International Review of Mathematical Sciences
5 –10 December 2010 Contents
Executive Summary iv
Table of Acronyms v
Acknowledgements vi
Foreword vii
1. Introduction and Background 1
1.1 Purpose and scope of the review 1
1.2 Structure of the review 1
1.3 Review Panel activities 2
1.4 Relevant external events 3
1.5 Evidence used by the Panel 3 1.5.1 Data used by the Panel 3 1.5.2 Evidence provided by site visits and panel members’ expertise 4
1.6 Overview of the Panel’s report 4
1.7 On names of individuals and lists of institutions 5
1.8 The International Panel 5
2. Findings and Recommendations 6
2.1 Findings 6
2.2 Broad recommendations 6
2.3 Field-specific recommendations – challenges and opportunities 7
3. Nature of the Mathematical Sciences 10
3.1 Unity 10
3.2 Abstraction and long time scales 10
3.3 Community structure and research needs 12
4. Excellence and Capability through Diversity 13
International Review of Mathematical Science i Contents
5. Subfields of the Mathematical Sciences 15
5.1 Algebra 15
5.2 Analysis 16
5.3 Combinatorics and discrete mathematics 17
5.4 Dynamical systems and complexity 17
5.5 Fluid mechanics 18
5.6 Geometry and topology 19
5.7 Logic and foundations 20
5.8 Mathematical physics 20
5.9 Number theory 21
5.10 Numerical analysis/scientific computing 21
5.11 Operational research 22
5.12 Probability 23
5.13 Statistics 24
6. Applications Connected with the Mathematical Sciences 26
6.1 Computational science and engineering 26
6.2 Financial mathematics 27
6.3 Materials science and engineering 27
6.4 Mathematical biology and medicine 28
7. Industrial Mathematics 30
8. Institutes 31
9. Learned Society Activities 32
10. Collaborations 33
10.1 Manufacturing 33
10.2 Energy 33
10.3 Health and healthcare 34
10.4 Economic efficiency 34
11. Industrial Users 35
11.1 The range of interactions with industry 35
11.2 Strategies to enhance industrial connections 36
11.3 Issues in industrial connections 37
ii International Review of Mathematical Science Contents
12. The Need for Increased EPSRC–Community Connections 38
13. The Need for Diverse Funding Structures 39
14. Making Connections for the Mathematical Sciences 41
14.1 Multidisciplinary connections 41 14.1.1 Ensuring a substantive role for the mathematical sciences 41 14.1.2 Proposal review 41
14.2 Broadening connections via workshops 42
14.3 Assessing best practices 42
15. Structural Issues Specific to Statistics 43
15.1 Weakening of small statistics departments 43
15.2 Diminution of statistics as a separately recognised field 43
15.3 Strategies for strengthening statistics 44
16. Training and Nurturing the Next Generation 45
16.1 Students seeking undergraduate degrees in mathematics 45
16.2 Education and support of PhD students 45 16.2.1 Doctoral Training Accounts 45 16.2.2 Taught Course Centres and Centres for Doctoral Training 46 16.2.3 Funding of PhD students 46 16.2.4 A new kind of Master’s degree 47
16.3 PhD student concerns 47
16.4 Postdocs and junior faculty 47
16.5 Participation of women 48
17. International Connections 49
18. Annotated Evidence Framework 50
References 53
Annex A: Steering Committee 55
Annex B: Members of the International Panel – Brief Biographies 56
Annex C: Review Week Itinerary 63
Annex D: Supporting Evidence and Information Provided 64
International Review of Mathematical Science iii Executive Summary
An International Review of Mathematical Sciences today’s time of great change, understanding between research in the United Kingdom (UK) was conducted the mathematical sciences community and EPSRC is in early December 2010 by a panel of sixteen experts especially important. whose research interests span the range of the Engineering and Physical Sciences Research Council Mathematical sciences researchers participate actively (EPSRC) Mathematical Sciences Programme. The Panel in multidisciplinary collaborations involving important received extensive data from EPSRC before the review and complex problems and serve as valuable partners and gathered further information in six intense days for industry in addressing its long-term challenges. that included site visits at universities throughout Even so, better mechanisms are needed to encourage the country. Broadly framed, the Panel’s charge and strengthen the links between the mathematical was to assess UK mathematical sciences research in sciences, other disciplines and industry. comparison with the rest of the world and to respond to a list of related questions. The most worrying factor in education and training is that, to a large extent, UK PhDs are not competitive An overall finding is that actions taken by EPSRC since for academic positions in today’s global market. The the 2004 International Review of Mathematics and UK has been able to attract outstanding research the 2004 Review of Operational Research have greatly mathematicians from other countries, but the situation contributed to invigoration of mathematical sciences is fragile and needs continuing attention. research, including improved structures for PhD education. High-level recommendations of the Panel include: The backdrop for all of the Panel’s judgements includes several principles: the mathematical sciences provide • Preserving and strengthening the present a universal language for expressing abstractions excellence of the UK’s mathematical sciences in science, engineering, industry and medicine; research through a variety of funding programmes mathematical ideas, even the most theoretical, suited to the diversity and distributedness of the can be useful or enlightening in unexpected ways, mathematical sciences research community; sometimes several decades after their appearance; the • Creating a new structure for enhancing mathematical sciences play a central role in solving communication between EPSRC and the problems from every imaginable application domain; mathematical sciences community; and, because of the unity of the mathematical sciences, advances in every sub-area enrich the entire field. • Actions and strategies focused on individual subfields of the mathematical sciences; UK mathematical sciences research is world-leading in • An array of mechanisms to encourage and some fields, outstanding in many others and strong strengthen links within the mathematical sciences overall, although there are, of course, areas that could and between the mathematical sciences, other be strengthened. Two major factors that contribute disciplines and industry; and to the present excellence of the UK academic mathematical sciences enterprise are its diversity – • Continued action and attention directed toward in area, group size and size of institution – and its improving the quality of PhD training. geographically distributed nature. To preserve and increase the present level of quality, it is essential for A complete list of findings and recommendations is research funding structures to honour this diversity. In given in Section 2.
iv International Review of Mathematical Science Table of Acronyms
AHRC Arts and Humanities Research Council BBSRC Biotechnology and Biological Sciences Research Council BIS Department for Business, Innovation and Skills (established 2009, formerly DIUS and BERR) CAF Career Acceleration Fellowship (an EPSRC scheme) CASE Collaborative Awards in Science and Engineering CDT Centre for Doctoral Training DTA/DTG Doctoral Training Account/Grant EPSRC Engineering and Physical Sciences Research Council ESRC Economic and Social Research Council EU European Union FTE Full-Time Equivalent ICMS International Centre for Mathematical Science INI Isaac Newton Institute IRM International Review of Mathematics KTN Knowledge Transfer Network LMS London Mathematical Society MRC Medical Research Council NERC Natural Environment Research Council NSF National Science Foundation (US counterpart to UK Research Councils) OECD Organisation for Economic Co-operation and Development OR Operational Research PDRA Postdoctoral Research Assistant RA Research Assistant RAE Research Assessment Exercise RCUK Research Councils United Kingdom or Research Councils UK SFRA Scottish Financial Risk Academy STFC Science and Technology Facilities Council (created 2007 by merger of PPARC and CCLRC) TCC Taught Course Centre TSB Technology Strategy Board WIMCS Wales Institute of Mathematical and Computational Sciences
International Review of Mathematical Science v Acknowledgements
Panel members are grateful to the Steering Committee during the site visits were uniformly of high quality, for their excellent reparatory work that led to a obviously requiring substantial preparation, and the well-structured, albeit busy, schedule. The Panel Panel’s frank and lively discussions with members also offers enormous thanks to the EPSRC staff of the mathematical sciences community were very involved in managing the review, and to the other enlightening. The Panel expresses particular gratitude Research Council staff who assisted and provided to collaborators and users who spent their valuable information throughout the review process. The Panel time informing the Panel about their connections with is particularly grateful for the tireless efforts of EPSRC the mathematical sciences. PhD students, postdocs staff to ensure that members of the Panel were in the and junior faculty members are due special thanks for right place at the right time; for their overall project providing helpful insights about their experiences and management and preparation, including distribution perspectives. The Panel also appreciates members of of documentation for the review; and for their the mathematical sciences community and a variety organisation of what would have been first-rate travel of organisations who responded to EPSRC’s call for arrangements if the UK transport system and weather consultation responses. had cooperated. All of these elements contributed to a (pleasantly) memorable experience and the success of Finally, the Panel is especially thankful to members of the review. the mathematical sciences community who prepared the ‘landscape documents’ summarising the state of The Panel is deeply appreciative of the time and each subfield. These documents were extraordinarily effort expended by the participants in the site visits, valuable in providing background and context for the especially those who travelled long distances under Panel. adverse weather conditions. The presentations made
vi International Review of Mathematical Science Foreword
This is a challenging time for science, when the UK seeks to extend both its international reputation for cutting edge fundamental research and its economic and social impact. This is the second International Review of Mathematical Sciences and reflects the important contribution of the area to the UK. This contribution, which arises from advances in fundamental knowledge and understanding of mathematics and the mathematical sciences, has a direct impact on areas as disparate as security, telecommunications, finance, industry, transport and medicine. Mathematical Sciences research underpins a wide range of activities that benefit society, including engineering, economics and computer science. Just as technology plays an increasingly vital part in virtually every aspect of modern society, mathematical sciences research continues to be indispensable.
