Past

Consistent truncations have proved to be powerful tools in the construction of new string theory solutions. Recently, they have been employed in the holographic description of condensed matter systems. In the talk, I will present a rich class of supersymmetric consistent truncations of higher-dimensional supergravity which are based on geometric structures, focusing on the tri-Sasakian case. Then I will discuss some applications, including a general result relating AdS backgrounds to solutions with non-relativistic Lifshitz symmetry.

Yves Couder and co-workers have recently reported the results of a startling series of experiments in which droplets bouncing on a fluid surface exhibit several dynamical features previously thought to be peculiar to the microscopic realm. In an attempt to 

develop a connection between the fluid and quantum systems, we explore the Madelung transformation, whereby Schrodinger's equation is recast in a hydrodynamic form. New experiments are presented, and indicate the potential value of this hydrodynamic approach to both visualizing and understanding quantum mechanics.

A new approach for data-based stochastic parametrisation of unresolved scales and processes in numerical weather and climate prediction models is introduced. The subgrid-scale model is conditional on the state of the resolved scales, consisting of a collection of local models. A clustering algorithm in the space of the resolved variables is combined with statistical modelling of the impact of the unresolved variables. The clusters and the parameters of the associated subgrid models are estimated simultaneously from data. The method is tested and explored in the framework of the Lorenz '96 model using discrete Markov processes as local statistical models. Performance of the scheme is investigated for long-term simulations as well as ensemble prediction. The present method clearly outperforms simple parametrisation schemes and compares favourably with another recently proposed subgrid scheme also based on conditional Markov chains.

In this paper we deal with the utility maximization problem with a

preference functional of expected utility type. We derive a new approach

in which we reduce the utility maximization problem with general utility

to the study of a fully-coupled Forward-Backward Stochastic Differential

Equation (FBSDE).

The talk is based on joint work with Ying Hu, Peter Imkeller, Anthony

Reveillac and Jianing Zhang.

10am Radius Health - Mark Evans

10:30am NAG - Mick Pont and Lawrence Mulholland

Please note, that Thales are also proposing several projects but the academic supervisors have already been allocated.

The mechanisms for the selection of the propagation speed of waves

connecting unstable to stable states will be discussed in the

spatially non-homogeneous case, the differences from the very

well-studied homogeneous version being emphasised.

Let $x$ be a CM point in the moduli space $\mathcal{A}_g(\mathbb{C})$ of principally

polarized complex abelian varieties of genus $g$, corresponding to an

Abelian variety $A$ with complex multiplication by a ring $R$. Edixhoven

conjectured that the size of the Galois orbit of x should grow at least

like a power of the discriminant ${\rm Disc}(R)$ of $R$. For $g=1$, this reduces to the

classical Brauer-Siegel theorem. A positive answer to this conjecture

would be very useful in proving the Andr\'e-Oort conjecture unconditionally.

We will present a proof of the conjectured lower bounds in some special

cases, including $g\le 6$. Along the way we derive transfer principles for

torsion in class groups of different fields which may be interesting in

their own right.

We will discuss the use of hypergraph-based methods for orderings of sparse matrices in Cholesky, LU and QR factorizations. For the Cholesky factorization case, we will investigate a recent result on pattern-wise decomposition of sparse matrices, generalize the result and develop algorithmic tools to obtain effective ordering methods. We will also see that the generalized results help us formulate the ordering problem in LU much like we do for the Cholesky case, without ever symmetrizing the given matrix $A$ as $A+A^{T}$ or $A^{T}A$. For the QR factorization case, the use of hypergraph models is fairly standard. We will nonetheless highlight the fact that the method again does not form the possibly much denser matrix $A^{T}A$. We will see comparisons of the hypergraph-based methods with the most common alternatives in all three cases.

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This is joint work with Iain S. Duff.

Cubature on Wiener space" is a numerical method for the weak

approximation of SDEs. After an introduction to this method we present

some cases when the method is computationally expensive, and highlight

some techniques that improve the tractability. In particular, we adapt

the Multilevel Monte-Carlo framework and extend the Milstein-scheme

based version of Mike Giles to higher dimensional and higher degree cases.

We will give an introduction to the theory of d-manifolds, a new class of geometric objects recently/currently invented by Joyce (see http://people.maths.ox.ac.uk/joyce/dmanifolds.html). We will start from scratch, by recalling the definition of a 2-category and talking a bit about $C^\infty$-rings, $C^\infty$-schemes and d-spaces before giving the definition of what a d-manifold should be. We will then discuss some properties of d-manifolds, and say some words about d-manifold bordism and its applications.

We will start off with a crash course in General relativity, and then I'll describe a 'recipe' for a time machine. This will lead us to the question whether or not the topology of the universe can change. We will see that, in some sense, this is topologically allowed. However, the Einstein equation gives a certain condition on the Ricci tensor (which is violated by certain quantum effects) and meeting this condition is a more delicate problem.

In biological cells, molecules are transported actively or by diffusion and react with each other when they are close.

The reactions occur with certain probability and there are few molecules of some chemical species. Therefore, a stochastic model is more accurate compared to a deterministic, macroscopic model for the concentrations based on partial differential equations.

At the mesoscopic level, the domain is partitioned into voxels or compartments. The molecules may react with other molecules in the same voxel and move between voxels by diffusion or active transport. At a finer, microscopic level, each individual molecule is tracked, it moves by Brownian motion and reacts with other molecules according to the Smoluchowski equation. The accuracy and efficiency of the simulations are improved by coupling the two levels and only using the micro model when it is necessary for the accuracy or when a meso description is unknown.

Algorithms for simulations with the mesoscopic, microscopic and meso-micro models will be described and applied to systems in molecular biology in three space dimensions.

Cell motility is a crucial part of many biological processes including wound healing, immunity and embryonic development. The interplay between mechanical forces and biochemical control mechanisms make understanding cell motility a rich and exciting challenge for mathematical modelling. We consider the two-phase, poroviscous, reactive flow framework used in the literature to describe crawling cells and present a stripped down version. Linear stability analysis and numerical simulations provide insight into the onset of polarization of a stationary cell and reveal qualitatively distinct families of travelling wave solutions. The numerical solutions also capture the experimentally observed behaviour that cells crawl fastest when the surface they crawl over is neither too sticky nor too slippy.

We introduce the notion of a real cubing. Roughly speaking, real cubings are to CAT(0) cube complexes what real trees are to simplicial trees. We develop an analogue of the Rips’ machine and establish the structure of groups acting nicely on real cubings.

To identify the Martin boundary for a transient Markov chain with Green's function G(x,y), one has to identify all possible limits Lim G(x,y_n)/G(0,y_n) with y_n "tending to infinity". For homogeneous random walks, these limits are usually obtained from the exact asymptotics of Green's function G(x,y_n). For non-homogeneous random walks, the exact asymptotics af Green's function is an extremely difficult problem. We discuss several examples where Martin boundary can beidentified by using large deviation technique. The minimal Martin boundary is in general not homeomorphic to the "radial"  compactification obtained by Ney and Spitzer for homogeneous random walks in Z^d : convergence of a sequence of points y_n toa point on the Martin boundary does not imply convergence of the sequence y_n/|y_n| on the unit sphere. Such a phenomenon is a consequence of non-linear optimal large deviation trajectories.

Symplectic implosion is a construction in symplectic geometry due to Guillemin, Jeffrey and Sjamaar, which is related to geometric invariant theory for non-reductive group actions in algebraic geometry. This talk (based on joint work in progress with Andrew Dancer and Andrew Swann) is concerned with an analogous construction in hyperkahler geometry.