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 <dan@math.uiuc.edu> 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 individuals.

To apply for support, please send email to Dan Grayson <dan@math.uiuc.edu>, 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 applications.

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 cohomology. Slides - 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 non-commutative tori.

- 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.
- See http://www.math.uiuc.edu/~dan/travel.html for a listing of other hotels.

See http://www.math.uiuc.edu/~dan/travel.html for instructions on traveling to the University of Illinois.

See http://www.math.uiuc.edu/K-theory/Calendar/GL10/ for up to date information.