The preparation for this review has been under way for over a year and we would like to thank our colleagues on the Steering Committee, which included representation from the Edinburgh Mathematical Society, Industrial Mathematics KTN, Institute of Mathematics and its Applications, Institute of Physics, London Mathematical Society, Operational Research Society and the Royal Statistical Society. We also thank our Research Council colleagues who also supported and helped to guide the review. Specific thanks must go to the EPSRC staff for their unwavering support and hard work which enabled the Panel to do its work so effectively.
This report, the culmination of the whole review process, is entirely the work of the International Review Panel to whom we are very grateful - their expertise, teamwork, enthusiasm and capacity for sheer hard work impressed all those who came into contact with them. To Professor Margaret Wright, Chair of the International Review Panel, we are hugely indebted; her commitment and leadership were vital to both the review and the completion of this report.
We also warmly thank all those in the academic research community, together with their collaborators in industry and elsewhere who are so vital to the health of UK Mathematical Sciences research, for rising to the challenges and opportunities that this review presented. We are especially grateful to those who coordinated and participated in each visit, often travelling some distance to meet the Panel in what were often difficult weather conditions, and being able quickly to organise video conferencing when the weather made it impossible to travel. The close working with the community meant that the Panel was able to interact with a great many researchers and to witness a wider range of exciting advances than would otherwise have been possible in the short time available.
We hope that this report will stimulate further debate around the findings and recommendations highlighted and we genuinely welcome feedback on any issues raised. Comments should be sent to the Mathematical Sciences International Review team at [email protected].
Professor David Delpy Professor Tim Pedley Chief Executive, EPSRC Steering Committee Chair
International Review of Mathematical Science vii 1. Introduction and Background
Figures shown in square brackets [ ] refer to references which are listed at the end of the report
1.1 Purpose and scope of the review 3. Comment on progress since the 2004 Reviews of The Engineering and Physical Sciences Research Mathematics and Operational Research (including Council (EPSRC) holds regular international reviews comment on any changed factors affecting the to inform itself and the community (including recommendations); and stakeholders, industrial bodies, learned societies, 4. Present findings and recommendations to the UK academia and government departments) about the research community and Research Councils. quality and impact of the science base in the United Kingdom (UK) compared to the rest of the world and The review focused mainly on research and training in to highlight any gaps or missed opportunities. Each UK academic institutions, but also considered international review provides a broad perspective collaborations and users outside academia. Other on the research activity in a particular discipline in EPSRC international reviews were addressed when the UK, and is undertaken with the relevant learned relevant. Although most of the covered activity falls institutions and other research councils as appropriate; within EPSRC’s remit, the review also encompassed it has been a rolling programme in which the research areas such as mathematics embedded within base in each discipline is reviewed approximately every environmental research (in NERC’s remit); mathematical five years. Twelve reviews have been conducted since biology (in BBSRC’s remit); biomedical informatics, 1999. statistical genetics and computational biomedicine (in MRC’s remit); and mathematical physics (in STFC’s This report presents the conclusions of an international remit). panel of sixteen experts convened by a Steering Committee on behalf of all UK Research Councils 1.2 Structure of the review to review mathematical sciences research in the UK. The review was commissioned and managed by The scope of the present review covers the entire EPSRC and guided by a Steering Committee (listed in mathematical sciences portfolio of the Research Annex A) chaired by Professor Tim Pedley, University Councils, including all of mathematics, statistics of Cambridge. After receiving nominations from and the more mathematical aspects of operational the community, this Steering Committee selected research (OR). This collection of areas represents a the Panel Chair, Professor Margaret Wright, Silver broadening of the scope of the 2004 International Professor of Computer Science and Mathematics in Review of Mathematics [13] in that OR was the the Courant Institute of Mathematical Sciences, New subject of a separate review [21] in 2004; the present York University, USA to take on this role for the review. panel therefore specifically includes researchers with In concert with the Chair, the Steering Committee expertise in operational research and related fields. selected the other fifteen members, all based outside the UK. Panel members represented a balanced mix The broad tasks to be addressed by the Panel – its of international researchers with expertise spanning Terms of Reference1 – are: the mathematical sciences and relevant Research 1. Assess the quality of the UK research base in Council disciplines. The names and affiliations of Panel mathematical sciences in comparison with the rest members are given in Annex B, which also contains of the world; brief academic biographies.
2. Assess the impact of the research base activities in In concert with the Chair, the Steering Committee mathematical sciences internationally and on other accomplished the following tasks: agreeing on the disciplines nationally, on wealth creation and quality of life; 1 See www.epsrc.ac.uk/research/intrevs/2010maths/Pages/scope.aspx
1 International Review of Mathematical Science Introduction and Background
high-level questions to be addressed by the Review findings and recommendations, with cross-references Panel (the Evidence Framework; see Section 18); to sections in the report. agreeing on the institutions to be visited by the Panel; advising on the background data to be provided to 1.3 Review Panel activities the Panel; agreeing on the agenda for the review During the week starting Sunday, 5 December 2010, period; receiving a preliminary briefing from the Panel the full Panel convened at Heathrow, UK, for a at the end of the review period; and facilitating the preliminary assessment of the quality and impact of disposition and use of this final report. Throughout, academic mathematical sciences research in the UK. EPSRC provided support for the organisation, planning After the briefing meeting on Sunday, the Panel divided and logistics. into three sub-panels for ‘site visits’, with each sub- panel visiting a separate set of venues during the The eight areas of the Evidence Framework assessment ensuing Monday to Wednesday for an intense period of (given in full, with annotations, in Section 18) address review. During the site visits, the sub-panels interacted the following questions: with researchers from 42 institutions that receive A. What is the standing on a global scale of the UK mathematical sciences funding, holding separate mathematical sciences research community both meetings at each site with collaborators (academic and in terms of research quality and the profile of industrial) and with early career researchers. During researchers? each site visit, EPSRC colleagues were not present during a block of time, typically 30 minutes, in which B. What evidence is there to indicate the existence panel members continued their discussions with site of creativity and adventure in UK mathematical visit participants; the Panel and EPSRC representatives sciences research? agreed, in advance, on this format. C. To what extent are the best UK-based researchers The full Panel reassembled in London on the morning in the mathematical sciences engaged in of Thursday 9 December for a meeting with industrial collaborations with world-leading researchers based ‘users’ of mathematical sciences research, and then in other countries? moved outside London to discuss and develop D. Is the UK mathematical sciences community actively preliminary findings and recommendations. engaging in new research opportunities to address key technological/societal challenges? Throughout the week, panel members considered the eight areas of the evidence assessment framework and E. Is the mathematical sciences research base also added additional topics as appropriate. EPSRC interacting with other disciplines and participating provided an overview of research in mathematical in multidisciplinary research? sciences in the UK in terms of its people, funding, F. What is the level of interaction between the organisation and policy; further details about these research base and industry? data are given in Section 1.5.1.
G. How is the UK mathematical sciences research In closed meetings on 9 and 10 December, the Panel activity benefiting the UK economy and global reached a common understanding about the context, competitiveness? vision and opportunities afforded by the Mathematical Sciences Programme; made judgements on strengths H. How successful is the UK in attracting and and weaknesses of the programme to date; and developing talented mathematical sciences developed recommendations related to research researchers? How well are they nurtured and excellence, knowledge exchange, people and research supported at each stage of their career? infrastructure, in accordance with the Panel’s terms The framework was used extensively by the Panel in of reference (see Section 1.1) and to ‘help inform the the review process, although these questions are not a development of future strategies by EPSRC and other 2 template for the organisation of the report. Responses key stakeholders’. to framework questions are embedded in the report. This report is the Panel’s final product, developed from In addition, for the reader’s convenience Section 18 further analysis and refinement of findings following contains the questions in the Evidence Framework, from the evidence available to the Panel (Section 1.5). annotated with report section numbers that address each question. Section 2 summarises the Panel’s 2 www.epsrc.ac.uk/research/intrevs/2010maths/Pages/more.aspx.
International Review of Mathematical Science 2 Introduction and Background
1.4 Relevant external events and discussions at the sites visited by the Panel (see A report on research typically does not describe the Sections 1.3 and 1.5.2); and the extensive and varied political context in which it occurred, but a short scientific and professional expertise of panel members discussion is warranted by the unusual circumstances (see Section 1.5.2). during and shortly after this review. The relevant context is that a new UK coalition government, which 1.5.1 Data used by the Panel took office on 12 May 2010, announced plans on The Panel was provided with a hefty document, 21 October for an ‘austerity budget’ in which most of Information for the Panel, which contained the Research Councils escaped the deepest cuts. information, data and commentary to supplement the information acquired in site visits. Evidence in On 9 December 2010, when the Panel was in London this document was compiled from the Research to meet industrial users of the mathematical sciences, Councils’ management records, the Higher Education Parliament voted to adopt the recommendations Statistics Agency and Thomson Reuters. The document of the ‘Browne Review’, officially titled ‘Securing a contained 85 pages of evidence prepared by EPSRC, Sustainable Future for Higher Education in England’ 95 pages of ‘Landscape Documents’ and 206 pages [10]. Student demonstrations with some violence of ‘consultation responses’ to EPSRC’s call for public occurred in London to protest against a substantial comment on the Evidence Framework. increase to the upper limit on fees for undergraduate education (the Panel left London before the main Selected bibliometric data from Thomson Reuters were protests began). The Panel is therefore aware of a included in the evidence prepared by EPSRC, along high level of concern at many universities about how with appropriate cautions as to the interpretation of implementation of the Browne report’s ‘consumer this information (the mathematical sciences community preference’ model, in which student willingness to pay is, to a large degree, highly aware of the dangers is likely to guide the courses offered by universities, in over-reliance on ‘impact factors’ and ‘citation will affect undergraduate education in mathematical indices’, based on a 2008 report [3] prepared by sciences and, consequently, research as well as three international organisations in the mathematical preparation for graduate education. sciences).
