Cornell Math - MATH 731, Fall 2003
MATH 731
Seminar in Algebra: Noncommutative Geometry and Applications
(Fall 2003)
Instructor: Yuri Berest
In this seminar we will attempt to overview several areas of Noncommutative (NC) Geometry of high current interest. The list of topics may include:
- NC projective geometry (after M. Artin, Tate, Stafford, Van den Bergh,...),
- NC differential geometry (Connes,...),
- NC differential forms and de Rham cohomology (Cuntz, Quillen),
- NC symplectic and formal geometry (Kontsevich, Kapranov, Ginzburg,...).
Our intention is to focus on basic ideas and examples. We may also discuss some applications to other areas (including mathematical and theoretical physics). Your suggestions are welcome.
Some references:
1. M. Artin and J. Zhang, Noncommutative projective geometry, Adv. Math. 109 (1994), 228–287.
2. A. Connes, Noncommutative Geometry, Academic Press, 1994.
3. J. Cuntz and D. Quillen, Algebra extensions and nonsingularity, Journal of AMS 8 (1995), 251–289.
4. V. Ginzburg, Noncommutative symplectic geometry, quiver varieties, and operads, Math. Res. Lett. 8 (3) (2001), 377–400.
5. M. Kapranov, Noncommutative geometry based on commutator expansions, J. Reine Angew. Math. 505 (1998), 73–118.
6. M. Kontsevich, Formal noncommutative symplectic geometry, Gel'fand Mathematical Seminars, 1990-1992, Birkhauser 1993, pp. 173–187.
7. J. T. Stafford and M.Van den Bergh, Noncommutative curves and noncommutative surfaces, Bull. Amer. Math. Soc. 38 (2) (2001), 171–216.