Robert Brignall

I am a Lecturer in Combinatorics in the Department of Mathematics and Statistics at The Open University. My research interests primarily focus on the study of infinite antichains, well-quasi-ordering, and the interplay between permutation patterns and similar concepts in graph theory. Until 30 September 2013 my research into infinite antichains is being funded by EPSRC grant EP/J006130/1. You may read more about my research, view my list of publications or my list of talks.

I am the department's Research Director, and I also organise our Seminar Series.

Previously, I was a research fellow in the Department of Mathematics at the University of Bristol, and before that I was a PhD student in the School of Mathematics and Statistics at the University of St Andrews.

In the past, I organised the Bristol Combinatorics Seminar, and was on the organising committees for Techniques and Problems in Graph Theory, Permutation Patterns 2010 and Permutation Patterns 2011.

**Email**: r.brignallopen.ac.uk

This page last modified on 05 November 2013 at 12:42. [Disclaimer] [Cookie info]

I am the department's Research Director, and I also organise our Seminar Series.

Previously, I was a research fellow in the Department of Mathematics at the University of Bristol, and before that I was a PhD student in the School of Mathematics and Statistics at the University of St Andrews.

In the past, I organised the Bristol Combinatorics Seminar, and was on the organising committees for Techniques and Problems in Graph Theory, Permutation Patterns 2010 and Permutation Patterns 2011.

### Contact Details

**Address**: Department of Mathematics and Statistics, The Open University, Milton Keynes, MK7 6AA**Telephone**: +44 (0)1908 3x32744### Upcoming Mathematics Seminars

- Tuesday 28 October 2014, 4.00pm

Matthieu Astorg (Université de Toulouse)*Immersion of the dynamical Teichmüller space into the moduli space of rational maps*

Teichmüller theory's goal is to study deformations of the complex structure of a Riemann surface. In the 80's, McMullen and Sullivan introduced an analogue of this theory in the context of iterations of a rational map f. In particular, they constructed a "dynamical Teichmüller space" which is a simply connected complex manifold, with a holomorphic map F defined on Teich(f) and taking values in the space of rational maps of the same degree as f, and whose image is exactly the quasiconformal conjugacy class of f. A natural question, raised in their article, is to know if this map F is an immersion: it turns out the answer is affirmative. A. Epstein has an unpublished proof of this; we will expose a different approach. - Tuesday 11 November 2014, 4.00pm

Dave Sixsmith (The Open University)*Maximally and non-maximally fast escaping points of transcendental entire functions*

We partition the fast escaping set of a transcendental entire function into two subsets, the maximally fast escaping set and the non-maximally fast escaping set. These sets have strong dynamical propertoes. We show that the intersection of the Julia set with the non-maximally fast escaping set is never empty. It was shown by Rippon and Stallard that the fast escaping set has no bounded components. In contrast, by studying a function considered by Hardy, we give an example of a transcendental entire function for which the maximally and non-maximally fast escaping sets each have uncountably many singleton components. - Tuesday 18 November 2014, 4.00pm

Emilio Pierro (Birkbeck, University of London)*The Möbius function of the small Ree groups*

In 1936 Hall showed that Möbius inversion could be applied to the lattice of subgroups of a finite group G in order to determine the number of n-bases of G, that is, generating sets of G of size n. The question can be modified and n-bases subject to certain relations can also be enumerated with applications to the theory of Riemann surfaces, Hurwitz groups, dessins d'enfants and various other algebraic, topological and combinatorial enumerations. In order to determine the Möbius function of a group it is necessary to understand the subgroup structure of a group and so we also give a description of the simple small Ree groups R(q)=²G_2(q), in particular their maximal subgroups, in terms of their 2-transitive permutation representations of degree q³+1. - Tuesday 25 November 2014, 4.00pm

Fabian Essler (University of Oxford)*Title to follow*

Abstract to follow - Monday 1 December 2014, 4.00pm

Nick Watkins (Max Planck Institute for the Physics of Complex Systems, Dresden)*Mandelbrot's eyes and 1/f noise*

More than 100 years ago, Thomson and Tait's classic "Treatise on Natural Philosophy" cautioned its readers against "considering the formula and not the fact as physical reality". Deciding what the facts actually *are*, however, tends to be left as an exercise for the student. My own research [1,2] in modelling time series from complex systems, including space plasma, atmospheric temperature and animal foraging datasets, has exposed me to many instances of the problem Thomson & Tait identified, and I am sure I have been no exception to it myself. Today I will focus on two related aspects of this problem -the "1/f" spectral shape seen in many areas of physics, and the heavier than Gaussian amplitude distributions seen in finance, insurance and physics. I will tell the story [3] of part of Mandelbrot’s intellectual journey: from heavy tails in cotton price fluctuations in 1963, via a stationary long range dependent (LRD) model for the water levels in the Nile in 1968, to multifractal models for turbulence and finance. A little known part of this tale is his work in 1965-67 on nonstationary models of 1/f noise, so I will also talk about how these models relate to the LRD concept. I will recount how, late in his life, he made a special effort to explain the differences between his fractal models, and to urge us to use our eyes as well as formalism, making him an unexpected (to some) ally of Thomson and Tait. I will discuss how Mandelbrot’s visual approach affected his science, and speculate on how the history of science and maths more generally has been affected by cognitive diversity. Finally I will touch on several results inspired by these approaches, including new Bayesian methods for choosing between LRD models [4], and work on a dynamical origin for the Hurst effect [5]. [1] Watkins, Bunched Black Swans, GRL, 2013 [2] Watkins and Freeman, Natural Complexity, Science, 2008 [3] Graves et al, A Brief History of Long Memory, Statistical Science, Submitted 2014 [4] Graves et al, Efficient Bayesian inference for long memory processes, CSDA, Submitted 2014 [5] Franzke et al, PNAS, submitted 2014. - Thursday 4 December 2014, 4.00pm

Nuria Fagella (Universitat de Barcelona)*Title to follow*

Abstract to follow - Tuesday 16 December 2014, 4.00pm

Ben Fairbairn (Birkbeck, University of London)*Title to follow*

Abstract to follow

This page last modified on 05 November 2013 at 12:42. [Disclaimer] [Cookie info]