The Panel heard repeatedly that severe recent Each landscape document covers UK research in a visa/work permit restrictions for non-EU citizens, specific subfield, providing an overview of activity imposed by the Government in November 2010, in the area, relevant data collected during the most are jeopardising new research appointments, recent (2008) Research Assessment Exercise (RAE) collaborations, visitors and PhD student intake. [20], and (most usefully) commentary on strengths, weaknesses and opportunities. The landscape It was apparent to Panel members that these factors documents were prepared by small groups of UK had caused great anxiety among the researchers, PhD researchers and vetted with their colleagues. Because students and postdocs whom we met during our site these documents will be made public after publication visits. of the present Panel’s report, they have, perhaps inevitably, the flavour of ‘laundry lists’, including lists A final element of the external context is that the of names, locations and research areas, mentioning EPSRC Delivery Plan for 2011-2015 [6] was published primarily generic rather than specific strengths, on 20 December 2010. The chart on page 21 of weaknesses and concerns. that plan shows that EPSRC’s planned expenditure in 2014/2015, measured in real terms, represents a There was a noticeable degree of agreement among 3% decrease in programme expenditure and a 50% the many opinions in the consultation responses to the decrease in capital expenditure compared to 2010/11. Evidence Framework.
1.5 Evidence used by the Panel Each panel member received a folder of ‘case studies’. These included a series of press releases, titled The evidence used by the Panel in agreeing on its ‘Mathematics Matters’ and written for a general findings and recommendations (Section 2) includes audience, that describe how the mathematical three elements: the data described in Section sciences have contributed to the solution of real-world 1.5.1; information gathered from presentations problems.
3 International Review of Mathematical Science Introduction and Background
The data provided for use by the International Review Section 5 reviews subfields of the mathematical was published on the EPSRC website on completion of sciences in some detail, providing the Panel’s the review (documentation provided in confidence was assessment of strengths and points of concern; Section not published). The Panel requested some additional 6 does the same for application areas that are tightly information from EPSRC during the review week. connected to the mathematical sciences. Section 7 describes the UK’s research capability in the imprecisely The Panel acknowledges three papers produced by the defined but crucial area of industrial mathematics. London Mathematical Society [16]: on the relationship between research and teaching, UK government Sections 8 and 9 comment on the importance of funding for mathematical sciences research and institutes and learned societies in the quality and doctoral training in the UK. visibility of UK mathematical sciences research.
The data listed above will not, for the most part, be Multidisciplinary collaborations constituted a major cited explicitly in this report. For the record, the Panel focus of the questions posed to the Panel. At every affirms that they formed an important foundation for site visit, the Panel met research collaborators; Section our discussions and conclusions. 10 describes several multidisciplinary interactions that were presented at those meetings. 1.5.2 Evidence provided by site visits and panel members’ expertise Section 11 reports on the many topics touched upon During the site visits, panel members heard from a at the Panel’s session with industrial users, including broad cross section of the mathematical sciences comments about how to improve connections with community (as noted in Section 1.3, each site visit industry. contained sessions that included only panel members and site visit participants). Hence panel members Based on the site visits and the Panel’s own impressions, acquired, while in the UK for the review week, a Section 12 makes a strong recommendation for a new substantial amount of information from mathematical mechanism to enhance communication between sciences community members about their views and EPSRC and the mathematical sciences community. experiences related to research excellence, knowledge exchange, people and research infrastructure. Research excellence is necessarily related to funding and support. The crucial role of diversity in the high All panel members were chosen in part for their quality of the UK’s mathematical sciences research experience and knowledge of mathematical sciences is the theme of Section 13, which stresses that research policy in their home countries, to provide the preserving and strengthening excellence implies the international perspective needed for this review. These need for funding structures that honour diversity. experiences and knowledge appropriately informed the Panel’s discussions as well as its findings and Section 14 discusses various ways for improving recommendations. connections between the community, academic colleagues in other areas and industry. 1.6 Overview of the Panel’s report Like the 2004 International Review of Mathematics The main body of the report begins with Section 2, [13], this Panel devotes a section of its report (Section which lists the Panel’s findings and recommendations 15) to special concerns about structural fragility in UK along with a subfield-by-subfield list of the Panel’s statistics research. views on challenges and opportunities in those subfields. Section 16 addresses issues concerning undergraduate students, PhD students, postdocs and early career As background for the remainder of the report, researchers. One of the questions posed to the Panel Section 3 describes key elements that characterise the involves gender diversity, which is explicitly discussed in mathematical sciences. Section 4 explains why panel Section 16.5. members view ‘diversity’ as a defining and essential feature of the UK mathematical sciences research Finally, Section 17 considers the extent of community. collaborations of UK mathematical scientists with leading international researchers.
International Review of Mathematical Science 4 Introduction and Background
1.7 On names of individuals and lists of 1.8 The International Panel institutions The panel members and their home institution or This report does not intend, nor does it attempt, to company are shown in Table 1. Brief biographies of the assess or rank individual researchers or institutions. panel members are found in Annex B. Individuals are named only when their standing or contribution is unique. Lists of institutions are alphabetical, with no implied ranking.
Table 1: Composition of International Review Panel
Title Organisation Professor Margaret Wright (Chair) New York University, USA Professor Anthony Davison École Polytechnique Fédérale, Switzerland Professor Stephen Fienberg Carnegie Mellon University, USA Professor Andrew Granville University of Montreal, Canada Professor Peter Hall University of Melbourne, Australia Professor Gary Horowitz University of California, Santa Barbara, USA Professor Patrick Huerre Le Laboratoire d’Hydrodynamique de l’École Polytechnique (LadHyX), France Professor Willi Jäger University of Heidelberg, Germany Professor Zhi-Ming Ma Institute of Applied Mathematics, Beijing, China Professor Robert MacPherson Institute of Advanced Study, USA Professor Dusa McDuff Columbia University, USA Professor Stefan Müller University of Bonn, Germany Professor Cheryl Praeger University of Western Australia, Australia Professor David Ryan University of Auckland, New Zealand Professor Andreas Schuppert RWTH Aachen University, Germany Professor Ruth Williams University of California, San Diego, USA
Left to right: Peter Hall, Willi Jäger, David Ryan, Robert MacPherson, Cheryl Praeger, Stefan Müller, Anthony Davison, Margaret Wright, Dusa McDuff, Gary Horowitz, Stephen Fienberg, Patrick Huerre, Ruth Williams, Andreas Schuppert, Andrew Granville and Zhi-Ming Ma.
