K-theory Lunch Seminar: Spring 2009

K-theory Lunch Seminar

A semester-long lunch seminar devoted to understanding connections between crystalline cohomology, algebraic K-theory, and topological cyclic homology. The seminar is intended to provide enough background so that both algebraic topologists and algebraic geometers can understand enough to make the content accessible.

When: Thursdays, 11:30-1:00 during spring 2009.
Where: MIT, room 2-151.
Who: The seminar is being organized by Mark Behrens, with the help of Kiran Kedlaya and Clark Barwick. Funding is provided by the MIT NEC fund.
Format: Lunch will be provided to participants. Please contact Mark Behrens at

to be added to the mailing list.

Schedule of talks:

Below is a list of talks. Some talks still need speakers, volunteers welcome! Pdf files of my electronic notes are also posted (any mathematical errors in these notes are probably introduced by me!)

Feb 12
De Rham cohomology and the infinitesimal site
(Anatoly Preygel)
abstract notes
Feb 19
Crystals and the crystalline site I
(Kiran Kedlaya) notes
Feb 26
The de Rham-Witt complex
(Chris Davis) abstract notes handout
Mar 5
Crystals and the crystalline site II
(Kiran Kedlaya) notes
Mar 12
Miscellanea on Crystalline Cohomology
(Jay Pottharst) abstract notes
Mar 19
Homotopical background I: simplicial objects, homotopy (co)limits
(Samuel Isaacson)
notes pset
Mar 20 (Fri)
Homotopical background II: infinite loop spaces and spectra
(Mark Behrens)
Special time and place: 2:00-3:00, MIT room 2-136
Mar 26
No seminar
(MIT spring break)
Apr 2
Definitions of algebraic K-theory (Inna Zakharevich)
abstract notes Inna's Texed notes
Apr 9
K-theory of rings, K_0, K_1, K_2
(Angelica Osorno)
notes
Apr 16
Bloch's work on crystals and K-theory I: overview of the theory
(Clark Barwick)
notes
Apr 17 (Fri)
Bloch's work on crystals and K-theory II: more details
(Clark Barwick)
Special time and place: 2:00-3:00, MIT room 2-105
notes
Apr 23
Topological Hochschild homology and topological cyclic homology
(Andrew Blumberg)
notes
Apr 24
Homotopical Background III: Spectra and stable homotopy, continued
(Mark Behrens)
Special time and place: 2:00-3:00, MIT room TBA
Apr 30
Calculational overview of the K-theory of fields, relationship to TC
(Mark Behrens)
notes
May 7
Calculations of Bockstedt-Madsen of the K-theory of unramified extensions of Q_p via TC
(Mark Behrens)
notes slides
May 14
Work of Hesselholt-Madsen: K-theory of local fields and the de Rham-Witt complex
(Christian Ausoni) notes
May 21
The Lichtenbaum Conjectures
(Clark Barwick)
abstract notes