Ktheory Lunch Seminar: Spring 2009
Ktheory Lunch Seminar
A semesterlong lunch seminar devoted to understanding connections between
crystalline cohomology, algebraic Ktheory, 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, 11:301:00
during spring 2009.
 Where: MIT, room 2151.
 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 RhamWitt 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: 2:003:00, MIT room 2136

Mar 26
No seminar
(MIT spring break)

Apr 2
Definitions of algebraic Ktheory
(Inna Zakharevich)
abstract
notes
Inna's Texed notes

Apr 9
Ktheory of rings, K_0, K_1, K_2
(Angelica Osorno)
notes

Apr 16
Bloch's work on crystals and Ktheory I:
overview of the theory
(Clark Barwick)
notes
Apr 17 (Fri)
Bloch's work on crystals and Ktheory II:
more details
(Clark Barwick)
Special time and place: 2:003:00, MIT room 2105
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: 2:003:00, MIT room TBA

Apr 30
Calculational overview of the Ktheory of fields, relationship to TC
(Mark Behrens)
notes

May 7
Calculations of BockstedtMadsen of the Ktheory of unramified
extensions of Q_p via TC
(Mark Behrens)
notes
slides

May 14
Work of HesselholtMadsen:
Ktheory of local fields and the
de RhamWitt complex
(Christian Ausoni)
notes

May 21
The Lichtenbaum Conjectures
(Clark Barwick)
abstract
notes