Mon, 01 Jun 2009
14:15
L3

Monoids of moduli spaces of manifolds

Oscar Randal-Williams
(Oxford)
Abstract

Joint work with Soren Galatius. We study categories C of d-dimensional cobordisms, from the perspective of Galatius, Madsen, Tillmann and Weiss. Their main result is the determination of the homotopy type of the classifying-space of such cobordism categories, as the infinite loop space of a certain Thom spectrum. One can investigate subcategories D of C having the property that the classifying-space BD is equivalent to BC, the smaller such D one can find the better.

We prove that in may cases of interest, D can be taken to be a homotopy commutative monoid. As a consequence, the stable cohomology of many moduli spaces of surfaces can be identified with that of the infinite loop space of certain Thom spectra.

Mon, 11 May 2009

12:00 - 13:00
L3

Twistor Methods for Scattering Amplitudes

David Skinner
(Oxford)
Abstract
Abstract:  Modern techniques for computing multi-particle and multi-loop scattering amplitudes rely on a sophisticated use of on-shell recursion relations and generalised unitarity methods. I will show that these methods are ideally suited to interpretation in twistor space, where superconformal properties become manifest. In fact, the recursion relations of Britto, Cachazo, Feng & Witten provide a clear framework for the twistor diagram program initiated in the 1970s.
 Tree-level scattering amplitudes in N=4 SYM are now known to possess a Yangian symmetry, formed by combining the original PSU(2,2|4) superconformal invariance with a second "dual" copy. I will also discuss very recent work constructing scattering amplitudes in a twistor space in which this dual superconformal symmetry acts geometrically.
Mon, 27 Apr 2009

12:00 - 13:00
L3

Twistor diagrams for gauge-theoretic amplitudes

Andrew Hodges
(Oxford)
Abstract
Abstract: The recent paper by Arkani-Hamed, Cachazo, Cheung and Kaplan on 'The S-matrix in Twistor Space' (hep-th/0903.2110v2) has envigorated the project of expressing scattering amplitudes for (supersymmetric) gauge theory and gravity entirely in terms of twistor geometry. I shall review these new developments of twistor diagram theory, with some illustrations of its computational value. I shall also emphasise the many outstanding problems in the formalism. One of these, which Arkani-Hamed has highlighted, is the asymmetry in the representation of the amplitudes and the 'spurious poles' that arise. So far, the twistor diagram formalism has simply reproduced the less than satisfactory features of the (supersymmetrised) BCFW recursion. I will outline some new twistor-geometric results which address and partially resolve this problem.
Thu, 30 Apr 2009

12:00 - 13:00
SR1

Spaces of surfaces and Mumford's conjecture

Oscar Randal-Williams
(Oxford)
Abstract

I will present a new proof of Mumford's conjecture on the rational cohomology of moduli spaces of curves, which is substantially different from those given by Madsen--Weiss and Galatius--Madsen--Tillmann--Weiss: in particular, it makes no use of Harer--Ivanov stability for the homology of mapping class groups, which played a decisive role in the previously known proofs. This talk represents joint work with Soren Galatius.

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