Stanford
University Topology Seminar 20067 Unless otherwise noted,
all seminars are on Tuesdays 4:00  5:00 pm in Room 383N
(Third floor of Math Building, Bldg 380). 

Autumn 2006 Schedule
Speaker:
No seminar this week.
Title:
Abstract:
Speaker:
Dan Ramras (Stanford)
Title:
Deformation Ktheory and Group Completion
Abstract: Deformation Ktheory provides a homotopy theoretical setting for the study of representations of infinite discrete groups. After introducing deformation Ktheory, I'll discuss the McDuffSegal form of the Group Completion Theorem. This theorem normally provides a homological model for the group completion of a topological monoid, but I'll explain how in certain settings (including deformation Ktheory) it actually provides a homotopy theoretical model. Two applications of this result will be discussed. The first uses YangMills theory to relate deformation Ktheory of surface groups to topological Ktheory of the underlying surface, and the second involves the ``excision problem'' for free products.
Speaker:
Sverre LunoeNielsen (Oslo and Stanford)
Title:
A homological approach to topological cyclic homology
Abstract:
I will explain a way of studying the fixed points of Bokstedt's
topological Hochschild homology spectrum THH(B) of an Salgebra B, under the action of
finite cyclic psubgroups G of the circle group.
While the strict equivariant structure of THH(B) is generally hard to calculate directly,
there is always a natural comparison map from the fixed points to the homotopy fixed points.
In favorable cases, this map is a pequivalence or a pequivalence when restricted to sufficiently high degrees.
When B is the sphere spectrum, this statement is equivalent to Segal's Burnside ring
conjecture for the group acting. For G = Z/p, Segal's conjecture was proven by
W.H. Lin (p=2) and Gunawardena (p>2) via calculations in cohomology and the Steenrod algebra.
This homological approach can be generalized to derive good comparison results between the
fixed points and the homotopy fixed points when G is cyclic of prime order and
B = BP and BP
Speaker:
Andrei Pajitnov (Nantes and Ohio State)
Title:
Circlevalued Morse theory for knots and links
Abstract:
Speaker:
Grace Lyo (Berkeley and Stanford)
Title:
Semilinear Representations in Ktheory and the Grothendieck Ring of a
Semisimple Twisted Group Ring
Abstract:
In this talk, we will begin by discussing a conjectural model for the
completed Ktheory spectrum of a field in terms of the Ktheory of the
category of continuous semilinear representations of its absolute Galois
group G_F. We will outline a strategy for showing that the conjecture
holds in a special case. This strategy requires an understanding of the
Grothendieck ring K_0 of the twisted group ring k
Speaker:
Alexandra Pettet (Stanford)
Title:
Cohomology of the Torelli subgroup of Aut(F_n)
Abstract: The Torelli subgroup of Aut(F_n) consists of those automorphisms of the free group F_n which act trivially on the homology of F_n. It is often compared with the Torelli group of a surface, the subgroup of the mapping class group which acts trivially on the homology of the surface. Little is known about the finiteness properties of these groups, including whether or not they are finitely presented. I will describe some methods for studying the cohomology of the Torelli subgroup of Aut(F_n).
BAY AREA TOPOLOGY SEMINAR (BATS)
This quarter BATS will be held at Stanford. Both talks will be in
Room 383 N on the third floor of the Mathematics Department (Building 380).
2:40 pm:
Speaker:
Eric Babson (UC Davis)
Title:
Homotopy theory for graphs
Abstract:
4:15 pm:
Speaker:
Ciprian Manolescu (Columbia)
Title:
A combinatorial description of knot Floer homology
Abstract:
Knot Floer homology is an invariant of knots in the
threesphere, which detects the genus of the knot, and can be used to
recover the Heegaard Floer homology of any surgery on that knot. The
original definition, due to OzsvathSzabo and Rasmussen, involved counts
of pseudoholomorphic disks in a symplectic manifold. In joint work with
Peter Ozsvath and Sucharit Sarkar, we found a purely combinatorial
description of this invariant. Starting with a grid presentation of the
knot, we construct a special Heegaard diagram for the knot complement, in
which the count of pseudolomorphic disks is elementary.
Speaker:
Andre Henriques (Univ. of Muenster)
Title:
Orbispaces are equivalent to a diagram category
Abstract:
A classical theorem of Elmendorf says that the homotopy theory of
Gspaces is equivalent to that of continuous functors O_G > Spaces, where
O_G is the orbit category of G. We prove an analog of this result for
orbispaces.
The category that plays the role of O_G is now a topological category
whose objects are groups, and whose morphisms for H to G are given by
(Mono(H,G) x EG)/G, where G acts by conjugation in the target.
Speaker:
Boris Botvinnik (Oregon)
Title:
Rational homotopy groups of the moduli space of positive scalar
curvature metrics
Abstract: The problem of determining when a smooth compact manifold admits a positive scalar curvature (psc) Riemannian metric is comparatively well understood. However, even for the nsphere, surprisingly little work has been done to date concerning the topological stucture of the space of all pscmetrics. In this talk, I will present some new results concerning the rational homotopy groups of this space for the nsphere with n>4. My approach uses results on higher analytical/topological torsion due to Hatcher, Igusa, and Goethe.
Speaker:
There will be no seminar this week due to the Thanksgiving break.
Title:
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Speaker:
No seminar this week due to the special algebraic geometry seminars.
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TBA
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