Algebraic K-theory seminar
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.
List of speakers:
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).
Description of talks:
1) & 2)
Vector bundles, Swan's theorem
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.
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
Relative K_0 and relative K_1.
The notion of a homology theory.
The (somewhat) long exact sequence relating K_0 and K_1.
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.
Higher algebraic K-theory groups.
The plus construction.
Other definitions of higher algebraic K-theory.
The Bass-Heller-Swan theorem.