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Stanford
University Topology Seminar 2007-8 Unless otherwise noted,
all seminars are on Tuesdays 4:00 - 5:00 pm in Room 383-N
(Third floor of Math Building, Bldg 380). |
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Spring 2008 Schedule
Tuesday, April 1 , 2008
Speaker:
No Seminar Scheduled
Title:
Abstract:
Tuesday, April 8
Note: We will have two speakers this week!
First lecture: 4:00 pm:
Speaker:
Nathalie Wahl, Univ. of Copenhagen
Title:
Homological Conformal Field Theories
Abstract:
Second lecture: 5:15 pm:
Speaker:
Mikael Vejdemo-Johansson, Jena, Sweden Title:
On the computation of A-infinity algebras and Ext-algebras
Abstract:
For a ring R, the Ext algebra Ext_R^*(k,k) carries rich information about the ring and its module category. The algebra Ext_R^*(k,k) is a finitely presented k-algebra for most nice enough rings. Computation of this ring is done by constructing a projective resolution P of k and either constructing the complex Hom(P_n,k) or equivalently constructing the complex Hom(P,P). By diligent choice of computational route, the computation can be framed as essentially computing the homology of the differential graded algebra Hom(P,P).
Speaker:
Graeme Segal, Oxford Univ.
Title:
Non-commutative geometry and quantum field theory
Abstract:
There is a rough equivalence between the category of commutative rings
and the category of topological spaces, which is the basis of the way in
which quantum physics describes the world. Thinking about the
equivalence leads us towards variants and generalizations of the objects
on both sides of the picture. On the algebraic side we can consider
non-commutative rings, but also more subtle kinds of algebraic
structures such as quantum field theories. I shall describe how these
variants are reflected in the homotopy theory on the geometrical side.
Speaker:
Matt Clay, Univ. of Oklahoma
Title:
Growth rate of intersection numbers for free group automorphisms
Abstract:
P. Scott has defined a notion of intersection number between
splittings of a group which generalizes the familiar notion of
intersection number between curves on a surface. We investigate the
asymptotic behavior of this intersection number between trees in Culler
Vogtmann Outer Space when one of the trees is iterated by a fully
irreducible free group automorphism. This is joint work with Jason
Behrstock and Mladen Bestvina.
Speaker:
Jesper Grodal, Univ.of Copenhagen
Title:
Local-to-global principles for groups and p-local finite groups
Abstract:
A p-local finite group is an algebraic structure which mimics the p-local structure in a finite group, and topologically corresponds to the p-completed classifying space. A central question in group theory is to what extend the local structure determines the global structure. In this talk I will present a homotopical approach to this question via p-local finite groups, and give some concrete local-to-global results for specific classes of finite groups. This talk is joint work with Bob Oliver.
Speaker:
Title:
Abstract:
Speaker:
J. McClure, Purdue Univ.
Title:
Commutativity for Quinn bordism-type spectra
Abstract:
Joint with Gerd Laures. Frank Quinn defined ``bordism-type
theories'' and their associated spectra in his thesis, and since then they
have played an important role in surgery theory. The most important examples
are quadratic and symmetric L-spectra. The talk will give a new account of the
foundations and a simple sufficient condition for a bordism-type spectrum to be
$E_\infty$ (this problem was a motivation for Quinn's work on $E_\infty$ ring
spectra that appears in the May-Quinn-Ray volume).
Speaker:
Nathan Habegger, Univ. of Nantes
Title:
On the work of Xiao-Song Lin (1957-2007); from classical to
quantum topology.
Abstract:
In 1954, John Milnor introduced the notion of link homotopy and
his invariants of links which he used to classify 3 component links up to
homotopy. In 1987 the speaker and XS Lin acheived the classification,
for any number of components, essentially by refining the Milnor invariants.
The Habegger-Lin classification scheme was extended to other equivalence
relations in Lin's thesis and to more general concordance-type relations
satisfying a list of 6 axioms. Axioms 1-4 are local, axiom 5 says that
any string link (or 'pure tangle' as in pure braid) has an inverse, while
axiom 6 says the equivalence relation on links is generated by isotopy and
the equivalence relation on string links (every string link yields a link
after 'closure').
In the early 90's Birman and Lin studied the work of Vassiliev on links
and described in simple terms the Vassiliev filtration. Bar-Natan adopted
their description as a definition of 'finite type' invariants and
eventually all this was tied back to the perturbative Chern Simons quantum
invariants via the Kontsevich Integral.
Early on, Lin suggested the Milnor invariants were of finite type, but
this is strictly true only of the string link invariants because Milnor's
invariants are only 'partially' defined, i.e. their indeterminacy depends
on the lower order invariants. The speaker and G. Masbaum actually gave
in 1997 a formula computing the Milnor string link invariants from the
Kontsevich Integral. The tree-like Feynman diagrams correspond to the
Milnor invariants.
The nagging problem that Vassiliev invariants of links are universally
defined, but Milnor invariants, which ultimately gave the link-homotopy
classification, are only partially defined, suggests that finite-type
invariants of links are deficient. It turns out that axiom 6 of the
aforementioned classification sheme is not satisfied so that Vassiliev
(finite type) invariants of links can and ought to be refined, as shown in
a recent preprint by the speaker and JB Meilhan.
See http://www.math.sciences.univ-nantes.fr/~habegger/) for the
aforementioned works. (For those interested in the non-perturbative CS
theory, one can also find at this address the work of BHMV on Topological
Quantum Field Theory derived from the Kauffman bracket, e.g. the Jones'
Polynomial.)
Speaker:
Tibor Beke, U. Mass., Lowell
Title:
Higher Cech Theory
Abstract:
Cech cohomology has two faces: over a paracompact, Hausdorff topological space it is isomorphic to sheaf cohomology in all degrees, while over a Grothendieck topology it need not be except in degrees 0 and 1. I explain why it stops at 1, and how to change the notion of "cover" and define corresponding Cech cohomology groups that are isomorphic to sheaf cohomology, over an arbitrary Grothendieck topology, in degrees 0 through n. Unlike Verdier's hypercovers, n-covers are finitary combinatorial objects. The construction involves no homological algebra, but explicit manipulations of simplicial sets. This technique also lets one replace abelian coefficients by suitable simplicial sheaves, and introduce a tower of pro-homotopy types for a topos, serving as approximations of the Artin-Mazur "etale" homotopy type.
Speaker:
Chris Douglas, UC Berkeley and Stanford
Title:
Three-Dimensional Local Field Theory
Abstract:
I will describe the classification of 3-dimensional local topological field theories: corresponding to each transposable object of a symmetric monoidal 3-category C, there is a 3-d local TFT with target C. The key technical ingredient is the classification of flag foliated singularities. As an application, I will introduce a local field theory corresponding to the conformal net of local fermions. This is joint work in progress with Arthur Bartels and Andre Henriques. Time permitting I will describe joint work in progress with Chris Pries on the corresponding classification in dimension 4.
Speaker:
Anssi Lahtinen, Stanford
Title:
Twisted K-theory and Loop Spaces (Area Exam lecture)
Abstract:
Speaker:
Title:
Abstract:
Tuesday, April 15
Special Colloquium
Tuesday, April 22
Tuesday, May 13
4:00 pm, room 381-U. Special Topology Seminar: Note new day and place. It replaces the Topology Progress Seminar on that day.