Past

As part of a suite of products that provide a drive thorough vehicle tyre inspection system the assessment of wheel alignment would be useful to drivers in maintaining their vehicles and reducing tyre wear.  The current method of assessing wheel alignment involves fitting equipment to the tyre and assessment within a garage environment. 

The challenge is to develop a technique that can be used in the roadway with no equipment fitted to the vehicle.  The WheelRight equipment is already capturing images of tyres from both  front and side views.  Pressure sensors in the roadway also allow a tyre pressure footprint to be created.  Using the existing data to interpret the alignment of the wheels on each axle is a preferred way forward.

The stability of structures continues to be scientifically fascinating and technically important.  Shell buckling emerged as one of the most challenging nonlinear problems in mechanics more than fifty years ago when it was intensively studied.  It has returned to life with new challenges motivated not only by structural applications but also by developments in the life sciences and in soft materials.  It is not at all uncommon for slightly imperfect thin cylindrical shells under axial compression or spherical shells under external pressure to buckle at 20% of the buckling load of the perfect shell.  A historical overview of shell buckling will be presented followed by a discussion of recent work by the speaker and his collaborators on the buckling of spherical shells.  Experimental and theoretical work will be described with a focus on imperfection-sensitivity and on viewing the phenomena within the larger context of nonlinear stability. 

We prove higher differentiability of bounded local minimizers to some degenerate functionals satisfying anisotropic growth conditions. In the two-dimensional case we also study the Lipschitz regularity of such minimizers without any limitation on the exponents of anisotropy.

I will discuss on the existence and regularity results for the heat flow of the so called H-systems and for more general parabolic p-laplacian problems with critical growth.

In two dimensional topological phases of matter, processes depend on gross topology rather than detailed geometry. Thinking in 2+1 dimensions, the space-time histories of particles can be interpreted as knots or links, and the amplitude for certain processes becomes a topological invariant of that link. While sounding rather exotic, we believe that such phases of matter not only exist, but have actually been observed (or could be soon observed) in experiments. These phases of matter could provide a uniquely practical route to building a quantum computer. Experimental systems of relevance include Fractional Quantum Hall Effects, Exotic superconductors such as Strontium Ruthenate, Superfluid Helium, Semiconductor-Superconductor-Spin-Orbit systems including Quantum Wires. The physics of these systems, and how they might be used for quantum computation will be discussed.

The mathematical design of the table flood demonstrator Wetropolis will be presented. Wetropolis illustrates the concepts of extreme rainfall and flooding.

It shows how extreme rainfall events  can cause flooding of a city due to groundwater and river flood peaks. Rainfall is supplied randomly in space using four outcomes (in a reservoir, on a moor, at both places or nowhere) and randomly in time using four rainfall intensities (1s, 2s, 4s, or 9s during a 10s Wetropolis day), including one extreme event, via two skew-symmetric discrete probability distributions visualised by two Galton boards. Wetropolis can be used for both public outreach and as scientific testing environment for flood mitigation and data assimilation.

More information: https://www.facebook.com/resurging.flows

In this talk, we present and analyse a class of “filtered” numerical schemes for second order Hamilton-Jacobi-Bellman (HJB) equations, with a focus on examples arising from stochastic control problems in financial engineering. We start by discussing more widely the difficulty in constructing compact and accurate approximations. The key obstacle is the requirement in the established convergence analysis of certain monotonicity properties of the schemes. We follow ideas in Oberman and Froese (2010) to introduce a suitable local modification of high order schemes, which are necessarily non-monotone, by “filtering” them with a monotone scheme. Thus, they can be proven to converge and still show an overall high order behaviour for smooth enough value functions. We give theoretical proofs of these claims and illustrate the behaviour with numerical tests. 

This talk is based on joint work with Olivier Bokanowski and Athena Picarelli.

Hotels.com is one of the world’s leading accommodation booking websites featuring an inventory of around 300.000 hotels and 100s of millions of users. A crucial part of our business is to act as an agent between these two sides of the market, thus reducing search costs and information asymmetries to enable our visitors to find the right hotel in the most efficient way.

From this point of view selling hotels is one large recommendation challenge: given a set of items and a set of observed choices/ratings, identify a user’s preference profile.  Over the last years this particular problem has been intensively studied by a strongly interdisciplinary field based on ideas from choice theory, linear algebra, statistics, computer science and machine learning. This pluralism is reflected in the broad array of techniques that are used in today’s industry applications, i.e. collaborative filtering, matrix factorization, graph-based algorithms, decision trees or generalized linear models.

The aim of this workshop is twofold.

Firstly we want to give some insight into the statistical modelling techniques and assumptions employed at hotels.com, the practical challenges one has to face when designing a flexible and scalable recommender system and potential gaps between current research and real-world applications.

Secondly we are going to consider some more advanced questions around learning to rank from partial/incomplete feedback (1), dealing with selection-bias correction (2) and how econometrics and behavioral theory (eg Luce, Kahneman /Tversky) can be used to complement existing techniques (3).

After giving some motivation, I will discuss work in progress with Harry Schmidt in which we give a pfaffian definition of Weierstrass elliptic functions, refining a result due to Macintyre. The complexity of our definition is bounded by an effective absolute constant. As an application we give an effective version of a result of Corvaja, Masser and Zannier on a sharpening of Manin-Mumford for non-split extensions of elliptic curves by the additive group. We also give a higher dimensional version of their result.

I will compare features of (classical) cohomology theory of groups to the rather exotic features of bounded (or continuous bounded) cohomology of groups.
Besides giving concrete examples I will state classical cohomological tools/features and see how (if) they survive in the case of bounded cohomology. Such will include the Mayer-Vietoris sequence, the transfer map, resolutions, classifying spaces, the universal coefficient theorem, the cup product, vanishing results, cohomological dimension and relation to extensions. 
Finally I will discuss their connection to each other via the comparison map.

I will discuss some recent work, joint with R. Maffucci, concerning random Laplace eigenfunctions on the torus T^3=R^3/Z^3. Studying various statistics of these 'random waves' we will be confronted with an arithmetic question about linear relations among integer points on spheres.

We develop a Bayesian methodology for systemic risk assessment in financial networks such as the interbank market. Nodes represent participants in the network and weighted directed edges represent liabilities. Often, for every participant, only the total liabilities and total assets within this network are observable. However, systemic risk assessment needs the individual liabilities. We propose a model for the individual liabilities, which, following a Bayesian approach, we then condition on the observed total liabilities and assets and, potentially, on certain observed individual liabilities. We construct a Gibbs sampler to generate samples from this conditional distribution. These samples can be used in stress testing, giving probabilities for the outcomes of interest. As one application we derive default probabilities of individual banks and discuss their sensitivity with respect to prior information included to model the network. An R-package implementing the methodology is provided. (This is joint work with Axel Gandy (Imperial College London).)

A computational and asymptotic analysis of the solutions of Carrier's problem  is presented. The computations reveal a striking and beautiful bifurcation diagram, with an infinite sequence of alternating pitchfork and fold bifurcations as the bifurcation parameter tends to zero. The method of Kuzmak is then applied to construct asymptotic solutions to the problem. This asymptotic approach explains the bifurcation structure identified numerically, and its predictions of the bifurcation points are in excellent agreement with the numerical results. The analysis yields a novel and complete taxonomy of the solutions to the problem, and demonstrates that a claim of Bender & Orszag is incorrect.