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Topology Seminar (past)

Thu, 16/05
10:00 		Alain Valette (Neuchatel) Topology Seminar Add to calendar L3
Metric aspects of generalized Baumslag-Solitar groups
A generalized Baumslag-Solitar group is a group G acting co-compactly on a tree X, with all vertex- and edge stabilizers isomorphic to the free abelian group of rank n. We will discuss the $ L^p $-metric and $ L^p $-equivariant compression of G, and also the quasi-isometric embeddability of G in a finite product of binary trees. Complete results are obtained when either $ n=1 $, or the quotient graph $ G\X $ is either a tree or homotopic to a circle. This is joint work with Yves Cornulier.
Mon, 13/05
15:45 		George Raptis (Osnabrueck) Topology Seminar Add to calendar L3
The moduli space of topological realisations of an unstable coalgebra
The mod p homology of a space is an unstable coalgebra over the Steenrod algebra at the prime p. This talk will be about the classical problem of realising an unstable coalgebra as the homology of a space. More generally, one can consider the moduli space of all such topological realisations and ask for a description of its homotopy type. I will discuss an obstruction theory which describes this moduli space in terms of the André-Quillen cohomology of the unstable coalgebra. This is joint work with G. Biedermann and M. Stelzer.
Mon, 29/04
15:45 		Ivan Smith (Cambridge) Topology Seminar Add to calendar L3
Exact Lagrangian immersions in Euclidean space
Exact Lagrangian immersions are governed by an h-principle, whilst exact Lagrangian embeddings are well-known to be constrained by strong rigidity theorems coming from holomorphic curve theory. We consider exact Lagrangian immersions in Euclidean space with a prescribed number of double points, and find that the borderline between flexibility and rigidity is more delicate than had been imagined. The main result obtains constraints on such immersions with exactly one double point which go beyond the usual setting of Morse or Floer theory. This is joint work with Tobias Ekholm, and in part with Ekholm, Eliashberg and Murphy.
Mon, 22/04
15:45 		David Hume (Oxford) Topology Seminar Add to calendar L3
Metric Geometry of Mapping Class and Relatively Hyperbolic Groups
We prove that quasi-trees of spaces satisfying the axiomatisation given by Bestvina, Bromberg and Fujiwara are quasi-isometric to tree-graded spaces in the sense of Dru\c{t}u and Sapir. We then present a technique for obtaining `good' embeddings of such spaces into $ \ell^p $ spaces, and show how results of Bestvina-Bromberg-Fujiwara and Mackay-Sisto allow us to better understand the metric geometry of such groups.
Mon, 04/03
15:45 		David Barnes (Belfast) Topology Seminar Add to calendar
Orthogonal Calculus and Model Categories.

Orthogonal calculus is a calculus of functors, inspired by Goodwillie calculus. It takes as input a functor from finite dimensional inner product  spaces to topological spaces and as output gives a tower of  approximations by well-behaved functors.  The output captures a lot of important homotopical information and is an important tool for calculations.

In this talk I will report on joint work with Peter Oman in which we use model categories to improve the foundations of orthogonal calculus. This provides a cleaner set of results and makes the role of O(n)-equivariance clearer.  The classification of n-homogeneous functors in terms of spectra with O(n)-action can then be phrased as a zig-zag of Quillen equivalences.
Mon, 25/02
15:45 		Martin Bridson (Oxford) Topology Seminar Add to calendar L3
The complexity of group presentations, manifolds, and the Andrews-Curtis conjecture
Many natural problems concerning the geometry and topology of manifolds are intimately connected with the nature of presentations for the fundamental groups of the manifolds. I shall illustrate this theme with various specific results, then focus on balanced presentations. I'll explain the (open) Andrews-Curtis conjecture and it's relation to the smooth 4-dimensional Poincare conjecture, and I'll present a construction that gives (huge) lower bounds on how hard it is to distinguish a homology 4-sphere from a genuine sphere.
Mon, 18/02
15:45 		Nathalie Wahl (Copenhagen) Topology Seminar Add to calendar L3
Mapping class groups, Sullivan diagrams and string topology
Mon, 11/02
15:45 		John MacKay (Oxford) Topology Seminar Add to calendar L3
Quasi-hyperbolic planes in hyperbolic and relatively hyperbolic groups
In 2005, Bonk and Kleiner showed that a hyperbolic group admits a quasi-isometrically embedded copy of the hyperbolic plane if and only if the group is not virtually free. This answered a question of Papasoglu. I will discuss a generalisation of their result to certain relatively hyperbolic groups (joint work with Alessandro Sisto). Key tools involved are new existence results for quasi-circles, and a better understanding of the geometry of boundaries of relatively hyperbolic groups.
Mon, 04/02
15:45 		Topology Seminar Add to calendar
NO SEMINAR
Mon, 28/01
15:45 		Brian Bowditch (Warwick) Topology Seminar Add to calendar L3
Coarse median spaces
By a "coarse median" we mean a ternary operation on a path metric space, satisfying certain conditions which generalise those of a median algebra. It can be interpreted as a kind of non-positive curvature condition, and is applicable, for example to finitely generated groups. It is a consequence of work of Behrstock and Minsky, for example, that the mapping class group of a surface satisfies this condition. We aim to give some examples, results and applications concerning this notion.
Mon, 21/01
15:45 		Dror Bar-Natan (Toronto and Newton Institute) Topology Seminar Add to calendar L3
Balloons and Hoops and their Universal Finite Type Invariant, BF Theory, and an Ultimate Alexander Invariant
Balloons are two-dimensional spheres. Hoops are one dimensional loops. Knotted Balloons and Hoops (KBH) in 4-space behave much like the first and second fundamental groups of a topological space - hoops can be composed like in π1, balloons like in π2, and hoops "act" on balloons as π1 acts on π2. We will observe that ordinary knots and tangles in 3-space map into KBH in 4-space and become amalgams of both balloons and hoops. We give an ansatz for a tree and wheel (that is, free-Lie and cyclic word) -valued invariant ζ of KBHs in terms of the said compositions and action and we explain its relationship with finite type invariants. We speculate that ζ is a complete evaluation of the BF topological quantum field theory in 4D, though we are not sure what that means. We show that a certain "reduction and repackaging" of ζ is an "ultimate Alexander invariant" that contains the Alexander polynomial (multivariable, if you wish), has extremely good composition properties, is evaluated in a topologically meaningful way, and is least-wasteful in a computational sense. If you believe in categorification, that's a wonderful playground. For further information see http://www.math.toronto.edu/~drorbn/Talks/Oxford-130121/
Mon, 14/01
15:45 		Vincent Guirardel (Toulouse) Topology Seminar Add to calendar
Automorphisms of relatively hyperbolic groups and McCool groups

We define a McCool group of G as the group of outer automorphisms of G acting as a conjugation on a given family of subgroups. We will explain that these groups appear naturally in the description of many natural groups of automorphisms. On the other hand, McCool groups of a toral relatively hyperbolic group have strong finiteness properties: they have a finite index subgroup with a finite classifying space. Moreover, they satisfy a chain condition that has several other applications.
This is a joint work with Gilbert Levitt.
Wed, 19/12/2012
16:30 		Dennis Sullivan Topology Seminar Add to calendar
Graeme's work and stratified string topology
Wed, 19/12/2012
15:00 		Dan Freed Topology Seminar Add to calendar
4-3-2-8-7-6
Wed, 19/12/2012
10:00 		David Ben-Zvi Topology Seminar Add to calendar
Loops, Characters and Elliptic Curves
Tue, 18/12/2012
16:30 		Nigel Hitchin Topology Seminar Add to calendar
A line bundle in hyperkähler geometry
Tue, 18/12/2012
15:00 		Constantin Teleman Topology Seminar Add to calendar
Langlands duality in 2-dimensional gauge theory
Tue, 18/12/2012
11:30 		Kevin Costello Topology Seminar Add to calendar
Quantum field theory and quantum groups
Tue, 18/12/2012
10:00 		Gregory Moore Topology Seminar Add to calendar
Operads in the infrared

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

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