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)
Title: 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)
Title: 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.