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