5 International Review of Mathematical Science 2. Findings and Recommendations
For convenience, all of the Panel’s findings and light of the likely future funding environment. recommendations are contained in this section, with Section 12. cross-references to the parts of the report where they F-7. Despite improvements, many UK educated PhDs are discussed. in the mathematical sciences are not adequately trained to be competitive on the international 2.1 Findings academic job market; hence a large proportion F-1. Overall, mathematical sciences research in the of postdocs and junior faculty consists of UK is excellent on an international scale, with researchers trained outside the UK. Sections world-leading researchers in every subfield and 16.3 and 16.4. closely connected application area considered by the Panel. All subsections of Sections 5 and 6; F-8. Action about gender diversity is not a sufficiently Section 7. high priority for the UK mathematical sciences research community. Section 16.5. F-2. The high quality of UK mathematical sciences research depends critically on the diverse and 2.2 Broad recommendations distributed research community, where ‘diverse’ R-1. To research funders: To preserve and includes research area, group size and institution strengthen the international excellence of size, and ‘distributed’ refers to geographical mathematical sciences research (Finding F-1) location. Section 4. in light of Finding F-2 (the UK’s diverse and distributed research community), it is essential F-3. Actions taken by EPSRC since the 2004 to have flexible funding structures that support International Review of Mathematics and the excellent researchers wherever they are located, 2004 Review of Operational Research have and that encourage long-term interactions and greatly contributed to invigoration of the collaborations among excellent researchers mathematical sciences, including improved in diverse areas, in groups of diverse sizes, at structures for PhD education. Sections 5, 6 and geographically distributed institutions of all sizes. 16.2.2. Sections 4, 13, 15.2 and 16.2.2. F-4. Newly established institutes and centres R-2. To research funders, learned societies and dedicated to furthering research in specific the mathematical sciences community: topics, interdisciplinary research and Open, frank and timely communication connections with industry have improved the between EPSRC and the mathematical sciences UK’s international visibility and standing in the community is extremely important. In light of associated areas. Sections 5.2, 5.3, 5.5, 5.10, Finding F-6, the Panel strongly recommends the 5.11, 5.12, 5.13, 6.1, 6.3, 6.4, 7, 10 and 14. establishment, as soon as possible, of a new F-5. The institutes make a significant contribution structure for communication between EPSRC to the visibility and quality of UK mathematical and the mathematical sciences community. A sciences research, as do activities of the learned joint effort between EPSRC and leadership of societies. Sections 8 and 9. the learned societies is an obvious way to begin to define such a structure. Section 12. F-6. Communication between the mathematical sciences research community and EPSRC is less R-3. To research funders, institutes and learned open and clear than it should be, especially in societies, and the mathematical sciences community: Activities such as workshops,
International Review of Mathematical Science 6 Findings and Recommendations
possibly arranged by the institutes or learned from their technical knowledge and experience societies, should continue to be organised in in collaboration. Section 11.3. order to encourage and enhance connections R-8. To research funders: The review panels for within the mathematical sciences, with multidisciplinary proposals whose topics include academic colleagues in other areas and with the mathematical sciences should include industrial collaborators, and to involve the members with expertise in both multidisciplinary mathematical sciences community in proposed research and relevant areas of the mathematical or contemplated major research initiatives. sciences. Sections 14.1.1 and 14.1.2. Sections 3.2, 14.1.1 and 14.2. A separate panel is desirable for reviewing R-4. To research funders, universities and the proposals in operational research and statistics. mathematical sciences community: Strong Sections 14.1.2, 5.11 and 15.2. efforts should be made to ensure that UK PhD training meets the highest international R-9. To universities and research funders: In standards. This recommendation relies on the statistics, decisive action is needed to enhance provision of PhD student funding during an the ability of small departments to compete on adequate period of training. Section 16.3. the international level for new faculty. A more flexible grant structure such as the one proposed R-5. To universities, funders of PhD research and in Recommendation R-1 would help to address the mathematical sciences community: To this issue. Section 15.1. complement existing EPSRC programmes that support PhD education (such as Taught Course R-10. To universities: Strong statistics research and Centres and Centres for Doctoral Training), teaching programmes should be supported at a UK universities should consider establishing, large number of UK universities. Section 15.2. as a norm, a PhD programme that begins with a special one year research Master’s degree, R-11. To research funders, the mathematical followed by three years of PhD education and sciences community and universities: Urgent training. Sections 16.2.2 and 16.2.4. action should be taken to improve participation of women in the mathematical sciences R-6. To research funders, industry, universities community, with special reference to EPSRC’s and the mathematical sciences community: strategy for developing leaders. Section 16.5. In addition to existing programmes that connect industry and mathematical sciences research, R-12. To EPSRC: After enough time has passed, long-term collaborations focusing on basic EPSRC should assess and analyse the outcomes research driven by industrial challenges should of the variety of institutes and centres that be explicitly encouraged. These collaborations are intended to further multidisciplinary should include multi-year, close relationships and industrial collaborations involving the that involve academics and one or more mathematical sciences. Section 14.3. financially committed industrial partners, as 2.3 Field-specific recommendations - well as graduate education in the theory and challenges and opportunities methods needed to solve industrial problems. These recommendations represent field-specific Companies of all sizes should take full opportunities for universities, research funders and advantage of the Industrial Mathematics the mathematical sciences community to strengthen Knowledge Transfer Network. Larger companies the quality of UK mathematical sciences research. The should explore establishing long-term strategic ordering of the topics follows that in the main body of relationships with universities. Sections 11.2 and the report. 11.3. C-1. Algebra: Several outstanding young R-7. To universities, industry, the mathematical appointments provide an opportunity to sciences community and research funders: establish new vital research areas in an array of Arrangements should be explored to create sub-disciplines and to pursue synergies between appropriate roles within academia for experts them and beyond. Section 5.1. from industry so that universities can benefit
7 International Review of Mathematical Science Findings and Recommendations
C-2. Analysis: Despite progress since 2004, analysis in the UK is still under-represented compared to the rest of the world, with a notable shortage of home-grown talent; efforts to strengthen existing excellent groups in analysis of all sizes should accordingly be continued. Opportunities should be exploited for fruitful collaborations with other fields of the mathematical sciences and with applications. Section 5.2.
C-3. Combinatorics : Further improvements should be made to build and strengthen connections among discrete mathematics, combinatorics, theoretical computer science and related areas such as graph theory; this applies as well to number theory (C-9, below). Section 5.3.
C-4. Dynamical systems and complexity: Connections should continue to be developed with theoretical and applied analysis (Section 5.2), fluid mechanics (Section 5.5), computer science and a wide range of areas in science and engineering. Section 5.4. forms, including the Langlands programme. UK research in number theory should look C-5. Fluid mechanics: Joint projects with to build in important new directions, rather engineering and physics departments would be than reinforcing areas that are already well beneficial, as would recruitment of outstanding represented. Stronger connections are needed computational fluid dynamicists and numerical with computer science to develop work in analysts of partial differential equations. Section cryptography (as for combinatorics; C-3, above). 5.5. Section 5.9. C-6. Geometry and topology: A big challenge in C-10. Numerical analysis/scientific computing: geometry is exploring the relations of quantum Numerical analysis should become more closely field theory to geometry and number theory. The connected with computational science and part of geometry that most needs strengthening engineering. Optimisation researchers should in the UK is the connection between geometric develop closer ties with analysis, operational analysis and partial differential equations. research, probability and statistics. Section 5.10. Section 5.6. C-11. Operational research: Further strengthening C-7. Logic and foundations: This area should would be beneficial for research in simulation, continue its successful efforts to build risk, forecasting, revenue management, supply connections with fields such as computer chain problems, and applications in production, science and systems biology as well as other manufacturing, bioinformatics and data mining. parts of mathematics. Section 5.7. Closer links are encouraged with optimisation C-8. Mathematical physics: Since work in researchers in numerical analysis. Section 5.11. mathematical physics often falls between C-12. Probability: Because of likely retirements of traditional areas of mathematics and physics, prominent probabilists during the next few special attention should be paid to ensuring that years, attention needs to be paid to preserving excellent proposals in all areas of mathematical the UK’s excellence in the areas they represent. physics continue to be supported. Section 5.8. Due to emerging applications, support is needed C-9. Number theory: More links should be for in-depth engagement between highly developed with ergodic theory. There should trained probability researchers and first-class be more analytic and algebraic expertise scientists. Section 5.12. in all aspects of modular and automorphic
International Review of Mathematical Science 8 Findings and Recommendations
C-13. Statistics: For reasons discussed in detail in Section 15, measures are needed to avoid the loss of the UK’s high international stature in statistics; see Recommendations R-9 and R-10, above.
C-14. Computational science and engineering: Additional support is needed for collaborative computational science and engineering research, with research teams that include mathematical scientists in key roles. UK programmes should be integrated as much as possible with related international networks. Section 6.1.
C-15. Financial mathematics: The UK research field should continue its expansion into study of commodity markets, including resources like oil, gas, electric power and agricultural products. Section 6.2.
C-16. Materials: Mathematical research in materials science and solid mechanics remains under- represented in the UK compared to the rest of the world. Section 6.3.
C-17. Mathematical biology and medicine: More systematic integration of the mathematical sciences in the established systems biology centres would increase UK strength. With respect to funding, new ‘high-risk’ funding programmes for mathematical biology are desirable. It is perceived that progress is sometimes impeded by differences between the funding structures of Research Councils. Section 6.4.
9 International Review of Mathematical Science 3. Nature of the Mathematical Sciences
The mathematical sciences form an essential part of science, engineering, medicine, industry and technology and serve as one of the pillars of education at all levels. Major contributions to the health and prosperity of society arise from insights, results and algorithms created by the entire sweep of the mathematical sciences, ranging across the purest of the pure, theory inspired by applications, hands-on applications, statistics of every form and the blend of theory and practice embodied in operational research. Although the Panel’s charge focuses on research, an underlying message of this report is that mathematical sciences research is inextricably linked to both undergraduate and graduate education, including teaching university students in all disciplines the mathematical skills that are needed to function as informed citizens.
Every field of science and engineering is unique in some ways and the mathematical sciences are no exception. Some distinctive properties of the mathematical sciences are sketched next as a mathematical sciences, as discussed in several parts of foundation for the remainder of this report. Sections 5 and 6.
