Winter Term 2017/2018

Lecturer:  Prof. Dr. Holger Reich, Prof. Dr. Elmar Vogt

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• Time and Place:  Tuesday, 14:00-16:00 h, Arnimallee 7, SR 031

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Content: 

In this seminar we want to study algebraic K-theory. To every ring R (or more generally to every exact category, or Waldhausen category, or stable infinity-category) one associates a space (or spectrum), whose homotopy groups are denoted K_i(R). While K_0(R) and K_1(R) have very simple and concrete algebraic descriptions, higher algebraic K-theory groups are more involved and usually very difficult to compute.
Whereas the first talks in the seminar may only need basic knowledge in algebra, we will later also use concepts from algebraic topology and in particular homotopy theory. 

The seminar language is English.

Talks

Date	Title	Speaker
17.10.	Preliminary Discussion	Holger Reich /  Elmar Vogt
24.10.	Discussion
07.11.	1. Wall’s finiteness obstruction	Tatiana Levinson
14.11.	2. K_0 of Dedekind domains	Alberto Richtsfeld
21.11.	3. K_2 and universal central extensions	Alexander Müller
28.11.	4. The K-theory space I	Georg Lehner
05.12.	5. The K-theory space II	Robert Cardona
12.12.	6. The additivity theorem I	Vincent Boelens
19.12.	7. The additivity theorem II	Vincent Boelens
09.01.	8. Quillen’s Q-construction	Anna Buhné
16.01.	9. Quillen’s plus construction
23.01.	10. Negative K-theory
30.01.	11. Assembly maps
06.02.	TBA
13.02.	TBA

Literature:

J. Milnor: Introduction to Algebraic K-Theory, Ann. of Mathematics Studies Number 72, 1971
I. Madsen and I. Patchkoria: Notes for Categories and Toplogy, Univ. Copenhagen, 2016