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Some relish the idea of working with users of research and having an impact on the outside world - some view it as a ridiculous government agenda which interferes with academic freedom.  We’ll give an overview of  the political and practical aspects of impact and identify things you might want to consider when deciding whether, and how, to get involved.

How might you prepare talks for different audiences (specialised seminar, colloquium-style talk, talk to a non-mathematical audience, job interview)?  Join us for advice on this, and on how to connect with your audience and get them to feel involved.

Ambitious mathematical models of highly complex natural phenomena are challenging to analyse, and more and more computationally expensive to evaluate. This is a particularly acute problem for many tasks of interest and numerical methods will tend to be slow, due to the complexity of the models, and potentially lead to sub-optimal solutions with high levels of uncertainty which needs to be accounted for and subsequently propagated in the statistical reasoning process. This talk will introduce our contributions to an emerging area of research defining a nexus of applied mathematics, statistical science and computer science, called "probabilistic numerics". The aim is to consider numerical problems from a statistical viewpoint, and as such provide numerical methods for which numerical error can be quantified and controlled in a probabilistic manner. This philosophy will be illustrated on problems ranging from predictive policing via crime modelling to computer vision, where probabilistic numerical methods provide a rich and essential quantification of the uncertainty associated with such models and their computation. 

We study some features of the energy of a deterministic chordal Loewner chain, which is defined as the Dirichlet energy of its driving function in a very directional way. Using an interpretation of this energy as a large deviation rate function for SLE_k as k goes to 0, we show that the energy of a deterministic curve from one boundary point A of a simply connected domain D to another boundary point B, is equal to the energy of its time-reversal i.e. of the same curve but viewed as going from B to A in D. In particular it measures how far does the chord differ from the hyperbolic geodesic. I will also discuss the relation between the energy of the curve with its regularity, some questions are still open. If time allows, I will present the Loewner energy for loops on the Riemann sphere, and open questions related to it as well.


 

The class of log-concave densities on $\mathbb{R}^d$ is a very natural infinite-dimensional generalisation of the class of Gaussian densities.  I will show that it also allows the statistician to have the best of both the parametric and nonparametric worlds, in that one can obtain a fully automatic density estimator in the class (via maximum likelihood), with no tuning parameters to choose.  I'll discuss its computation, methodological consequences and theoretical properties, and in particular very recent results on minimax rates of convergence and adaptation.

A system of interacting particles described by stochastic differential equations is considered. As opposed to the usual model, where the noise perturbations acting on different particles are independent, here the particles are subject to the same space-dependent noise, similar to the (no interacting) particles of the theory of diffusion of passive scalars. We prove a result of propagation of chaos and show that the limit PDE is stochastic and of in viscid type, as opposed to the case when independent noises drive the different particles. Moreover, we use this result to derive a mean field approximation of the stochastic Euler equations for the vorticity of an incompressible fluid.

Permutations of finitely many elements are often drawn as permutation diagrams. We take this point of view as a motivation to construct and describe more complicated algebras arising for instance from differential operators, from operators acting on (co)homologies, from invariant theory, or from Hecke algebras. The surprising fact is that these diagrams are elementary and simple to describe, but at the same time describe relations between cobordisms as well as categories of represenetations of p-adic groups. The goal of the talk is to give some glimpses of these phenomena and indicate which role categorification plays here.
 

The cover of the December 2016 AMS Notices shows an eye-like region picked out by blue and red dots and surrounded by green rays. The picture, drawn by Yasushi Yamashita, illustrates Gaven Martin’s search for the smallest volume 3-dimensional hyperbolic orbifold. It represents a family of two generator groups of isometries of hyperbolic 3-space which was recently studied, for quite different reasons, by myself, Yamashita and Ser Peow Tan.

After explaining the coloured dots and their role in Martin’s search, we concentrate on the green rays. These are Keen-Series pleating rays which are used to locate spaces of discrete groups. The theory also suggests why groups represented by the red dots on the rays in the inner part of the eye display some interesting geometry.
 

The law of quadratic reciprocity and the celebrated connection between modular forms and elliptic curves over Q are both examples of reciprocity laws. Constructing new reciprocity laws is one of the goals of the Langlands program, which is meant to connect number theory with harmonic analysis and representation theory.

In this talk, I will survey some recent progress in establishing new reciprocity laws, relying on the Galois representations attached to torsion classes which occur in the cohomology of arithmetic hyperbolic 3-manifolds. I will outline joint work in progress on better understanding these Galois representations, proving modularity lifting theorems in new settings, and applying this to elliptic curves over imaginary quadratic fields.

In recognition of a lifetime's contribution across the mathematical sciences, we are initiating a series of annual Public Lectures in honour of Roger Penrose. The first lecture will be given by his long-time collaborator and friend Stephen Hawking.

Registration will open at 10am on 4 January 2017. Please email:

@email from that time only.

When registering please give your name and affiliation - your position, department & organisation/institution as appropriate. Or if you are a member of the General Public, please say so. Places will be allocated on a first come, first served basis with only one place per person. We will only be able to respond if you have a place or are on the waiting list.

We will be podcasting the lecture live. More details to follow.