3.1 Unity Invoking the moral of Aesop’s Four Oxen and the Lion A long-standing practice has been to divide the [1], the Panel urges the UK mathematical sciences mathematical sciences into categories that are, community, relevant learned societies and government by implication, close to disjoint. Two of the most funding bodies to adopt ‘united we stand’ as the common distinctions are drawn between ‘pure’ and most appropriate perspective on mathematical ‘applied’ mathematics, and between ‘mathematics’ sciences research in the context of this review, where and ‘statistics’. These and other categories can be the features that unite the mathematical sciences useful to convey real differences in style, culture dominate those that divide them. Our discussion and methodology, but in the Panel’s view, they have (Sections 5 and 6) of separate subfields for purposes of produced an increasingly negative effect when the a more detailed assessment in no way contravenes this mathematical sciences are considered in the overall unified view. context of science and engineering, by stressing divisions rather than unifying principles. Furthermore, 3.2 Abstraction and long time scales such distinctions can create unnecessary barriers and Much of the content of mathematical sciences research tensions within the mathematical sciences community is expressed in terms of general relationships such as by absorbing energy that might be expended more equations, formulae and diagrams, which constitute productively. In fact, there are increasing overlaps and a universal language for expressing abstractions in beneficial interactions between different areas of the science, engineering, industry and medicine. Without
International Review of Mathematical Science 10 Nature of the Mathematical Sciences
the convenient forms provided by the mathematical Examples abound where: sciences, other disciplines might develop their own i. A mathematical idea initially viewed as purely specialised terminology for mathematical concepts, abstract turns out, much later, to be important in thereby inhibiting communication outside their field. real-world applications. A quintessential instance Happily, the same (or closely related) abstractions arises in tomography, a ubiquitous non-invasive can provide insights and intellectual tools for imaging technique that recovers the internal understanding and solving problems that seem structures of an object, such as the heart, from disparate when represented in their ‘natural’ form. For external measurements. The Radon transform, example, the mathematical ideas in modelling the flow published in 1917, provides the mathematical basis around swimming multicellular organisms might seem for recovering images from measured projection or far removed from designing the Internet or controlling scattering data [5]. congested traffic because experts in each area use a different vocabulary; see Figure 1. But underlying Much more recently, algebraic topology is being similarities, as well as differences, are often revealed applied to analyse complex data in a variety of through mathematical abstractions, which also serve to fields (including biology, imaging and neural translate fundamental concepts with different names science) that resist application of classical methods from one field to another. (see [4]).
Since mathematical results can be expressed, analysed ii. In all areas of the mathematical sciences, ideas from and verified in an abstract form independent of one subfield serve as the inspiration and foundation physical reality, the broad significance and multiple for major results in a seemingly different subfield. interpretations of some mathematical ideas are, in a For example, the 1960s ‘Langlands programme’ of real sense, everlasting, even when their importance conjectures in number theory led to the ‘geometric is not fully recognised until decades after their Langlands programme’ of conjectures in complex publication. A mathematical theorem remains true algebraic geometry, which were then shown to and a counterexample remains false, regardless of be related to quantum field theory (an important subsequent advances in technology or computing topic in mathematical physics). Very recently, as power; the passage of time does not make mentioned in Section 5.6, Ngô’s Fields Medal- mathematical ideas obsolete. winning work, which established the ‘Fundamental
Figure 1: Three real-world settings in which the underlying mathematical models are closely related. In the first figure, streamlines (red) and magnitude of velocity field (colour) are shown around a colony of multicellular green alga Volvox carteri swimming freely upward (image courtesy of K. Drescher, M. Polin, I. Tuval, and R.E. Goldstein, DAMTP, University of Cambridge). The second image depicts the structure of the Internet, and is a featured picture on the English language Wikipedia, shown under the Creative Commons Attribution 2.5 Generic Licence. The third picture, taken by Ian Britton, depicts congested traffic near Newcastle upon Tyne and is shown under the Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 Licence, reference number 41-17-74.
11 International Review of Mathematical Science Nature of the Mathematical Sciences
Lemma’ of the Langlands programme, relied on Across the spectrum of the field, the research of the Hitchin fibration (developed in the context of many mathematical scientists relies on computing, geometry and mathematical physics). which enables complex symbolic manipulation and formal verification of intricate hypotheses as well as iii. Algorithms once dismissed as unsuitable or number-crunching simulations, visualisations and unstable are shown to be efficient following the data mining. Mathematical scientists working in development of new insights or the availability computational science and engineering (Section 6.1) of new computer architectures. A well known typically require access to high end computing. Even instance in numerical linear algebra is the iteration mathematical scientists who work on their own and proposed in 1950 by Lanczos for eigenvalue use computers only to process email and search the problems [14], which, despite its welcome novelty, Web need financial support to attend conferences, visit provably suffered from a loss of orthogonality. Only colleagues and host visitors. in 1971 was it shown how this weakness could be overcome and variants of the Lanczos method pervade today’s state-of-the-art software for large- scale eigensystem computation.
It is essential to keep these unpredictable shifts in interpretation and applicability in mind when assessing the impact of the mathematical sciences on key technological/societal challenges (Question D in the Evidence Framework). The not-to-be-missed point is that the contributions of the mathematical sciences community should be considered as a whole. Although some researchers focus some of the time on addressing real-world challenges, other researchers devise remarkable insights and results that advance and strengthen the entire discipline by pursuing self- directed adventurous research.
3.3 Community structure and research needs A significant fraction of excellent research in the mathematical sciences is carried out by individuals or small groups of collaborators. But this property does not hold uniformly: some mathematical scientists regularly work, and do their best work, as part of a large, focused team. Using a description from the 2004 IRM [13], the mathematical sciences are ‘people- intensive’. Attempts to generalise at a finer level about the conduct of research within the entire community are almost certainly misleading.
Special care is needed when placing the mathematical sciences within the context of research funding in science and engineering. Although many mathematical sciences researchers have ‘modest’, or even ‘negligible’, equipment needs, especially compared with areas such as high-energy physics that require expensive, high-maintenance shared facilities, there are mathematical scientists - for example, in fluid mechanics or mathematical biology - whose research requires complicated equipment and ‘wet lab’ space.
International Review of Mathematical Science 12 4. Excellence and Capability through Diversity
A metaphor used at the initial presentation (10 The most recent (2008) UK Research Assessment December 2010) of the Panel’s findings was that the Exercise [20] identified world-leading, internationally mathematical sciences research strength of the UK recognised mathematical scientists at a wide variety of can usefully be interpreted by analogy with the UK’s institutions throughout the UK. An extensive official world-renowned greatness in theatre. The UK has, assessment thus confirms the existence of research without question, the best theatre in the world, and excellence and capability at an array of geographically this is universally explained by its deliberately diverse, distributed universities. geographically distributed nature. For example, a lively article in The Times on 15 July 2010 [22] attributes the During site visits, the three sub-panels consistently met success of UK theatre to ‘both culture and structure’ outstanding researchers at institutions of varying sizes and an ‘instinct to keep taking risks’ within an array located around the country; Sections 5 and 6 clearly of ‘beacons of excellence, …smaller fry punching well indicate the presence and productivity of first-rate above their weight, …and a host of provincial houses mathematical sciences researchers at geographically with local audiences’, where ‘every layer matters, distributed locations. Given the competitive global bringing joy in its own right and feeding talent to the academic job market, such researchers are likely to next’. leave their current institutions if there is significantly reduced support for their research, with unfortunate In the same way, the UK’s internationally excellent consequences because those researchers and, mathematical sciences research community is both indirectly, their institutions, play several essential roles diverse and distributed. Here ‘diverse’ has three that could not be maintained in their absence: meanings: (i) including a broad expanse of research areas, (ii) belonging to groups of varying sizes, and (iii) • In the past, graduate students, postdocs and junior representing institutions ranging from large to small. faculty at geographically distributed institutions ‘Distributed’ means that outstanding mathematical have become research leaders in the mathematical sciences research is done at geographically spread sciences. In particular, some of today’s luminaries institutions. In the Panel’s view, the UK’s excellence either did not receive their PhD from a university in mathematical sciences research is inseparable from usually described as ‘elite’, or else did not begin the diversity of its community in all three senses, as their faculty career at such an institution. The well as distributedness. Hence, it is essential to honour strategy of ‘Developing Leaders’ in EPSRC’s Delivery this diversity when defining the structures available Plan [6] refers to ‘world-leading individuals’, but for support of UK mathematical sciences research these individuals will not necessarily emerge from (recommendation R-1, Section 2). The Panel stresses one of a small number of universities. Without that this recommendation is fundamentally derived support for excellent researchers at a broad range of from the principle of supporting only internationally institutions, the Panel believes that there is a serious excellent research (repeated at the beginning of risk of irretrievably losing the talent of future world- Section 13). leading researchers in the mathematical sciences. • There appears to be an ample and growing The subsections of Section 3 detail why diversity is number of undergraduates in the UK who are crucial to excellence; the remainder of this section interested in studying the mathematical sciences explains the need to support outstanding researchers (see Table 5 in the first LMS position paper [16]). at geographically distributed institutions.
13 International Review of Mathematical Science Excellence and Capability through Diversity
If top mathematical sciences researchers were concentrated at only a small number of universities, undergraduates at other institutions would have less exposure to the interplay between high-level research and stimulating teaching that draws potential leaders into the field.
• Opportunities for close interaction with local industry will be lost if there are no, or very few, outstanding researchers at nearby universities, thereby foreclosing a crucial element in the contribution of mathematical sciences research to the UK’s economic prosperity and scientific/ technological strength.
