Fall 2011.

Run jointly by Tilman Bauer, Rob de Jeu, and André Henriques.

This seminar meets every Thursday at 9:00 alternatingly at UU and at VU.

1) Ludo (29 Sept), at VU, in room M664. Notes

2) Joost (6 Oct), at UU, in room BBL007 (BBL=Buys Ballot Laboratorium)

2a) Ralph (13 Oct), at VU, in room M664 Notes

3) Joey (20 Oct), at UU, in room BBL007

4) Julian (27 Oct), at VU, in room M664

5) Robin (3 Nov), at UU, in room BBL007 Notes

6) Daniel (10 Nov), at VU, in room P624 Notes

7) François (17 Nov), at UU, in room BBL - 322/325

8) Reinier (24 Nov), at VU, in room P624

9) Shan (1 Dec), at UU, BBL005 Notes.

10) Patrick (8 Dec), at VU, in room P624

11) Shan (15 Dec), at UU, in room 610 of the Wiskundegebouw (math building).

1) & 2) Projective modules Vector bundles, Swan's theorem Grothendieck construction K_0 of a ring Examples: fields, PID's, ring with K_0 = Z[1/2], ring with K_0 = 0.

2a) Computation of K_0 of some rings of integers in number fields.

3) Elementary matrices. The group GL_infty(R). K_1 of a ring defined as GL_infty(R)_ab. The two operations \oplus and matrix multiplication agree on K_1

4) Relative K_0 and relative K_1. The notion of a homology theory. The (somewhat) long exact sequence relating K_0 and K_1.

5) Morita equivalence of rings. K_0 and K_1 of a category. Morita invariance of the K groups.

6) & 7) Milnor's definition of K_2. Universal central extensions. K_2 as the center of the Steinberg group.

8) Classifying spaces. Simplicial sets.

9) Higher algebraic K-theory groups. The plus construction.

10) Other definitions of higher algebraic K-theory.

11) Negative K-theory The Bass-Heller-Swan theorem.