Midwest Topology Seminar

April 28-29, 2007
Wayne State University
Detroit, Michigan

Speaker: Andrew Blumberg (Stanford University)

Title: Approximation and localization in THH

Abstract: Approximation theorems in algebraic K-theory provide criteria for a functor between suitable categories to induce an equivalence of K-theory spectra.  Localization theorems provide criteria for a sequence of functors to give rise to a cofiber sequence of K-theory spectra.  Although approximation and localization are central to our understanding of algebraic K-theory, the corresponding phenomena in THH and TC are more complicated and mysterious.  In this talk, I will discuss a conceptual explanation of the situation and describe approximation and localization theorems in the setting of the THH of Waldhausen categories.

Speaker: Marco Schlichting (Louisiana State University)

Title: Karoubi-periodicity in hermitian K-theory via chain complexes

Abstract: I will explain a new and somewhat more general proof of Karoubi's fundamental theorem in hermitian K-theory using methods inspired by the work of Waldhausen and Thomason.

Speaker: Jeff Smith (University of British Columbia)

Title: Ideal spectra and topological schemes

Abstract: In this talk I play with the definition of ideal and of scheme with the idea of finding a definition that works for ring spectra. One hopes it would have some use.

Speaker: Veronique Godin (Harvard University)

The higher genus string topology

Abstract: I will highlight the construction of operations on the homology of the free loop space of a smooth manifold that are parameterized by the homology of some moduli space.

Speaker: Tyler Lawson (MIT)

Topological Hochschild homology of ku and ko

Speaker: Jack Morava (Johns Hopkins University)

Title: The Madsen-Tillmann 4D Spin cobordism spectrum

Abstract:  The techniques of Madsen, Tillmann, et al [math.AT/0605249], originally developed to study Riemann surfaces, can be applied to 4D Spin manifolds. Away from the prime two, the resulting spectrum seems to have an interpretation as some kind of endomorphism ring of a Madsen-Tillman spectrum for 3D Spin manifolds.

Contact Dan Isaksen (isaksen at math.wayne.edu) for more information.