Based on evidence gathered by its panel, the 2004 IRM report [13] made the same point: the UK’s capability and excellence in mathematical sciences research require a broad and deep field of excellent mathematical scientists, not only to produce outstanding research, but also to provide top-quality training across the UK for the next generation: 4]. An immediate consequence, stated explicitly in The UK cannot afford to concentrate its advanced Recommendation R-1, is the need for EPSRC’s research training in mathematics, which has to be maintained portfolio to include flexible funding structures that by the most up-to-date research, in a small number foster interactions and collaborations among excellent of highly competitive universities [13, page 31]. researchers at geographically distributed institutions of all sizes. A major ingredient in this Panel’s review is to make comparisons with the best research, and consequently the best research structures, in other countries. In this regard, one of the main conclusions in a 1997 US National Research Council report on international benchmarking of US mathematics [11] is that the continued attractiveness of the US to talented people rests in large part on ‘diversity and flexibility of the US research enterprise’:
Before World War II, only a handful of US research universities were distinguished in mathematics. ...Rather than being dominated by a few institutions or individuals, ... [today’s] diffuse structure allows a wide range of mathematicians from across the entire country, and their institutions, to excel [11, page 30].
In the Panel’s view, diversity and distributedness of the mathematical sciences research community are a necessary component of EPSRC’s goal to ‘create an environment that promotes excellence, encourages innovation, stimulates creativity and drives cultural, commercial and technological advances’ [6, page
International Review of Mathematical Science 14 5. Subfields of the Mathematical Sciences
Broadly speaking, this Panel found that mathematics in and Southampton, as well as flourishing links with the UK has been invigorated by measures undertaken topologists and geometers in places like Warwick. The responding to earlier reviews [13, 21] and the most UK continues as world leader in the area of profinite recent RAE [20]. In particular, the mathematical groups with, for example, proof of Serre’s conjecture sciences research base has been strengthened by by Nikolov and Segal on open subgroups of finitely outstanding new research appointments, often from generated profinite groups. The work in representation outside the UK, resulting in high international visibility theory is world-leading: since the 2004 IRM [13] there and connectivity. has been substantial growth in the strength and size of research groups in this area, especially at Scottish To answer Question A in the Evidence Framework, universities, with many new appointments of very high in this section and the next we discuss research in quality. individual subfields, where each assessment is based on data provided for the review, site visits and the Outstanding world-class work is done in finite group Panel’s own knowledge and opinions. The Panel has theory, with strong research groups in Aberdeen, chosen not to repeat the statistics and numerical data Birmingham, Imperial, Queen Mary and St Andrews, as that are available through the RAE [20] and in the well as high quality individual researchers throughout landscape documents (see Section 1.5.1). the UK. Major research programmes exploit and advance the theory of finite simple groups and their This section covers a selection of subfields of associated geometries. the mathematical sciences, listed in alphabetical order. Fields in which it is difficult to separate Excellent research at an international level is done the mathematical sciences and another area of also in asymptotic group theory, computational science or engineering are discussed in Section 6. algebra and non-commutative algebra. The group in Recommendations, challenges and opportunities for all St Andrews coordinates the computational discrete subfields are summarised in Section 2. algebra software system GAP3 (Groups, Algorithms, Programming). 5.1 Algebra Strong crossovers between algebra, combinatorics, Historically, the UK has led the world in the important number theory and algebraic geometry are evident field of algebra, from the 19th century work of giants in terms of problem inspiration, theory development like Cayley and Burnside to the 20th century seminal and applications. Impressive recent work, with algebraic applications by Fisher to statistics and the perhaps unanticipated impact internationally, involves design of scientific experiments. The requirements expansion in groups, spanning the boundaries of computational science and new communication between these sub-disciplines. The UK is a leader technologies, as well as from within mathematics in this area. The work has principal applications in itself, have led to a resurgence in activity in algebra. analytic number theory and expander graphs, showing Invitations to eight leading UK algebraists to lecture in particular that essentially all finite simple groups at the 2006 and 2010 International Congresses of give rise to expanders. Numerous other notable Mathematicians constitute a widely accepted mark of UK advances have arisen from fruitful interactions: prestige and high international standing. profinite groups and algebraic graph theory, group UK researchers in geometric group theory occupy a leading role in the world, with large groups in Oxford 3 www.gap-system.org/
15 International Review of Mathematical Science Subfields of the Mathematical Sciences
representations and zeta functions, geometric group Science and Innovation Awards established research theory and the structure of manifolds. centres in analysis: at Oxford on ‘Analysis of Nonlinear Partial Differential Equations’, and at Edinburgh In addition to already established research groups and Heriot-Watt on ‘Analysis and Nonlinear Partial in algebra, strong groups have grown recently Differential Equations’. The new Cambridge Centre (for example, at Aberdeen, East Anglia, Kent and for Doctoral Training in analysis will also train more Newcastle). Outstanding new appointments have been graduate students in this area. made, especially at Imperial, Oxford and Southampton. Added strength in analysis is attributable to the A challenge for mathematicians working in algebra UK’s successful attraction of a number of excellent is to realise the opportunities created by several researchers at both senior and junior levels. Today, outstanding young appointments, to establish new world-leading groups in analysis are located at vital research areas in the associated sub-disciplines Cambridge, Edinburgh, Oxford, Warwick and several and pursue synergies between them and beyond. smaller institutions. There is a cluster of excellent researchers in linear partial differential equations 5.2 Analysis and spectral theory in the London area and excellent Reflecting the unified view expressed in Section 3.1, groups in ergodic theory in Bristol and Warwick. this section covers the broad sweep of analysis from Since analysis is such a central subject, exceptionally pure theory to practical applications. important breakthroughs in analysis have also been Analysis plays a key role in the mathematical sciences, made by UK mathematicians whose main focus and first because of its deep connections to several other motivation lies in other areas. Ever since Atiyah’s subfields. For example, Perelman’s spectacular 2003 work, the profound contributions of geometers to proof of the Poincar´e conjecture emphasised the analysis have been recognised and valued. This great importance of analysis in topology and geometry, tradition continues with the work of Donaldson and the work of Green (Cambridge) and Tao on the (Imperial) and his school. A much more recent existence of arbitrarily long arithmetic progressions phenomenon is that work in additive combinatorics, is at the interface of number theory and harmonic led by UK mathematicians, has seen deep and analysis. In addition, analysis has long been, and important common themes developing in many remains, ubiquitous as an underpinning in the traditional analytic areas (harmonic and functional application of mathematics in science and engineering, analysis, ergodic theory, analytic number theory, in particular through the theory of ordinary and combinatorics and theoretical computer science), and partial differential equations. Knowledge of recent strongly influencing algebra and group theory through developments in analysis and of new analytical expanders. Although such unification of areas has concepts and methods is necessary for modelling been the most outstanding feature of the development real-world processes, characterising and computing of algebraic geometry and topology in the last fifty solutions to systems and describing fundamental years, this is new and exciting in analysis. There seems mathematical structures. no obvious end in sight to the revolution that such methods are causing and UK mathematicians should Analysis has always been strong in the UK in classical continue to be at the forefront of these developments. subfields and is at the leading edge of research in dynamical systems and ergodic theory, operator Analysis is a huge and extremely active field algebras, and operator theory. However, the 2004 worldwide, covering a wide spectrum of topics. The IRM [13] was concerned that UK research efforts were Panel therefore believes that, despite progress since ‘sparse and sporadic’ in ‘core areas of modern analysis 2004, analysis in the UK is still under-represented and related areas of partial differential equations’. compared to the rest of the world, with a notable The previous IRM report also noted that, because shortage of home-grown talent. The latter difficulty analysis is regarded as a difficult subject for a PhD, few may require attention to undergraduate teaching; prospective students chose that area of research. analysis is undoubtedly a demanding subject and may suffer if future undergraduate course offerings are The situation has noticeably changed since 2004, directly based on a philosophy of students as ‘course thanks to several EPSRC initiatives. In 2006, two consumers’ (see Section 1.4).
