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# Open University

## UOA 20 - Pure Mathematics

### RA5a: Research environment and esteem

**Introduction/ Research Environment**

The Department of Mathematics at the Open University conducts internationally excellent research in four areas: Analysis, Applied Mathematics, Combinatorics, and the History of Mathematics. There are international leaders in all four areas and a thriving research culture, with strong University support and commitment to the sustainability of each group. Altogether, 17 active researchers are entered for this RAE.

All our researchers enjoy productive international collaborations, as shown by their publications and esteem indicators. The University’s decision to award five professorships to the Department in the RAE period demonstrates institutional commitment to mathematics, as do the recent appointments and succession planning is in place for coming retirements. Research Council supported studentships add to the pool of institutionally funded doctoral candidates and RCUK post-doctoral researchers, and contribute to the Department’s overall research capacity. This community of researchers is supported by an active programme of seminars and research days. Further recognition of the impact of our research is measured by the involvement of our researchers in a wide range of international events; the largest among several important international conferences organised by members of the Department during the period was the *British Combinatorial Conference* (BCC, 2005), with 250 participants from 34 countries and over 170 contributed talks. Significant contributions to the public awareness and understanding of science are another element of our contribution to the discipline.

The University has deepened its commitment to higher degrees in mathematics in recent years. There are now six full-time PhD studentships for mathematics, and seven part-time PhD students are currently enrolled. Our MSc programme, the largest in the UK with 643 students currently registered (up from 314 in 2002), provides an effective route for potential PGR students for both the OU and other UKHEIs. Over the period, 34 of these students have gone on to study for PhDs at various universities – a significant contribution to the research community nationally.

Mathematics research has benefited from the flexible provision of excellent resources for the development and support of international collaborations in all four research groups. Administrative support is strong and secure, computing resources are regularly enhanced, and library and journal provision are also good.

Post-doctoral research assistants and full-time PhD students play an active role in our research life, with offices on the Milton Keynes campus and access to all the OU’s computing and library resources. There is a continuing workshop programme at Department, Faculty¸ and University level that provides training and advice in all aspects of research. Our part-time PhD students are geographically scattered and have diverse personal circumstances, so their support and training is personally tailored in conjunction with their supervisors, and comprises visits to the OU, local visits by their supervisors, telephone support, and communication through letters and e-mail. They are fully supported by the Faculty; all are encouraged to attend appropriate meetings and conferences and are offered financial support to attend a major conference. That four full-time and ten part-time PhDs completed successfully within the HEFCE/RCUK approved time period is testament to the success of this flexible system of support and the Department’s strong research culture.

All researchers benefit from the Department’s collaborative research culture, and academic staff are assured of time for research through our system of workload planning. Study-leave provision and the flexibility of distance teaching enhance national and international collaborative research opportunities. Career-young researchers are supported through our mentoring system and the steady provision of workshops. Training is provided on student supervision; the University’s *Research Supervisors’ Forum* and other seminars offer further guidance. The close community atmosphere of the Department fosters a deepening commitment to research, and, as evidenced by publications, discussion of work in progress often leads to co-authored papers; for example, most of the more than 80 papers published by the Combinatorics group are co-authored. Departmental research meetings add cohesion between the groups. Throughout their careers, research-active Departmental members are encouraged to attend relevant conferences and meetings.

The Department of Mathematics is committed to maintaining and enhancing its four research groups. The recent appointment of Professor **Jozef Širáň** in Combinatorics provides much needed sustainability for this group which will see senior members retiring during the next period. Its vitality was further enhanced by the appointment of the career-young researcher Dr **Katie Chicot**, whose research straddles Combinatorics and Logic and adds depth to the group’s work on infinite designs. Other recent appointments include Dr **Ben Mestel**, who strengthens the Applied group and facilitates links with Analysis, and Dr **Gareth Williams** who recently completed his PhD in *K*-theory. His first paper (Poincaré duality for *K*-theory of equivariant complex projective spaces, with John Greenlees) is to appear in the *Glasgow Mathematical Journal* in 2008.

