(University of Oxford)

(University of Durham)

(KU Leuven)

(UNISA)

(University of Bath)

(UWC)

(RWTH Aachen University)

(Università di Bologna)

- Jon Chapman (University of Oxford)
- The making of an Escher: conformal maps and the Droste effect
I will explain the mathematics behind the Escher print "Picture Gallery", and show how it can be used to create new Escher-style pictures.

- The making of an Escher: conformal maps and the Droste effect
- Patrick Dorey (University of Durham)
- Breaking integrability at the boundary
This talk will describe some work on the bouncing of particle-like (“kink”) solutions to a nonlinear wave equation, called the sine-Gordon equation, against a fixed boundary. Away from the boundary, this equation has a property known as integrability, making the scattering of the kinks particularly simple. However, if this integrability is broken at the boundary, then the scattering becomes surprisingly complicated, in ways that will be outlined in the talk with the help of some movies.

- Breaking integrability at the boundary
- Daan Huybrechs (KU Leuven)
- The benefits and pitfalls of redundancy in the approximation of functions
Continuous functions, for example solutions to partial differential equations, are usually represented in a basis. This is convenient once a basis is available, but unfortunately bases are inflexible and often hard to construct. What if the domain geometry is complicated? What if the function has singularities? What if you know properties about the function, that do not match well with the basis you're using? Such questions do have accepted answers, for example the use of meshes, and adaptive refinement. In this talk we present a simple alternative that enables a lot of flexibility: redundancy. With some redundancy, it becomes simple -in fact, as we will show, nearly trivial- to represent functions on domains of arbitrary shape, or to add features to an approximation space. On the other hand, redundancy rapidly leads to ill-conditioning in algorithms. Surprisingly, with the right approach and with suitable restrictions, high accuracy can be achieved in a numerically stable manner. Moreover, efficient algorithms can be devised for many cases. In this talk we explore the introduction of redundancy in approximations, and we give practical guidelines about what is the 'right approach' and what are the 'suitable restrictions'.

- The benefits and pitfalls of redundancy in the approximation of functions
- Kerstin Jordaan (UNISA)
- Properties of orthogonal polynomials characterized by structural relations
In this talk we consider orthogonal polynomials that are characterized either by a structural relation of type \begin{equation}\pi(x)SP_n(x)=\sum_{k=-r}^{s}a_{n,n+k}P_{n+k}(x), \label{1}\end{equation}where $\pi(x)$ is a polynomial and $S$ is a linear operator that maps a polynomial of precise degree $n$ to a polynomial of degree $n-1$ or by \begin{equation}\label{2}\Pi(x)TP_n(x)=\sum_{k=-p}^{q}a_{n,n+k}P_{n+k}(x),\end{equation}where $\Pi(x)$ is a polynomial and $T$ is a linear operator that maps a polynomial of precise degree $n$ to a polynomial of degree $n-2$. It is understood that $S$ annihilates constants while $T$ annihilates polynomials of degree $1$. When $S=\displaystyle{\tfrac{d}{dx}}$, the structure relation (1) characterizes semiclassical orthogonal polynomials. We discuss properties of certain classes of semiclassical orthogonal polynomials. We characterize Askey-Wilson polynomials and their special or limiting cases as the only monic orthogonal polynomial solutions of (2) when $T=\mathcal{D}_q^2$ where $\mathcal{D}_q$ is the Askey-Wilson divided difference operator and $\Pi(x)$ is a polynomial of degree at most $4$. We use the structure relation (2) to derive bounds for the extreme zeros of Askey-Wilson polynomials.

- Properties of orthogonal polynomials characterized by structural relations
- Paul Melewski (University of Bath)
- TBC

- Kailash Patidar (UWC)
- Modelling and robust simulations of slow-fast dynamical systems

- Holger Rauhut (RWTH Aachen University)
- Compressive sensing and its use for the numerical solution of parametric PDEs

- Valeria Simoncini (Università di Bologna)
- On the numerical solution of large-scale linear matrix equations
Linear matrix equations such as the Lyapunov and Sylvester equations and their generalizations have classically played an important role in the analysis of dynamical systems, in control theory and in eigenvalue computation. More recently, matrix equations have emerged as a natural linear algebra framework for the discretized version of (systems of) deterministic and stochastic partial differential equations ((S)PDEs), and new challenges have arisen.

In this talk we will review some of the key methodologies for solving large scale linear matrix equations. Emphasis will be put on rank-structured and sparsity-structured problems, as they occur in applications. If time allows, we will also discuss recent strategies for the numerical solution of advanced linear matrix equations, such as multiterm equations and bilinear systems of equations, which are currently attracting great interest due to their occurrence in new application models associated with (S)PDEs.

- On the numerical solution of large-scale linear matrix equations

Participants will be added once registration has opened, which will be in late 2017.

For now we encourage potential participants to register
here.

Please send us an email if any information on this page is in error or obsolete.