International Review of Mathematical Science 16 Subfields of the Mathematical Sciences
Efforts to strengthen existing excellent groups mathematics and the algorithmic side of theoretical in analysis of all sizes should be continued, and computer science (which is not as strong in the UK as opportunities should be exploited for fruitful elsewhere in the world). Thanks to EPSRC initiatives, collaborations between analysis and other fields of there has been improvement in connections between the mathematical sciences, most notably in geometry discrete mathematics and theoretical computer and topology, as well as in numerical analysis, science. The Centre for Discrete Mathematics and Its mathematical biology and medicine, materials science Applications5 (DIMAP) was established at Warwick and industrial mathematics. in 2007 by an EPSRC Science and Innovation Award, founded on a collaboration between the Department 5.3 Combinatorics and discrete of Computer Science, the Operational Research mathematics and Management Sciences group in the Warwick Business School, and the Warwick Mathematical In combinatorics, areas of strength at the time of the Institute. Nonetheless, the Panel believes that 2004 IRM [13], such as algebraic and probabilistic further improvements could be made to build and combinatorics, continue to flourish in the UK. As strengthen connections among discrete mathematics, well, many talented new appointments in this sub- combinatorics, theoretical computer science and discipline (often in computer science departments or related areas such as graph theory. business schools) have raised the international profile of UK research in combinatorics. In particular, there Another issue noted by the 2004 IRM was the is new internationally strong research in the areas of need to provide enough students with training in hypergraphs, extremal combinatorics and quantum combinatorics and discrete mathematics to industrial computation (Bristol); UK researchers remain world and government employers. For employers connected leaders in information security (Royal Holloway). with UK government intelligence, a supply of home-grown talent is obviously essential. The UK Discrete mathematics and combinatorics are inherently Government Communications Headquarters6 (GCHQ) cross-disciplinary and are routinely invigorated by seeks to hire a significant number of PhDs in the interactions with other areas. For example, the new mathematical sciences, but the Panel did not hear UK-led theory of synchronisation4 (Queen Mary, directly from a representative of GCHQ whether the University of London), inspired by the ‘celebrated’ situation has improved since 2004. The creation in Cˇerny´ conjecture from automata theory, impacts 2005 of the Heilbronn Institute of Mathematical on graph theory and permutation group theory; Research (see Section 8), as well as comments by the and combinatorial methods have been crucial for representative of the Defence Science Technology algorithms in computational biology. Moreover, the Laboratory7 at the users’ meeting (Section 11), indicate new UK-led developments in additive combinatorics that organisations with needs for highly trained people mentioned in Sections 5.1 and 5.6 also involve and in combinatorics are working hard to build connections energise combinatorics. A particularly interesting with UK universities. recent development was the solution of problems with a combinatorial flavour by a web-based team, initiated by Gowers (Cambridge). 5.4 Dynamical systems and complexity The 2004 IRM [13] described dynamical systems The fields of discrete mathematics and combinatorics and ergodic theory as ‘flourishing research areas have a strong tradition of interaction with industry, within the UK’. Although no member of the present representatives of which regularly attend the Panel is sufficiently expert in these areas to provide key biennial British Combinatorics Conferences. an authoritative international benchmarking, the Researchers in radio frequency allocation (City Panel confirms that there is a high-level of activity in University, London School of Economics, Oxford) dynamical systems and complexity. These fields are interact with the telecommunications industry; work strongly connected with numerous other subfields on statistical design theory (Queen Mary, University of the mathematical sciences, including analysis, of London) is essential to underpin the efficiency of scientific experiments. 4 www.maths.qmul.ac.uk/∼ pjc/LTCC-2010-intensive3 5 www2.warwick.ac.uk/fac/cross_fac/dimap The 2004 IRM [13] recommended that more 6 www.gchq.gov.uk. attention should be paid to research involving discrete 7 www.dstl.gov.uk.
17 International Review of Mathematical Science Subfields of the Mathematical Sciences
probability, mathematical physics, mathematical biology, industrial mathematics and mathematical finance. For example, ergodic theory is important in analysis (Section 5.2), and important work in fluid dynamics (Section 5.5) involving mathematical scientists and physicists is being done at the Manchester Centre for Nonlinear Dynamics.
The EPSRC Mathematical Sciences Programme has funded three multidisciplinary critical mass centres, each for approximately £1 million, in dynamical systems and complexity:
1. The Bath Institute for Complex Systems8 includes research on complex and multiphase materials (Section 6.3). The faculty who direct the institute’s themes come from the Departments of Mathematical Sciences, Mechanical Engineering and Electronic and Electrical Engineering;
2. The Bristol Centre for Applied Nonlinear Mathematics (BCANM),9 led by faculty from the Department of Engineering Mathematics, focuses on application areas in engineering and the life and ahead of Asian countries and of all other countries in social sciences; and Europe. This leadership rests not only on the excellence 3. The Interdisciplinary Programme in Cellular of the UK research in fluid dynamics but also on Regulation at Warwick10 includes faculty in the strong institutional vectors such as the Cambridge- mathematical sciences, biology and physics. based Journal of Fluid Mechanics. The Isaac Newton Institute and the International Centre for Mathematical Another example of EPSRC’s support for Sciences (see Section 8) also provide world-renowned dynamical systems and complexity is the Centre forums in the form of workshops for the international for Interdisciplinary Computational and Dynamical fluid dynamics community. Analysis11 (CICADA) at the University of Manchester, which encompasses research at the boundaries of There are many centres of excellence, including the mathematical sciences, computer science and Bristol, Cambridge, Imperial, Manchester, Nottingham, control engineering. The deliberately interdisciplinary Oxford, University College London (UCL) and Warwick composition of these centres visibly indicates their among others. The UK community is thus highly connections with research in engineering and in the diversified with excellent research in most of the main biological and physical sciences. sub-disciplines of fluid dynamics. UK researchers in fluid dynamics are masters at devising elegant quasi- Three EPSRC-funded centres for doctoral training analytical models that effectively capture the dominant (Section 16.2.2) are centred on complexity science: physical phenomena of a given flow configuration the Bristol Centre for Complexity Sciences12 (Bristol), without excessive formalism. They bring to bear on the founded in 2006; the Institute for Complex Systems discipline the full range of sophisticated mathematical Simulation13 (Southampton), launched in 2009; and methods and are the undisputed leaders in this type of the Complexity Science Doctoral Training Centre14 approach. (Warwick), founded in 2007.
8 www.bath.ac.uk/math-sci/BICS/index.html 5.5 Fluid mechanics 9 https://wikis.bris.ac.uk/display/ANMwiki/Home 10 The UK has a prestigious tradition in fluid mechanics, www2.warwick.ac.uk/fac/sci/systemsbiology/ipcr/. 11 www.cicada.manchester.ac.uk going back to Newton, with many twentieth century 12 bccs.bristol.ac.uk. giants such as Taylor, Batchelor and Lighthill. The UK 13 www.icss.soton.ac.uk remains a world leader in this field, behind the US, 14 www2.warwick.ac.uk/fac/cross_fac/comcom/dtcsite
International Review of Mathematical Science 18 Subfields of the Mathematical Sciences
The UK is world-leading in hydrodynamic stability (Section 5.10) should be strengthened. Other areas theory and transition, with recent landmark that could be strengthened include turbulence and investigations on a fundamental problem which had complex media. been poorly understood for a long time: the transition from a laminar state to fully turbulent flow in pipes. Fresh and insightful points of view at the interface with The UK is very strong in many diverse areas including aerospace and mechanical engineering, and with the astrophysical fluid dynamics, low Reynolds number macroscopic physics community, should be promoted hydrodynamics, interfacial phenomena, waves, vortex by fostering joint projects with engineering and physics flows, geophysical fluid dynamics, stratified and departments. Likewise, recruitment of outstanding rotating flows, and magnetohydrodynamics. computational fluid dynamicists and numerical analysts of partial differential equations is to be encouraged. It is significant that UK fluid dynamics research is Such developments are needed if the UK is to keep its not confined to mathematical sciences departments; pre-eminence in fluid dynamics in Europe. departments of engineering are also actively engaged. The Panel accordingly believes that UK 5.6 Geometry and topology research on both sides would benefit from joint The UK has been a world leader in geometry and research programmes in which (for example) topology for many years, and it continues that mathematical scientists would draw inspiration from tradition today. One indication of this status is that real configurations and validate predictions through four UK geometers/topologists gave invited talks at laboratory and numerical experiments. Such fruitful recent International Congresses of Mathematicians, interactions with engineers already take place in Wales while Donaldson (Imperial) has been the recipient of in the area of computational fluid dynamics. several prestigious international prizes (King Faisal, Nemmers and Shaw). Colleagues from the physics community have invigorated areas such as the dynamics of complex The past seven years have seen exceptional activity fluids (granular materials and non-Newtonian flows) and progress worldwide in geometry, with the solution and interfacial phenomena (bubbles and drops) by of the Poincar´e conjecture, finite generation of the relying on observations as the starting point for the canonical ring and solution of the Mumford and derivation of deceptively simple scaling laws. Such Kervaire invariant conjectures as particular highlights. a fresh point of view has proved to be particularly UK mathematicians were essential contributors to the successful. In contrast with the US and continental solutions of the second and third problems, which Europe, relatively few UK physicists have been involved lie in the areas of algebraic geometry and algebraic in fluid dynamics research. The Manchester Centre topology respectively. for Nonlinear Dynamics,15 which gathers applied mathematicians and physicists around a variety of There are also world-leading UK groups in mirror theoretical and experimental projects in nonlinear symmetry, moduli spaces, string topology, differential science, could serve as a model for enhancing these geometry, symplectic geometry and geometric group links. theory. There are very strong groups in many other parts of the subject such as surgery theory, integrable The 2004 IRM [13] recommended more active systems and low-dimensional topology. A notable development of computational fluid dynamics (CFD) recent phenomenon has been the rise of an excellent as a central means of investigation, on a par with group in geometry/topology distributed among the experiments and theory, because CFD has become London institutions. Although many of the other essential to investigate large Reynolds number leaders in this area work in main centres such as turbulent flows where wide ranges of length and Cambridge, Oxford and Warwick, this is not true timescales are dynamically relevant. Compared with in all cases; there are several smaller departments the US, the UK contribution to CFD still appears to (Aberdeen, for example) with world-class geometers/ be relatively modest. This research area could be topologists. more aggressively pursued by mathematical scientists without setting aside elegant asymptotic methods but One of the great strengths of UK geometry is its broad in conjunction with them. Hence the present Panel repeats the recommendation of the previous IRM that the interface between CFD and numerical analysis 15 www.mcnd.manchester.ac.uk.
