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

- Thursday 11 September 2014, 10.00am

Gray days*Valediction to Jeremy Gray, Day 1*

The first day of a two-day meeting to mark Jeremy Gray’s retirement from the Open University and to celebrate his many achievements For further information and registration, see https://sites.google.com/site/grayvalediction/ Day 1 schedule: 10:00 COFFEE 10:30 Snezana Lawrence (Bath Spa) History of Mathematics lessons for Mathematics Education 11.30 Umberto Bottazzini (Milan) Mathematics and politics: the Italian case 12:30 LUNCH 2:00 Karine Chemla (Paris) “Measuring the circle on the sea-mirror” 3:00 Leo Corry (Tel Aviv) The interaction between arithmetic and geometry in the Euclidean tradition: a longue durée issue in the historiography of mathematics (if there ever was one) 4:00 TEA 4:30 Niccolò Guicciardini (Bergamo) On Newton’s mathematical manuscripts: disciplinary boundaries, writing practices, and styles 5:30 Close 7:00 DINNER - Friday 12 September 2014, 9.30am

Gray days*Valediction to Jeremy Gray, Day 2*

The second day of a two-day meeting to mark Jeremy Gray’s retirement from the Open University and to celebrate his many achievements For further information and registration, see https://sites.google.com/site/grayvalediction/ Day 2 schedule: 9:30 Erhard Scholz (Wuppertal) ‘Localizing’ the geometry of special relativity: Why Cartan and Weyl posed their new ’problem of space’ differently 10:30 COFFEE 11:00 Moritz Epple (Frankfurt) Another look at mathematical modernism: Felix Hausdorff on dimension 12:00 Jesper Lützen (Copenhagen) Geometry, forces and models 1:00 LUNCH 2:00 Encomium by the Department of Mathematics & Statistics 2:15 June Barrow-Green (OU) GD Birkhoff and Poincaré’s ‘Last Geometric Theorem’ 3:15 Jeremy Gray Klein’s Galois theory: underneath the icosahedron 4:15 TEA 4:45 Close - Tuesday 16 September 2014, 4.00pm

Dan Nicks (University of Nottingham)*Escape to infinity: as slow as you like or (almost) as fast as possible*

A point $x$ is said to `escape to infinity' if the sequence of iterates $f^k(x)$ tends to infinity. The functions $f$ we consider are either analytic on the complex plane or quasiregular on $\mathbb{R}^n$; the latter being the natural higher-dimensional generalisation of analytic functions. For a complex polynomial $f$, all points that escape to infinity do so at roughly the same speed. For a transcendental (non-polynomial) entire function, Phil Rippon and Gwyneth Stallard showed that there are always points that escape to infinity arbitrarily slowly. We'll see that this result can be generalised to the quasiregular setting. Unexpectedly, part of the method used to prove this `slow escape' generalisation also allows us to say something about points that escape to infinity very fast. In particular, we can find points for which the escape rate is known asymptotically, and is related to the fastest possible speed of escape. This last result appears to be new even for entire functions. - Tuesday 14 October 2014, 11.30am

Luke Adamson (University of Portsmouth)*On the self-similarity and box-counting dimension of strange non-chaotic attractors*

Strange non-chaotic attractors (SNAs) have been shown to occur in a broad class of quasi-periodically forced systems and have been a prominent topic of research over the past three decades. In this seminar we will focus on SNAs arising as a result of the so-called “non-smooth pitchfork” bifurcation in systems of ``pinched skew-product” type. Firstly, we will investigate the box-counting dimension of the attractors at and near the point of bifurcation, providing evidence that the dimension is 2 for structurally stable SNAs and lies between 1 and 2 at the bifurcation point. We will also examine the self-similar behaviour of the attractors at and near the point of bifurcation using a renormalization analysis, revealing their multi-fractal nature.

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