Forthcoming events in this series


Mon, 18 Jan 2010
15:45
L3

Wick Rotation in Quantum Field Theory

Professor Graem Segal
(Oxford)
Abstract

Physical space-time is a manifold with a Lorentzianmetric, but the more mathematical treatments of the theory usually prefer toreplace the metric with a positive - i.e. Riemannian - one. The passage fromLorentzian to Riemannian metrics is called 'Wick rotation'. In my talk I shallgive a precise description of what is involved, and shall explain some of itsimplications for physics.

 

Mon, 26 Oct 2009
15:45
L3

Upper bounds onReidemeistermoves

Alex Coward
(Oxford)
Abstract

Given any two diagrams of the same knot or link, we

provide an explicit upper bound on the number of Reidemeister moves required to

pass between them in terms of the number of crossings in each diagram. This

provides a new and conceptually simple solution to the equivalence problem for

knot and links. This is joint work with Marc Lackenby.

Thu, 18 Jun 2009
11:00

The virtual fibering conjecture and related questions

Ian Agol
(Berkeley)
Abstract

Thurston asked a bold question of whether finite volume hyperbolic 3-manifolds might always admit a finite-sheeted cover which fibers over the circle. This talk will review some of the progress on this question, and discuss its relation to other questions including residual finiteness and subgroup separability, the behavior of Heegaard genus in finite-sheeted covers, CAT(0) cubings, the RFRS condition, and subgroups of right-angled Artin groups. In particular, hyperbolic 3-manifolds with LERF fundamental group are virtually fibered. Some applications of the techniques will also be mentioned.

Mon, 15 Jun 2009
15:45
L3

The Blob Complex

Kevin Walker
(Microsoft)
Abstract

We define a chain complex B_*(C, M) (the "blob complex") associated to an n-category C and an n-manifold M. This is in some sense the derived category version of a TQFT. Various special cases of the blob complex are

familiar: (a) if M = S^1, then the blob complex is homotopy equivalent to the Hochschild complex of the 1-category C; (b) for * = 0, H_0 of the blob complex is the Hilbert space of the TQFT based on C; (c) if C is a commutative polynomial ring (viewed as an n-category), then the blob complex is homotopy equivalent to singular chains on the configuration (Dold-Thom) space of M. The blob complex enjoys various nice formal properties, including a higher dimensional generalization of the Deligne conjecture for Hochschild cohomology.

If time allows I will discuss applications to contact structures on 3-manifolds and Khovanov homology for links in the boundaries of 4-manifolds. This is joint work with Scott Morrison.

Mon, 08 Jun 2009
15:45
L3

Decomposition complexity of metric spaces

Eric Guenter
(Hawaii)
Abstract

I shall describe the notion of finite decomposition complexity (FDC), introduced in joint work with Romain Tessera and Guoliang Yu on the Novikov and related conjectures. The talk will focus on the definition of FDC and examples of groups having FDC.

Mon, 01 Jun 2009
15:45
L3

The asymptotic geometry of mapping class groups and application

Dr Cornelia Drutu
(Oxford)
Abstract

I shall describe the asymptotic geometry of the mapping class

group, in particular its tree-graded structure and

its equivariant embedding in a product of trees.

This can be applied to study homomorphisms into mapping class

groups defined on groups with property (T) and on lattices in semisimple groups.

The talk is based upon two joint works with J. Behrstock, Sh. Mozes and M. Sapir.