**Analysis**

The Analysis Group consists of Dr **Toby O’Neil** (geometric measure theory), Professor **Phil Rippon** (complex analysis and complex dynamics) and Dr **Gwyneth Stallard** (complex dynamics). All have strong international reputations and collaborate with external academics; during the assessment period, academic visitors have included Professor Walter Bergweiler (Kiel, Germany), funded by the LMS, Professor Stephen Gardiner (Dublin), Dr Laura Wisewell (Glasgow) and regular visits from Professor Karl Barth (Syracuse, USA). All three play an active role in the mathematical community, receive many invitations to speak at seminars, colloquia and research meetings, and contribute significantly to the organisation of such meetings, as listed in the Evidence of Esteem. In addition, **Rippon** and **Stallard** organised the 2002 and 2006 *One Day Function Theory Meetings* at De Morgan House with grants from the LMS.

**O’Neil**, in a major paper in the *Transactions of the AMS*, has established for the first time that if a plane continuum has Hausdorff dimension at least 1, then for almost every point there is a non-trivial (uniform) upper bound on the Hausdorff dimension of the corresponding visible part of the continuum. He has been invited to speak about this result at Oxford, Bath, Edinburgh and in Canada, and was an invited plenary speaker at the conference *Real Analysis, Geometric Measure Theory, PDE and Banach Spaces,* Warwick, 2007. **O’Neil**’s recent work with colleagues at UCL, Oxford and Warwick solves a fundamental problem in the calculus of variations, and the resulting long paper, to appear in *Archive for Rational Mechanics and Analysis*, is sure to have great impact.

**Rippon** and **Stallard** have collaborated extensively on the dynamics of transcendental meromorphic functions, and are international leaders in this area. Their first joint paper, on hyperbolic meromorphic functions, has become one of the most highly cited in the field, and their two 2005 papers on the ‘escaping set’ introduced a fundamental new approach to understanding the structure of this set, giving unexpected results on important old questions of Fatou and Eremenko (for example, showing that the escaping set of an entire function has at least one unbounded component). This is now being exploited by other authors. **Rippon** was invited to describe these new techniques at European mini-courses in Barcelona and Warwick in 2005.

**Rippon** was invited to speak about the work of the late Professor Noel Baker at the *Tag der Funktionentheorie* (Germany, 2001), and he wrote a substantial account of Baker’s work as an obituary in the *Bulletin of the LMS*. **Rippon** also works on wider questions in complex analysis. For example, his work on the boundary behaviour of meromorphic functions feeds into complex dynamics; providing key new techniques for dealing with the connectedness properties of Julia sets.

**Stallard** has continued her outstanding work on the dimensions of Julia sets of meromorphic functions, which earned her the LMS Whitehead Prize in 2000. In 2001, she obtained the surprising result that, even for well-behaved meromorphic functions, the Hausdorff dimension and packing dimension of the Julia set can take different values. Since then **Stallard** has made further major progress on the dimensions of Julia sets, working with **Rippon** and using their results on the escaping set. More recently, Bergweiler, **Rippon** and **Stallard** have established a new version of Wiman-Valiron theory, thus greatly generalising these results on the escaping set and dimensions of Julia sets. Their long paper on the arXiv, ‘Dynamics of meromorphic functions with direct or logarithmic singularities’, also has applications to differential equations, and has already been cited (by Eremenko et al). **Rippon** and **Stallard** spoke about results on the escaping set at an Oberwolfach meeting in 2007 (including properties of multiply connected Fatou components from a paper to appear in JLMS), and several other talks referred to their work. They are also ‘associated members’ of the CODY (Conformal Structures and Dynamics) European Research Training Network, and both will be main speakers at the CODY conference in Bremen, 2008.

