Past Seminars › Seminar Series

Topology Seminar (past)

Mon, 20/10/2008
14:15 		Stefan Friedl (Warwick) Topology Seminar Add to calendar L3
"Fibered 3-manifolds and twisted Alexander polynomials"
It is a classical result that the Alexander polynomial of a fibered knot has to be monic. But in general the converse does not hold, i.e. the Alexander polynomial does not detect fibered knots. We will show that the collection of all twisted Alexander polynomials (which are a natural generalization of the ordinary Alexander polynomial) detect fibered 3-manifolds. As a corollary it follows that given a 3-manifold N the product S1 x N is symplectic if and only if N is fibered.
Mon, 13/10/2008
15:45 		Professor Martin Bridson (Oxford) Topology Seminar Add to calendar L3
The Andrew Curtis Conjecture
Tue, 29/07/2008
14:15 		Soren Galatius Topology Seminar Add to calendar L3
The space of graphs in Euclidean space.
A graph in R^n is a closed subset that locally looks like R (edges) or like a wedge of half intervals (vertices). I will describe a topology on the space of all such graphs and determine its homotopy type. This is one step in determining the homology of Aut(F_n), the automorphism group of a free group, in the limit where n goes to infinity.
Thu, 17/07/2008
11:00 		Hendryk Pfeiffer (UBC) Topology Seminar Add to calendar L3
2-dimensional extended Topological Quantum Field Theories and categorification
A 2-dimensional Topological Quantum Field Theory (TQFT) is a symmetric monoidal functor from the category of 2-dimensional cobordisms to the category of vector spaces. A classic result states that 2d TQFTs are classified by commutative Frobenius algebras.  I show how to extend this result to open-closed TQFTs using a class of 2-manifolds with corners, how to use the Moore-Segal relations in order to find a canonical form and a complete set of invariants for our cobordisms and how to classify open-closed TQFTs algebraically.  Open-closed TQFTs can be used to find algebraic counterparts of Bar-Natan's topological extension of Khovanov homology from links to tangles and in order to get hold of the braided monoidal 2-category that governs this aspect of Khovanov homology. I also sketch what open-closed TQFTs reveal about the categorical ladder of combinatorial manifold invariants according to Crane and Frenkel. references: 1] A. D. Lauda, H. Pfeiffer: Open-closed strings: Two-dimensional extended TQFTs and Frobenius algebras, Topology Appl. 155, No. 7 (2008) 623-666, arXiv:math/0510664 2] A. D. Lauda, H. Pfeiffer: State sum construction of two-dimensional open-closed Topological Quantum Field Theories, J. Knot Th. Ramif. 16, No. 9 (2007) 1121-1163,arXiv:math/0602047 3] A. D. Lauda, H. Pfeiffer: Open-closed TQFTs extend Khovanov homology from links to tangles, J. Knot Th. Ramif., in press, arXiv:math/0606331.
Mon, 09/06/2008
15:45 		Marc Lackenby (Oxford) Topology Seminar Add to calendar L3
Surface subgroups in dimension 3 (II)
Mon, 02/06/2008
15:45 		Marc Lackenby (Oxford) Topology Seminar Add to calendar L3
Surface subgroups in dimension 3 (I)
Mon, 26/05/2008
15:45 		Topology Seminar Add to calendar
No Seminar
Mon, 19/05/2008
17:00 		Francois Gueritaud (Paris) Topology Seminar Add to calendar L1
Canonical triangulations of quasifuchian convex cores
Quasifuchsian punctured-torus groups are the `simplest'Kleinian groups with an interesting deformation theory. I will show that the convex core of the quotient of hyperbolic 3-space by such a group admits a decomposition into ideal tetrahedra which is canonical in two completely independent senses: one combinatorial, the other geometric. One upshot is a proof of the Bending Lamination Conjecture for such groups.
Mon, 19/05/2008
15:45 		Yves de Cornulier (Rennes) Topology Seminar Add to calendar L3
On quasi-isometric embeddings of Lie groups into non-positively curved spaces
