Wed, 04 Jun 2008

12:00 - 13:00
L3

Techniques for one-loop amplitudes in QCD

Giulia Zanderighi
(Oxford)
Abstract
Abstract: We discuss recent techniques to compute one-loop amplitudes in QCD and show that all N-gluon one-loop helicity amplitudes can be computed numerically for arbitrary N with an algorithm which has a polynomial growth in N.
Mon, 05 May 2008

12:00 - 13:00
L3

MHV Rules: the missing one-loop amplitudes

Paul Mansfield
(Durham)
Abstract
Abstract: I will talk about how the reformulation of perturbative Yang-Mills theory in terms of MHV rules accounts for one-loop amplitudes for gluons of the same helicity, and some of the effects of introducing a regulator.
Mon, 28 Apr 2008

12:00 - 13:00
L3

$G_2$ manifolds with isolated conical singularities

Spiro Karigiannis
(Oxford)
Abstract
Abstract: Compact $G_2$ manifolds with isolated conical singularities arise naturally in M-theory. I will discuss such manifolds, and explain a method to ``desingularize'' them by glueing in pieces of asymptotically conical $G_2$ manifolds. There are topological obstructions to such desingularizations that depend on the rate of convergence to the cone at the singularities, and on the geometry of the links of the cones. If time permits, I will also briefly discuss a new related project with Dominic Joyce which could provide the first examples of such manifolds, as well as a possible new construction of smooth compact $G_2$ manifolds.
Mon, 21 Apr 2008

12:00 - 13:00
L3

Gauge Theory, Gravity and Twistor String Scattering Amplitudes

Mohab Abou Zeid
(Institute for Mathematical Sciences)
Abstract
I will present a modification of twistor string theory which gives the spectrum of super Yang-Mills theory coupled to Einstein supergravity instead of the higher derivative conformal supergravity arising in the original twistor strings of Witten and of Berkovits. After reviewing the world-sheet formulation of the Berkovits model, I will describe the symmetries of the so-called beta-gamma systems and their gauging. I will then explain how the analysis can be applied to the construction of a family of new gauged Berkovits twistor strings which are free from world-sheet anomalies. The new theories include one with the spectrum of N=8 supergravity, two theories with the spectrum of N=4 supergravity coupled to N=4 Yang-Mills, a family of N>0 models with the spectra of self-dual supergravity coupled to self-dual super-Yang-Mills, and a non-supersymmetric string with the spectrum of self-dual gravity coupled to self-dual Yang-Mills and a scalar. Time permitting, I will discuss what is known about the interactions in the new theories.
Tue, 03 Jun 2008
17:00
L3

Compactness properties of operator multipliers

Rupert Levene
(Queen's, Belfast)
Abstract

The Schur product is the commutative operation of entrywise

multiplication of two (possibly infinite) matrices. If we fix a matrix

A and require that the Schur product of A with the matrix of any

bounded operator is again the matrix of a bounded operator, then A is

said to be a Schur multiplier; Schur multiplication by A then turns

out to be a completely bounded map. The Schur multipliers were

characterised by Grothendieck in the 1950s. In a 2006 paper, Kissin

and Shulman study a noncommutative generalisation which they call

"operator multipliers", in which the theory of operator spaces plays

an important role. We will present joint work with Katja Juschenko,

Ivan Todorov and Ludmilla Turowska in which we determine the operator

multipliers which are completely compact (that is, they satisfy a

strengthening of the usual notion of compactness which is appropriate

for completely bounded maps).

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