3(1) (2001), 1-35.

3. V.Ginzburg, "Lectures on Noncommutative Geometry", book in preparation, Chicago 2002..