Loughborough University

The Jacobi Ensembles of random matrices have joint distribution of eigenvalues proportional to the integration measure in the Selberg integral. They can also be realised as the singular values of principal submatrices of random unitaries. In this talk we will review some old and new results concerning the distribution of the largest and smallest eigenvalues.

The talk will begin with an introduction to the science of what determines the behaviour of a liquid on a on a surface and giving an overview of some of the different theories that can be used to describe the shape and structure of the liquid in the drop. These include microscopic density functional theory (DFT), which describes the liquid structure on the scale of the individual liquid molecules, and mesoscopic thin film equation (PDE) and kinetic Monte-Carlo models. A DFT based method for calculating the binding potential ?(h) for a film of liquid on a solid surface, where h is the thickness of the liquid film, will be presented. The form of ?(h) determines whether or not the liquid wets the surface. Calculating drop profiles using both DFT and also from inputting ?(h) into the mesoscopic theory and comparing quantities such as the contact angle and the shape of the drops, we find good agreement between the two methods, validating the coarse-graining. The talk will conclude with a discussion of some recent work on modelling evaporating drops with applications to inkjet printing.

Given a Mori Dream Space X, we construct via tropicalisation a model dominating all the small Q-factorial modifications of X. Via this construction we recover a Minkowski basis for the Newton-Okounkov bodies of Cartier divisors on X and hence generators of the movable cone of X. 
This is joint work with Stefano Urbinati.
 

The cube attack of Dinur and Shamir and the AIDA attack of Vielhaber have been used successfully on 

reduced round versions of the Trivium stream cipher and a few other ciphers. 

These attacks can be viewed in the framework of higher order differentiation, as introduced by Lai in 

the cryptographic context. We generalise these attacks from the binary case to general finite fields, 

showing that we would need to differentiate several times with respect to each variable in order to have

a reasonable chance of a successful attack.

We also investigate the notion of “fast points” for a binary polynomial function f  

(i.e. vectors such that the derivative of f with respect to this vector has a lower 

than expected degree). These were  introduced by Duan and Lai, motivated by the fact that higher order 

differential attacks are usually more efficient if they use such points. The number of functions which 

admit fast points were computed by Duan et al in a few particular cases; we give explicit formulae for 

all remaining cases and discuss the cryptographic significance of these results.

Systems with delays frequently appear in engineering. The presence of delays makes system analysis and control design very complicated. In this talk, the standard H-infinity control problem of time-delay systems will be discussed. The emphasis will be on systems having an input or output delay. The problem is solved in the frequency domain via reduction to a one-block problem and then further to an extended Nehari problem using a simple and intuitive method. After solving the extended Nehari problem, the original problem is solved. The solvability of the extended Nehari problem (or the one-block problem) is equivalent to the nonsingularity of a delay-dependent matrix and the solvability conditions of the standard H-infinity control problem with a delay are then formulated in terms of the existence of solutions to two delay-independent algebraic Riccati equations and a delay-dependent nonsingular matrix.

The classical gravity-capillary water-wave problem is the

study of the irrotational flow of a three-dimensional perfect

fluid bounded below by a flat, rigid bottom and above by a

free surface subject to the forces of gravity and surface

tension. In this lecture I will present a survey of currently

available existence theories for travelling-wave solutions of

this problem, that is, waves which move in a specific

direction with constant speed and without change of shape.

The talk will focus upon wave motions which are truly

three-dimensional, so that the free surface of the water

exhibits a two-dimensional pattern, and upon solutions of the

complete hydrodynamic equations for water waves rather than

model equations. Specific examples include (a) doubly

periodic surface waves; (b) wave patterns which have a

single- or multi-pulse profile in one distinguished

horizontal direction and are periodic in another; (c)

so-called 'fully-localised solitary waves' consisting of a

localised trough-like disturbance of the free surface which

decays to zero in all horizontal directions.

I will also sketch the mathematical techniques required to

prove the existence of the above waves. The key is a

formulation of the problem as a Hamiltonian system with

infinitely many degrees of freedom together with an

associated variational principle.