**Applied Mathematics **

Research in Applied Mathematics is centred on a group that addresses problems in *Quantum and Statistical Physics*. The group consists of Dr **David Broadhurst** (quantum field theory), Dr **Uwe** **Grimm** (aperiodic order, mathematical biology, statistical mechanics), Dr **Ben Mestel** (aperiodic Schrödinger equations and renormalisation groups), Dr **Andrey Umerski** (modelling of magnetic materials) and Professor **Michael** **Wilkinson** (diffusion processes, theoretical quantum and solid-state physics). There are several areas in which the group has internationally outstanding expertise. **Grimm** is an acknowledged expert in the properties of aperiodic Schrödinger operators, **Broadhurst** is a leading authority on high-order Feynman diagrams and **Wilkinson** has had notable successes in several areas.

The group benefits from and contributes to a healthy research environment. A dynamic seminar agenda (mainly external speakers) provides a framework for regular peer engagement. Currently there are three full-time and several part-time postgraduate students, one university-funded postdoctoral fellow and two EPSRC funded postdoctoral appointments. Barbara Gabrys (Category B) had income in kind of about £190K when working at the Rutherford Appleton Laboratory in 2002-03.

**Broadhurst**'s research concerns the mathematical structure of quantum fields and in particular the polylogarithms and zeta values arising from the calculation of multi-loop Feynman diagrams. His prediction for the analytical structure of three-loop contributions to sum rules in deep-inelastic lepton scattering was confirmed in 2007 by results presented at the XI International Workshop on Advanced Computing and Analysis Techniques in Physics Research (Amsterdam). He has had numerous invitations to speak at conferences and workshops, including ‘Zeta functions, topology and quantum physics’, Osaka (2003) and 7th DESY Workshop on Elementary Particle Theory, Zinnowitz (2004).

**Grimm**’s research involves the application of mathematics in physics, biology, crystallography and materials science. Since 2001, he has published several papers on topics in statistical physics and in mathematical biology, supported by a British Council ARC award (2003-2005). The principal focus of his research has been on aperiodic order and quasicrystals, with more than twenty publications with collaborators in Bielefeld, Hamburg and Chemnitz. He was recently awarded a £215K EPSRC research grant (2006-2009), co-funded by the Mathematics, Fundamentals of Computing and Theoretical Materials Science committees. This enabled him to build up a research group on mathematics of aperiodic order, consisting of a postgraduate research student and two postdoctoral researchers, complemented by a visiting research student (for 2 years). **Grimm** has had numerous invitations to speak at international conferences and workshops, with visits to Brazil (2003) and Japan (2006) supported by the Royal Society. Major workshop invitations have included Oberwolfach (2001 and 2004), CIRM (2002), Erwin Schrödinger Institute (2002/3) and Banff (2004). Cambridge University Press have asked him to co-author a monograph and co-edit a further five volumes of a series on Aperiodic Order (*Encyclopaedia in Mathematics and its Application*, 2008-2014). He has attracted (for the first time in the UK) a major conference in this field (Aperiodic 2009), which he will be co-chairing.

**Mestel** is an applied analyst who joined the Open University in 2006. Since 2001 his work has had two principal themes. First, he has applied functional analysis to both the renormalization of quasiperiodic quantum models, including the quadratic-irrational generalised Harper equation (where he discovered a sequence of renormalization strange sets), and the calculation of the correlation for a quasiperiodically forced two-level quantum system. Second, in his study of critical chaotic transitions with symmetry breaking he established, for all critical degrees and all asymmetry moduli, the existence of the unstable eigenfunction, thereby obtaining rigorous bounds for the universal constants in asymmetric Feigenbaum period-doubling cascades.

**Mestel’s** work is supported by grants from the Leverhulme Trust, the Royal Society, and the LMS. He and his collaborator (Professor Andrew Osbaldestin, Portsmouth) have established strong links with the Dynamic Chaos group, Russian Academy of Sciences Institute of Electronics (Saratov). During the review period he supervised two research fellows and one PhD student, and was invited to visit the IHES and the Fields Institute.

**Umerski** models electronic phenomena in magnetic multilayers and other microscopic structures. His research in spintronics is applicable to magnetic storage devices such as hard disks, M-RAM and magnetic race-track memories; it involves exchange coupling, magnetoresistance phenomena, and current-induced switching of magnetisation. One of his publications (Phys. Rev. B, **63**, 220403R (2001)) has aroused intense interest, gaining 106 citations to date, the predictions having been verified by Japanese experimental groups, stimulating further activity. Another publication (*Jour. Mag. Soc. Japan* 27, 123 (2003)) received the MSJ Distinguished Publication Award for 2003. He collaborates with colleagues in London, Poland, and Japan: highlights include a visit by Dr Marek Cinal, funded by Polish Ministry of Science, an invitation to visit Professor J. Inoue (Nagoya) and to attend the ICMFS 2002 conference in Kyoto. He was a co-author on the Spin@RT: Room Temperature Spintronics EPSRC grant (£100K, PI Professor J. Mathon, City University, 2005) and has recently been awarded £152K by the EPSRC as one of three PIs on a project that will tackle the fundamental limitation for room temperature spintronics – the role of interfaces in electron spin detection and injection.

**Wilkinson** has made highly original contributions to theoretical solid-state physics, including the energy diffusion theory for dissipation and the explanation of fractal spectra of Bloch electrons in a magnetic field. His recent research has centred on novel diffusion processes, mainly in collaboration with Professor B. Mehlig (Gothenburg). They analysed the ‘path coalescence transition’ for particles suspended in random flow fields. This was extended to provide a quantitative explanation for clustering of inertial particles in turbulent flows, using a novel mapping to a diffusion process and then to a perturbation of a nine-dimensional quantum harmonic oscillator. A fundamental generalisation of the Ornstein-Uhlenbeck process was analysed in terms of a novel system of annihilation and creation operators. Work on rain showers showed the importance of caustics in the velocity field of water droplets, their formation being controlled by a diffusion process. These developments are discussed in the four selected papers. Other recent work includes the discovery of semilinear response, a widely applicable generalisation of quantum linear response. Over the review period there were more than 20 invitations to speak at international conferences and workshops, including meetings on solid-state physics, quantum mechanics, statistical physics, fluid dynamics and atmospheric physics. Examples include: ‘Chaos and Nonlinear Dynamics in Quantum Systems’, Kyoto, with JSPS sponsored lecture tour (2004), ‘Non-Equilibrium Statistical Mechanics’, Haifa (2004), ‘Stochastic Models for Turbulent Suspensions’, Nice (2006) and a lecture course on dissipation at Institut Henri Poincaré (2007).

**Combinatorics Group**

The Combinatorics Research Group is submitting six staff: Professors **Mike** **Grannell**, **Terry** **Griggs** and **Jozef Širáň**, Dr **Fred** **Holroyd**, and Dr **Bridget** **Webb**, all researchers of international standing, together with Dr **Katie** **Chicot** (Early Career Researcher). Research in combinatorics has focused on combinatorial designs, especially configurations, Latin squares and topological representations of designs, and on graph theory including graph decompositions and colourings. The appointment of **Širáň** in March 2007 added world-class expertise in topological graph theory. His appointment and **Chicot**’s make a major contribution to the vitality and sustainability of the Group.

Group members collaborate together and with many external academics, particularly from Australia, Canada and Slovakia. Grants from the EPSRC, LMS, BCC and the Leverhulme Trust, augmented by Departmental funding, have supported a steady stream of visitors to the OU and by OU staff to other universities. Collectively, in the assessment period, the group has over 80 refereed publications, with several more accepted, and more submitted. Combinatorics group members have also given numerous talks at other institutions; the group runs an annual conference at the OU, and in 2005 co-organised the *British Combinatorial Conference* at Durham. **Griggs**, **Širáň** and **Webb** are invited contributors to the revised *CRC Handbook of Combinatorial Designs*, writing on the History of Combinatorial Designs, Graph Embeddings and Designs, and Infinite Designs, respectively.

Within the mainstream of topological graph theory, **Širáň** has consistently produced work of the highest quality, notably, in collaboration with Dr Antonio Breda d'Azevedo (Aveiro, Portugal) and Professor Roman Nedela (Slovak Academy of Science), the first complete classification of regular maps for an infinite series of genera. He works with many other leading researchers in the field, such as Professors C. P. Bonnington, M. Miller, R. B. Richter, T. W. Tucker and M. E. Watkins, and is a member of several editorial boards including that of the *Journal of Combinatorial Theory* *Series B*. During the assessment period he has given eight invited plenary talks at conferences (see Evidence of Esteem) including the International Conference on Graph Theory, Slovenia (2003) and the International Conference on Graph Labellings, Indonesia (2004). During the assessment period he has been the PI on eight research grants and co-investigator on a further two.

Group members have been particularly active at the interface of topological graph theory and combinatorial design theory and their work has developed strongly during the assessment period. One fundamental and difficult question is whether or not every pair of Steiner triple systems admits a biembedding in a surface, and associated with this question are enumeration results and general methods for generating such embeddings. On these topics, **Grannell** has given the invited plenary talks listed in the Evidence of Esteem and, jointly with **Griggs**, at the *British Combinatorial Conference*, Reading University (2007). **Griggs**, together with **Grannell**, was awarded a grant of £15,000 by the Leverhulme Trust for collaborative work on topological design theory with colleagues in Slovakia in 2002-2006. The principal collaborators with **Grannell** and **Griggs** in this work are **Širáň**, Dr Martin Knor (Bratislava), Dr Vladimir Khorzhik (Ukraine), and Dr Geoff Bennett (OU research student).

With Professor Darryn Bryant (Queensland) and Dr Martin Mačaj (Comenius, Bratislava), **Grannell** and **Griggs** determined the minimum and maximum numbers of the smallest variable configuration in a 4-cycle system, the latter being an unsolved problem for Steiner triple systems (STSs). Working with Dr Tony Forbes (OU research student), **Grannell** and **Griggs** produced the first known examples of 6-sparse STSs, together with a recursive construction that yields an infinite class. Again, with Forbes, they constructed designs with certain colouring properties that long eluded other researchers. These designs include Steiner systems S(2, 4, *v*) containing disjoint embedded STSs spanning the point set. Work has also been undertaken analysing tradeable configurations in STSs and, with Professor Anne Street (Queensland), the surprising result obtained that an STS may sometimes be uniquely reconstructed from incomplete knowledge of a smallest defining set.

In the area of graph theory, **Holroyd** initiated investigation of the Erdős-Ko-Rado property in the context of families of sets defined by graphs. During the assessment period he made substantial progress on this with Dr John Talbot (UCL) and more recently with Peter Borg (OU research student). In graph colourings, his collaboration with Professor Martin Škoviera (Comenius, Bratislava) resulted in largely solving a difficult problem, originally posed by Professor Dan Archdeacon (Vermont), on colouring the edges of a cubic graph so that each vertex ‘sees’ a triple of a given Steiner triple system. Furthermore, in collaboration with **Grannell** and **Griggs**, he developed a novel approach to the notorious graceful tree conjecture, using the residue classes mod *k* of the labels.

Since 2002, **Webb** has been working on Latin squares, mostly with Dr Ian Wanless (Monash, Australia), and has helped solve some long-standing problems, for example, proving the existence of Latin squares without orthogonal mates, a problem unsolved since Euler’s work in the 18^{th} Century. She was an “All Institute” invited plenary speaker at the *DIMACS Connect Institute Combinatorial Conference*, Rutgers, USA (2003), and has spoken at international conferences and given invited seminar talks in the UK, Slovakia and Australia. **Webb** is an elected member of the BCC and holds their archive.

**Webb** has continued her innovative work on infinite designs including publishing, jointly with Professor Peter Cameron (QMUL), the definitive definition of an infinite design, thus resolving existing ambiguities on the subject. Her recent work has focussed attention on this topic resulting in an invitation, together with Cameron, to write a new chapter in the revised *Handbook of Combinatorial Designs*.

The appointment of **Chicot** to her first academic post in 2005 as a Regional Staff Tutor has added depth to the group’s work on infinite designs. She has published on infinite linear orders and partial orders. She not only uses combinatorial approaches, but also studies structures using Model Theoretic tools. Her expertise in this area complements **Webb**’s and in 2007 they were awarded grants in excess of £8000 from the EPSRC and LMS for a project on infinite STSs. With Dr Silvia Barbina (Barcelona) they will study the universal STS and new properties of STSs such as self-similarity. **Chicot**, with **Grannell**, **Griggs** and **Webb**, has prepared a paper on the existence of sparse countably infinite STS. Despite her career-young status she has given talks on her research at five academic conferences over the past three years.

**History of Mathematics Group**

The History of Mathematics Research Group is submitting all three category A staff: Dr **June** **Barrow-Green**, Professor **Jeremy** **Gray**, and Professor **Robin** **Wilson**. All collaborate with historians of mathematics around the world, carry out editorial jobs for major international journals and publishers, and receive numerous invitations to speak and organise international meetings. Their work on the history of mathematics in the modern period (1600-1950, with particular emphasis on the 19th and early 20th centuries) is both scholarly and popular, reflecting the two roles of history of mathematics within the international mathematical community.

The historians maintain the Centre for the History of the Mathematical Sciences (CHMS). In the seven years of its existence, CHMS has organised and co-organised seven conferences. One of these produced a rolling series of meetings and the book (*The Architecture of Modern Mathematics*, Oxford University Press, 2006, edited by **Gray** and Professor José Ferreirós (Seville)). Another conference was the basis for two special editions of *Historia Mathematica* in 2006. The Centre collaborates with the Archives Henri Poincaré, (Nancy), and has been invited to organise an international conference at the Institute for Mathematical Sciences, Singapore, in September 2008.

**Barrow-Green**’s interest in Poincaré and the three body problem has led her to investigate Mittag-Leffler and the rise of *Acta Mathematica*. She has restructured her database of British Mathematicians 1860-1940 to make it much more publicly accessible; this work resulted in the publication of the first study on Geometry at Cambridge in those years. This in turn has led her to work on a jointly-funded British Academy and CNRS study on mathematicians and the First World War. This innovative project in the history of mathematics has led to a number of other studies on different countries and a Société Mathématique de France conference on that theme in January 2007. Her work with Dr David Aubin (CNRS, Paris) comparing the use of British and French mathematicians in World War I will form part of a book of essays on Allied Mathematicians in the First World War.

In 2005 **Barrow-Green** began a three-year period as a Member of the International Commission on the History of Mathematics. She has been an invited speaker at the AMS/MAA Joint Meetings in five of the last seven years, and has also spoken at meetings in Luminy, Oberwolfach, the ETH (Zürich), and at Frankfurt University among other places. In 2007 she was the Gibson Lecturer at the University of Glasgow. From 2004 to 2006 she was President of the British Society for the History of Mathematics.

**Gray** is an international leader in the history of geometry, analysis and the philosophy of mathematics. *Worlds out of Nothing,*his study of the history of geometry, 1800-1914, is the first to investigate this theme in 60 years. Papers and a forthcoming book (Princeton, 2008) in the emerging field of the overlap between history and philosophy of mathematics have opened up avenues for historians of mathematics and science to explore jointly. In the last three years Professors Moritz Epple (Frankfurt), Erhard Scholz (Wuppertal) and José Ferreirós have visited him to work on various aspects of this project.

**Gray**’s work has led to many invitations. He was invited by the Clay Mathematics Institute to write an essay on Prizes in Mathematics for their book *The Millennium Prize Problems* (2006). He was a Visiting Fellow at the Erwin Schrödinger Institute (Vienna, 2005); and in 2007 gave the Enriques Lecture at the University of Milan. He has visited MSRI (Berkeley) for joint work with Professor David Eisenbud, and with Professor Karen Parshall (Virginia) organised an MSRI workshop in 2003, resulting in an edited book published in the AMS and LMS joint HMath series (2007). In 2006 he was appointed to the Peer Review College of the Arts and Humanities Research Council. **Gray** was also the supervisor of Jackie Stedall’s highly successful work on Wallis’s *Arithmetica Infinitorum*, supported with a Leverhulme grant that ended in 2003.

**Wilson** contributes to the history of combinatorics, and of mathematics in Britain, through a wide range of books and scholarly articles. He is regularly invited to speak at international meetings, including those of the AMS and MAA. His plenary talk at the joint meeting in Baltimore (2004) drew a record audience of 1400, and he is organising an MAA short course on *Combinatorics: past, present and future* for January 2008. He gave a plenary address in Thailand (2002) and was the only British speaker at the conference on *Euler and Modern Combinatorics* at the Euler Institute St. Petersburg (2007). In keeping with the OU’s mission, he is committed to making research in the history of mathematics accessible to mathematicians and the general public and, although designed primarily for a popular market, his book *Four Colours Suffice* contains much original historical research. In 2002 **Wilson** organised an LMS meeting on the Four Colour Theorem with four international speakers.

**Gray** and **Wilson** are editors of the joint AMS/LMS book series on the history of mathematics. Gray was a founder editor, Wilson chaired the LMS side from 2004 to 2007.

**Discipline and Public Engagement **

**Rippon**, as a member of the LMS Education Committee, organises the annual LMS Popular Lectures. **Stallard**, as chair of the LMS Women in Mathematics Committee, has had a

notable influence on the research opportunities for women mathematicians, for example, by successfully lobbying EPSRC to make their policy on part-time working and maternity leave for their Advanced Research Fellowships fairer. She also gave the main talk at the British Women in Mathematics Day 2003, and she was a member of the 2007 LMS Nominating Committee (elected by LMS members).

**Grimm** is engaged in public dissemination of his research, through publishing articles in science magazines (including *Spektrum der Wissenschaft*, the German edition of *Scientific American*), leading an exhibit at the Royal Society Summer Science Exhibition 2004, and local outreach events. As a member of the EPSRC college **Grimm** also served on Partnership for Public Engagement panels (2006 and 2007), and Mathematics Prioritisation Panels (twice in 2006). He was elected a Fellow of the Institute of Physics in 2001, and since 2004 has been the Honorary Secretary of its Mathematical and Theoretical Physics Group Committee.

In June 2004 **Chicot** was awarded the Clothworkers’ Fellowship in Mathematics at the Royal Institution of Great Britain. She works extensively in public engagement activities around the country with the Royal Institution, the LMS BA Mathematics Section committee and other partners, and was nominated by the LMS to give the Kelvin Award lecture at the BA Festival of Science 2007.

The historians are prominently involved in efforts to popularise mathematics. **Wilson** is currently Gresham Professor of Geometry (2004-08) at Gresham College, London, where he gives public lectures. He gave a prestigious Royal Institution Friday Evening Discourse in 2005. **Barrow-Green** and **Wilson** have appeared on Melvyn Bragg’s ‘In our Time’; **Gray** is an advisor on the volume on "History of Mathematics" for the UNESCO-project *Encyclopedia of Life Support Systems*.

**Evidence of Esteem **

**Analysis**

**O’Neil**

- Co-organiser of the 2003
*St Andrews Colloquium*and the 2007*Summer Symposium in Real Analysis*(Oxford). - Speaker at the invited workshop on geometric measure theory, International Research Station for Mathematical Innovation and Discovery, Banff, Canada, 2003.

**Rippon**

- Co-organiser of the one-week conference on
*Normal Families and Complex Dynamics*in 2007 at the Mathematisches Forschungsinstitut, Oberwolfach. - Invited editor (with Professor Milne Anderson, UCL) of the two 2008 volumes of
*Computational Methods and Function Theory*, dedicated to Professor Walter Hayman. - Invited speaker at the joint meeting of the American and Polish Mathematical Societies, Warsaw, 2007.

**Stallard**

- One of the 20 ‘influential mathematicians’ in the Faces of Mathematics exhibition, sponsored by EPSRC; see http://www.ma.hw.ac.uk/ndg/fom.html.
- One of only two invited foreign mathematicians to speak (on dimensions of Julia sets and the escaping set) at a workshop and colloquium in Japan in 2003.

**Applied Mathematics**

**Broadhurst**

- Keynote addresses at Osaka (2003) and the 7th DESY Workshop on Elementary Particle Theory, Zinnowitz (2004).
- Participation over the period in invited workshops, conferences and colloquia held at

the Erwin Schrödinger International Institute for Mathematical Physics (Vienna), the Institut des Hautes Études Scientifiques (Bures-sur-Yvette), the Centre International de Recontres Mathématiques (Marseilles).

**Grimm**

- British Council ARC award (2003-2005).
- EPSRC research grant of £215k (2006-2009).
- Member of the EPSRC college, serving on Partnership for Public Engagement panels (2006 and 2007) and Mathematics prioritisation panels (twice in 2006).

**Mestel**

- Invited visitor at the IHES (2001) and the Fields Institute (2005).

**Umerski **

- Received the MSJ Distinguished Publication Award for 2003 for his paper (
*Jour. Mag. Soc. Japan*27, 123 (2003)). - Co-author on the Spin@RT: Room Temperature Spintronics EPSRC grant in 2005 (£100K, PI Professor J. Mathon, City University).

**Wilkinson**

- Keynote address at Chaos and Nonlinear Dynamics in Quantum and Macroscopic Systems, Kyoto, 2004; Quantum Chaos and Non-Equilibrium Statistical Mechanics, Haifa, 2004, and Stochastic Models for Turbulent Suspensions, Observatoire de Nice, 2006.
- Invited lecture course on dissipation at Institut Henri Poincaré, 2007.

**Combinatorics**

**Chicot (career-young researcher)**

- Awarded the Clothworkers’ Fellowship in Mathematics at the Royal Institution of Great Britain, 2004.

**Grannell**

- Invited plenary speaker at the LMS/EPSRC short course “Design in Combinatorics and Statistics” in London, 2002, the Australasian Combinatorics Conference, Queensland, 2005, and at the British Combinatorial Conference, Reading University, 2007 (joint invitation with
**Griggs**). - Elected Member of the Council of the Institute of Combinatorics and its Applications, December 2005, for three years.

**Griggs**

- Co-investigator (with
**Grannell**) awarded a grant of £15K by The Leverhulme Trust for collaborative work on topological design theory with colleagues in Slovakia in 2002-2006. - Guest associate editor for the special editions of
*Discrete Mathematics*comprising the contributed talks at the British Combinatorial Conferences in 1999, 2001, 2003, and (with**Webb**) 2005, 2007.

**Širáň**

- Member of several editorial boards including the
*Journal of Combinatorial Theory, Series B*. - Eight invited plenary talks at conferences, including those at the International Conference SIGMAC'02, Portugal, 2002 and the 6th International Symposium on Graph Theory, Combinatorics, Algorithms and Applications, Charles University, Prague, 2006.

**Webb**

- ‘All Institute’ invited plenary speaker at the
*DIMACS*Connect Institute combinatorial conference, Rutgers, USA, 2003. - Awarded (with
**Chicot**) £8K by the LMS and EPSRC, for a project investigating infinite Steiner triple systems with Dr Barbina (Barcelona) 2007-2009.

**Collectively**

- Co-organised the British Combinatorial Conference at Durham in 2005.

**History of Mathematics**

**Barrow-Green **

- Awarded (with
**Gray**) British Academy and CNRS (France) grant in 2004 of £2,500 to conduct a joint study on mathematicians and the First World War. - Managing Editor of
*Historia Mathematica*since 2006.

**Gray**

- Invited plenary lecturer at the Conference on the 200th anniversary of the birth of János Bolyai, Budapest, Hungary (2002).
- Member at Large on the International Commission on the History of Mathematics (ICHM), a division of the International Mathematical Union, from 2003 to 2006.
- Appointed one of the two editors of
*Archive for history of exact sciences*in 2006.

**Wilson**

- Plenary lecturer to the MAA in Baltimore (2004) on the history and proof of the Four Colour Theorem.
- Gresham Professor of Geometry (2004–08) at Gresham College, London.