Cambridge

Abstract: We consider deformations of torsion-free $ G_2 $ structures, defined by the $ G_2 $-invariant 3-form $ \phi $ and compute the expansion of the Hodge star of $ \phi $ to fourth order in the deformations of $ \phi $. By considering M-theory compactified on a $ G_2 $ manifold, the $ G_2 $ moduli space is naturally complexified, and we get a Kahler metric on it. Using the expansion of the Hodge star of $ \phi $ we work out the full curvature of this metric and relate it to the Yukawa coupling.

Abstract: I show that the effective action of string compactifications has astructure that can naturally solve the supersymmetric flavour and CP problems. At leading order in the $g_s$ and $\alpha'$ expansions, the hidden sector factorises. The moduli space splits into two mirror parts that depend on K\"ahler and complex structure moduli. Holomorphy implies the flavour structure of the Yukawa couplings arises in only one part. In type IIA string theory flavour arises through the K\"ahler moduli sector and in type IIB flavour arises through the complex structure moduli sector. This factorisation gives a simple solution to the supersymmetric flavour and CP problems: flavour physics is generated in one sector while supersymmetry is broken in the mirror sector. This mechanism does not require the presence of gauge, gaugino or anomaly mediation and is explicitly realised by phenomenological models of IIB flux compactifications.

Glauber dynamics on $\mathbb{Z}^d$ is a dynamic representation of the zero-temperature Ising model, in which the spin (either $+$ or $-$) of each vertex updates, at random times, to the state of the majority of its neighbours. It has long been conjectured that the critical probability $p_c(\mathbb{Z}^d)$ for fixation (every vertex eventually in the same state) is $1/2$, but it was only recently proved (by Fontes, Schonmann and Sidoravicius) that $p_c(\mathbb{Z}^d)

Let N(A) be the number of integer solutions of x^2 + y^2

 

If new particles are produced at the LHC, it is vital that we can extract as much information as possible from them about the underlying theory.  I will discuss some recent work on extracting spin information from invariant mass distributions of new particles.  I will then introduce the Kullback-Leibler method of quantifying our ability to distinguish different scenarios.