Great Lakes K-theory Conference, X
The tenth annual Great Lakes K-theory Conference will be held May 8 - 9, 2004, at the University of Illinois at Urbana-Champaign. The conference is
being organized locally by Dan Grayson and Randy McCarthy with the help and scientific advice of Eric
Friedlander, Rick Jardine, and Manfred Kolster.
For planning the banquet, it would be helpful if you would let Dan Grayson <firstname.lastname@example.org> know by Wednesday,
May 5, that you would like to attend.
This time we are pleased to announce that the conference is generously funded by the National Science
Foundation and the University of Illinois. At least half of the funds made available by the NSF grant
must go to US-based graduate students, junior faculty, underrepresented groups and/or otherwise
unsupported individuals, so we are eager to receive applications for financial support from such
To apply for support, please send email to Dan Grayson
<email@example.com>, estimating your expenses and stating what other monetary support is
potentially available to you. Please include references to publications and/or solicit a brief email
letter of reference from an advisor or mentor. US-based Graduate students are especially encouraged to
apply. For full consideration please submit your application by March 26, 2004. If you miss the
deadline, don't hesitate to apply after that date, for there may be cancellations or not enough
The talks will take place in Altgeld
Hall, 1409 W. Green St., Urbana, IL 61801, in room 245. The
refreshments will be served in room 321 upstairs, and that room
can serve as a gathering place before the talks.
- Saturday, May 8, 2004:
10:00 am: gather in 321 Altgeld before the talks for coffee and snacks
- 11:15 am - 12:15 pm :
Gunnar Carlsson, Stanford University, on "Derived representation theory and the K-theory of fields". Abstract:
This talk describes a program for identifying the homotopy type of
the algebraic K-theory spectrum of a field in terms of a model built
entirely out of the absolute Galois group of the field, and the
K-theory spectrum of an algebraically closed field. The ingredients
are the complex representation theory of the absolute Galois group,
together with a homotopy invariant version of completion. I will
describe the current state of the program.
- 2:00 - 3:00 pm:
Christian Haesemeyer, University of Illinois at Urbana-Champaign, on "Homotopy K-theory of
blow-ups". Abstract: We give a proof that Weibel's homotopy invariant K-theory satisfies the
expected descent property for arbitrary blow-ups, at least over a base field of characteristic zero. We
give applications regarding the negative K-groups of singularities, obtaining partial results on the
relevant conjecture of C. Weibel.
3:00 pm: coffee break, 321 Altgeld
- 3:45 - 4:45 pm:
Marc Levine, Northeastern University, on "The Postnikov tower in motivic stable homotopy
theory". Abstract: Voevodsky has defined a version of the Postnikov tower in the motivic stable
homotopy category and has shown that the "slices" in this tower have the natural structure of
motives. We will describe how the homotopy coniveau tower used by Friedlander-Suslin in their
interpretation and generalization of the Bloch-Lichtenbaum motivic cohomology to K-theory spectral
sequence generalizes further to give another construction of Voevodsky's Postnikov tower. This gives a
direct relation of the motivic Postnikov tower with the Friedlander-Suslin tower, showing that the
slices of the motivic Postnikov tower for K-theory are motivic
- 5:15 - 6:15 pm:
Steve Mitchell, University of Washington, on "K(1)-local homotopy theory, Iwasawa theory, and the algebraic
K-theory of number rings". Abstract: The Iwasawa algebra is a power series ring in one variable
over the p-adic integers. It arises in number theory as the pro-group
ring of the Galois group of cyclotomic p-extensions, and in homotopy
theory as a ring of operations in p-adic complex K-theory. These two
incarnations of the Iwasawa algebra are connected in an interesting way
by the algebraic K-theory spectra of number rings. We will explore this
connection, and discuss some recent applications to Stiefel-Whitney
classes of real embeddings of number rings.
- 7:30 pm: catered banquet at Dan Grayson's house, partially subsidized for graduate students.
- Sunday, May 9, 2004:
8:00 am: gather in 321 Altgeld before the talks
- 9:00 - 10:00 am:
Holger Reich, University of Muenster, on "The Farrell-Jones Conjecture for higher algebraic
K-Theory". Abstract: The Farrell-Jones Conjecture predicts that the algebraic K-Theory of a group
ring RG can be expressed in terms of the algebraic K-Theory of the coefficient ring R and homological
information about the group. After an introduction to this circle of ideas the talk will report on
recent joint work with A. Bartels which builds up on earlier joint work with A. Bartels, T. Farrell and
L. Jones. We prove that the Farrell-Jones Conjecture holds in the case where the group is the
fundamental group of a closed Riemannian manifold with strictly negative sectional curvature. The result
holds for all of K-Theory, in particular for higher K-Theory, and for arbitrary coefficient rings R.
10:00 am: coffee break, 321 Altgeld
- 10:30 am - 11:30 am:
Jonathan M. Rosenberg, University of Maryland, on "A K-theory perspective on T-duality in string theory".
Abstract: An idea which is now well established in the physics literature
is that "charges" on "branes" should take values in twisted (topological)
K-theory, where the twisting is given by a cohomology class that
represents the field strength. It is also expected that "T-duality"
should hold, meaning that the theory on one space-time (with
background field) is equivalent to that on another, where tori are
replaced by their duals. I will describe recent joint work with Mathai
Varghese in which we show how to make this rigorous for space-times
which are principal torus bundles. A surprising conclusion is that
sometimes the T-dual of a torus bundle turns out to involve
We have reserved (until April 7) a block of 40 rooms at the Illini Union, the building just East of
Altgeld Hall. Call 217-333-1241 to make a reservation. Rates are $72-$83 for 1 person, $83-88 for 2
persons, $93 for 3 persons, $97 for 4 persons, and $165 for a suite. Hotel tax is 11% extra. Parking
is available nearby. Refer to our conference when making a reservation, and send me email, too, so I
can confirm your identity to the hotel, if necessary.
We have also reserved (until April 23) a block of 15 rooms at Hampton Inn
at University of Illinois, about 0.2 miles east and then 0.4 miles north of Altgeld Hall,
217-337-1100. Rates are $60 for 1 person and $65 for 2 persons. Refer to our conference when making a
reservation, and send me email, too, so I can confirm your identity to the hotel, if necessary.
Anne Martel has a basement bedroom in Champaign about 1.0 miles west of Altgeld Hall, with a trundle bed (that
converts into two twin beds) for $45 per night. Call her at 217-398-6686.
for a listing of other hotels.
for instructions on traveling to the University of Illinois.
for up to date information.
Previous Great Lakes K-theory conferences: