Forthcoming events in this series


Mon, 11 Nov 2013
15:30
L5

Poincare Koszul duality and factorization homology

David Ayala
(University of Southern California)
Abstract

Factorization homology is an invariant of an n-manifold M together with an n-disk algebra A. Should M be

a circle, this recovers the Hochschild complex of A; should A be a commutative algebra, this recovers the

homology of M with coefficients in A. In general, factorization homology retains more information about

a manifold than its underlying homotopy type.

In this talk we will lift Poincare' duality to factorization homology as it intertwines with Koszul

duality for n-disk algebras -- all terms will be explained. We will point out a number of consequences

of this duality, which concern manifold invariants as well as algebra invariants.

This is a report on joint work with John Francis.

Mon, 10 Jun 2013

15:45 - 16:45
L3

On Sofic Groups

Derek Holt
(Warwick)
Abstract

The class of sofic groups was introduced by Gromov in 1999. It
includes all residually finite and all amenable groups. In fact, no group has been proved
not to be sofic, so it remains possible that all groups are sofic. Their
defining property is that, roughly speaking, for any finite subset F of
the group G, there is a map from G to a finite symmetric group, which is
approximates to an injective homomorphism on F. The widespread interest in
these group results partly from their connections with other branches of
mathematics, including dynamical systems. In the talk, we will concentrate
on their definition and algebraic properties.

Mon, 03 Jun 2013

15:45 - 16:45
L3

Derived A-infinity algebras from the point of view of operads

Sarah Whitehouse
(Sheffield)
Abstract

A-infinity algebras arise whenever one has a multiplication which is "associative up to homotopy". There is an important theory of minimal models which involves studying differential graded algebras via A-infinity structures on their homology algebras. However, this only works well over a ground field. Recently Sagave introduced the more general notion of a derived A-infinity algebra in order to extend the theory of minimal models to a general commutative ground ring.

Operads provide a very nice way of saying what A-infinity algebras are - they are described by a kind of free resolution of a strictly associative structure. I will explain the analogous result for derived A_infinity algebras - these are obtained in the same manner from a strictly associative structure with an extra differential.

This is joint work with Muriel Livernet and Constanze Roitzheim.

Mon, 20 May 2013

15:45 - 16:45
L3

Fibering 5-manifolds with fundamental group Z over the circle

Yang Su
(Beijing)
Abstract

 In this talk I will introduce my joint work with Kreck on a classification of
certain 5-manifolds with fundamental group Z. This result can be interpreted as a
generalization of the classical Browder-Levine's fibering theorem to dimension 5.

Thu, 16 May 2013

10:00 - 12:00
L3

Metric aspects of generalized Baumslag-Solitar groups

Alain Valette
(Neuchatel)
Abstract

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 May 2013

15:45 - 16:45
L3

The moduli space of topological realisations of an unstable coalgebra

George Raptis
(Osnabrueck)
Abstract

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 Andr\'{e}-Quillen cohomology of the unstable coalgebra. This is joint work with G. Biedermann and M. Stelzer.

Mon, 29 Apr 2013

15:45 - 16:45
L3

Exact Lagrangian immersions in Euclidean space

Ivan Smith
(Cambridge)
Abstract

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 Apr 2013

15:45 - 16:45
L3

Metric Geometry of Mapping Class and Relatively Hyperbolic Groups

David Hume
(Oxford)
Abstract

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 Mar 2013

15:45 - 16:45

Orthogonal Calculus and Model Categories.

David Barnes
(Belfast)
Abstract

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 Feb 2013

15:45 - 16:45
L3

The complexity of group presentations, manifolds, and the Andrews-Curtis conjecture

Martin Bridson
(Oxford)
Abstract
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, 11 Feb 2013

15:45 - 16:45
L3

Quasi-hyperbolic planes in hyperbolic and relatively hyperbolic groups

John MacKay
(Oxford)
Abstract

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, 28 Jan 2013

15:45 - 16:45
L3

Coarse median spaces

Brian Bowditch
(Warwick)
Abstract

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 Jan 2013

15:45 - 16:45
L3

Balloons and Hoops and their Universal Finite Type Invariant, BF Theory, and an Ultimate Alexander Invariant

Dror Bar-Natan
(Toronto and Newton Institute)
Abstract

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 Jan 2013

15:45 - 16:45

Automorphisms of relatively hyperbolic groups and McCool groups

Vincent Guirardel
(Toulouse)
Abstract

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 Dec 2012

15:00 - 16:00

4-3-2-8-7-6

Dan Freed