I will give a characterization of connected Lie groups admitting a quasi-isometric embedding into a CAT(0) metric space. The proof relies on the study of the geometry of their asymptotic cones
Mon, 12/05/2008
15:45 		Topology Seminar Add to calendar
No Seminar
Mon, 05/05/2008
15:45 		Topology Seminar Add to calendar
No Seminar
Mon, 28/04/2008
15:45 		Brian Bowditch (Warwick) Topology Seminar Add to calendar L3
"Models for hyperbolic 3-manifolds"
Mon, 03/03/2008
14:45 		Alex Muranov (Lyon) Topology Seminar Add to calendar L3
Finitely generated simple groups of infinite commutator width.
If $ G $ is a group and $ g $ an element of the derived subgroup $ [G,G] $, the commutator length of $ g $ is the least positive integer $ n $ such that $ g $ can be written as a product of $ n $ commutators. The commutator width of $ G $ is the maximum of the commutator lengths of elements of $ [G,G] $. Until 1991, to my knowledge, it has not been known whether there exist simple groups of commutator width greater than $ 1 $. The same question for finite simple groups still remains unsolved. In 1992, Jean Barge and Étienne Ghys showed that the commutator width of certain simple groups of diffeomorphisms is infinite. However, those groups are not finitely generated. Finitely generated infinite simple groups of infinite commutator width can be constructed using "small cancellations." Additionally, finitely generated infinite boundedly simple groups of arbitrarily large (but necessarily finite) commutator width can be constructed in a similar way.
Mon, 25/02/2008
16:00 		Eric Opdam (Amsterdam) Topology Seminar Add to calendar L3
Representation theory of affine Hecke algebras and K-theory
In recent joint work with Maarten Solleveld we could give a complete classification of the set the irreducible discrete series characters of affine Hecke algebras (including the non simply-laced cases). The results can be formulated in terms of the K-theory of the Schwartz completion of the Hecke algebra. We discuss these results and some related conjectures on formal dimensions and on elliptic characters.
Mon, 25/02/2008
14:45 		Arthur Bartels (Imperial) Topology Seminar Add to calendar L3
Topological rigidity and word-hyperbolic groups
The Borel conjecture asserts that aspherical manifolds are topologically rigid, i.e., every homotopy equivalence between such manifolds is homotopic to a homeomorphism. This conjecture is strongly related to the Farrell-Jones conjectures in algebraic K- and L-theory. We will give an introduction to these conjectures and discuss the proof of the Borel conjecture for high-dimensional aspherical manifolds with word-hyperbolic fundamental groups.
Mon, 25/02/2008
13:15 		Jorgen Anderson (Aarhus) Topology Seminar Add to calendar L3
Hitchin's connection and Kazhdan's property T
Mon, 18/02/2008
14:45 		Luis Paris (Bourgogne) Topology Seminar Add to calendar L3
Small index subgroups of the mapping class group
Mon, 11/02/2008
14:45 		Teruji Thomas (Oxford) Topology Seminar Add to calendar L3
Quadratic forms and cobordisms
Taking the intersection form of a 4n-manifold defines a functor from a category of cobordisms to a symmetric monoidal category of quadratic forms. I will present the theory of the Maslov index and some higher-categorical constructions as variations on this theme.
Mon, 04/02/2008
14:45 		Tim Riley (Bristol) Topology Seminar Add to calendar L3
Hydra groups
I will describe a new family of groups exhibiting wild geometric and computational features in the context of their Conjugacy Problems. These features stem from manifestations of "Hercules versus the hydra battles." This is joint work with Martin Bridson.
Mon, 28/01/2008
14:45 		Ulrike Tillmann (Oxford) Topology Seminar Add to calendar L3
n-categories in topology : paths and cobordisms

For any corrections/updates to these listings, please contact seminars [-at-] maths [dot] ox [dot] ac [dot] uk.

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