19 International Review of Mathematical Science Subfields of the Mathematical Sciences
base. It combines ideas from numerous fields such since model theory has had some strong and as algebraic geometry, representation theory, string mutually reinforcing interactions with other areas of theory, topology and analysis and, in turn, its main mathematics in recent years. For example, there are results often have profound implications in these fields. important theorems in geometry whose proofs rely on As an example, the work by Hitchin (Oxford) on Higgs model theory. Indeed, some of these interactions have bundles and the geometry of the Hitchin fibration been the product of the work of UK mathematicians. played an important role in Ngˆo’s recent spectacular proof of the ‘Fundamental Lemma’ in the Langlands The size of the logic group in the UK is appropriate. programme that won a 2010 Fields Medal. Similarly, Logic is not as prominent on the international Donaldson and other members of his school have mathematical landscape, relative to other areas of made very significant contributions to the theory of mathematics, as it was 100 years ago. However, partial differential equations. New areas of the subject, several recent developments could cause it to such as geometric group theory, are of increasing increase in prominence and importance in the importance, building links to yet other areas such as future. For example, the advent of proofs that are dynamical systems. too complicated for any one person to referee could lead to new problems for logic. The UK logicians are Much of geometry and topology was initially unusually closely involved in interactions with other developed to understand questions arising in physics mathematicians and scientists, so the UK should be and astronomy, and its most significant applications well positioned to take a leadership role in future are still in those fields, for example string theory and applications of logic. the theory of relativity. However, now UK researchers are developing interesting applications in biology, for 5.8 Mathematical physics example the use of knot theory and three-dimensional The UK continues to have world-class research topology to study DNA/protein interactions or the programmes in several of the more mathematical study of the symmetries of the surfaces of viruses. areas of theoretical physics, including general relativity, There are also some applications in robotics. cosmology, string theory and quantum chaos. There is a very healthy interaction between these areas of A big challenge for geometry is to explore the relations theoretical physics and other areas of mathematics. of quantum field theory to geometry and number A few examples are: (1) physical arguments in string theory (e.g. mirror symmetry in geometry, Witten- theory have motivated new mathematical conjectures Kapustin in number theory). With its many brilliant and which algebraic geometers have later proved; (2) broadly trained geometers, the UK is very well placed physical questions in general relativity often require to contribute here. knowledge of the long time behaviour of solutions to nonlinear partial differential equations which people The part of geometry that needs most strengthening working in geometric analysis can sometimes provide; in the UK is the connection between geometric (3) string theory has recently provided a surprising analysis and partial differential equations. Since connection between general relativity and fluid Perelman’s solution of the Poincar´e conjecture dynamics; and (4) there are close interactions between using the Ricci flow, this approach to understanding researchers studying quantum chaos and number topological questions has become much more theory. important. Although the UK has one or two world- class mathematicians working in this area, it would Since the 2004 IRM [13], there have been several certainly benefit by having more. On the positive appointments of outstanding young researchers side, in the past few years the UK has attracted some (especially in Cambridge, Cardiff, Durham and brilliant young geometers from abroad; they should be Imperial) to continue the long-standing tradition of supported at a level that will encourage them to stay. excellence in these areas. Some of these appointments were in response to recent retirements, but others 5.7 Logic and foundations represent growth. Some of the more senior researchers The group in logic in the UK is small (35 researchers have won prestigious prizes. total) but excellent. The major areas of mathematical logic (model theory, proof theory, recursion theory A major concern for the future is the increasing and set theory) are all represented. Model theory is difficulty of obtaining financial support for research particularly strongly represented. This is felicitous, in mathematical physics that falls between traditional
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areas of mathematics and physics, and hence spans Many smaller excellent groups in number theory the remits of EPSRC and the Science and Technology are located at institutions throughout the UK and Facilities Council (STFC). EPSRC has recently refocused several of those include participants who have had support for mathematical physics on research where a large impact on the international stage. There it is judged that the primary focus is the development are significant strengths in most important areas of new mathematical knowledge or techniques of number theory, particularly in analytic number and, as a result, is recommending that proposals theory, higher dimensional arithmetic geometry (both outside this boundary should be submitted to STFC. geometric, as in obstructions to local-global principles, Especially in the present time of budget cuts, the Panel and quantitative), arithmetic geometry and algebraic recommends that EPSRC should work together with number theory, diophantine approximation, and STFC to ensure that top-quality proposals in all areas computational and algorithmic number theory. The of mathematical physics continue to be supported. The link with quantum chaos, via random matrix theory, UK’s excellence in research will certainly be threatened continues to be strong, and links with logic have if support disappears, even temporarily. become even stronger with some excellent recruitment (in both of these themes, UK researchers are world- 5.9 Number theory leading). The UK is the world leader in all aspects of the circle Some researchers are exploring the exciting method, in analytic number theory, in harmonic boundary between ergodic theory and diophantine analysis and in quantitative arithmetic geometry, led approximation (from the direction of Margulis/ by researchers at Cambridge, Bristol and Oxford. Lindenstrauss) and in modular and automorphic forms This includes some of the most exciting research (both analytic and algebraic), and the Panel would in analytic number theory worldwide (three of the like to see more work along these lines. Indeed much last six speakers at the International Congress of recent important number theory has taken place on Mathematicians in analytic number theory come from interdisciplinary boundaries, but, in the Panel’s view, this group in the UK). hiring has tended to focus on areas that are already very well represented rather than these new directions. Outstanding number theory research is being done at quite a few UK universities. Dynamic and Echoing a theme from Section 5.3 about discrete highly capable groups have emerged recently at mathematics, there is too much separation between Bristol, primarily younger researchers in analytic number-theoretic cryptographers in computer science and computational number theory, quantitative departments and interested number theorists in arithmetic geometry and ergodic theory; at the London mathematics departments. Efforts should be made by Universities, primarily younger researchers in a wide both communities to close this gap. array of subjects in arithmetic geometry; at Oxford, where there has long been a small, high-quality group. Although there is work in areas related to This group has been greatly enhanced very recently transcendental number theory, no specialists in the by several strong hires, including Sir Andrew Wiles (an subject are working in the UK at present. With the obviously world-leading figure). proximity of the strength in Paris, it would be good to see more interaction that might lead to more Cambridge has had a tradition of strength in development of this subject in the UK. arithmetic geometry in the last twenty years and many UK faculty received their training there. The internationally leading group in additive combinatorics 5.10 Numerical analysis/scientific at Cambridge has not only led a revolution in analytic computing number theory, but has been training excellent young As described in the 2004 IRM [13], the UK was a people with the potential for greatly strengthening UK pioneer in numerical analysis during the 1950s, combinatorics, analysis and number theory. when it was recognised that rigorous mathematical techniques were needed to understand the properties Recent work (led by UK researchers) in additive of algorithms implemented on computers. The dual combinatorics has had an important influence on name of this section arises because, in many parts group theory, ergodic theory and theoretical computer of the world, ‘numerical analysis’ is called ‘scientific science; the Panel hopes that future hiring in UK computing’. number theory might reflect these new directions.
21 International Review of Mathematical Science Subfields of the Mathematical Sciences
Numerical analysis in many areas, including but not limited to those that were strong in 2004 - linear algebra, multiscale and adaptive algorithms, ordinary and partial differential equations (especially stochastic) and numerical optimisation - remains at a very high international level in the UK, with world-leading individuals in several categories. UK researchers in numerical analysis have received significant international recognition, as confirmed by their list of honours, editorships and prestigious invited talks.
The selection of research topics in UK numerical analysis reflects the challenges seen as difficult in this area around the world, including problems involving multiple scales, complex systems, stochastic systems, high nonlinearity and sparse, high-dimensional data. A welcome and long-standing feature of UK numerical analysis research is its standard practice of producing general-purpose numerical software, which provides a highly efficient mechanism for knowledge transfer from research to practice.
The landscape document for numerical analysis 5.2) and fluid mechanics (Section 5.5), the Panel has provided to the Panel (Section 1.5.1) notes that, recommended a greater focus on computation, which based on the 2008 RAE data [20], the number of implies a complementary recommendation that UK active researchers in numerical analysis has noticeably numerical analysts should develop closer links with increased since 2001. In addition, there has been a those areas. welcome growth in scientific breadth and connections with other fields, especially science and engineering. 5.11 Operational research Nonetheless, the Panel believes that there should be In 2004, operational research (OR) received its a greater effort to encourage numerical analysis to own review [21]. The present review includes the become part of approaches labelled as ‘computational mathematical aspects of OR, which limits consideration science and engineering’ (Section 6.1). Such a push, of research activity to a relatively small number of if successful, would enhance the computational programmes of varying size and strength. The OR capabilities available to numerical analysts, as well landscape document provided to the Panel (Section as create added ties to key societal/technological 1.5.1) indicates clearly that other researchers in OR challenges. A related research theme, well-funded may well classify themselves in non-mathematical and actively pursued in several other countries, is the areas. development of innovative numerical methods that are provably reliable and efficient on changing computer OR is an interdisciplinary subject that arose after World architectures (as exemplified by the current widespread War II and was originally concerned with solving real- interest in multicore systems). Some steps along these world decision problems from military and industrial lines have been taken in the UK but more would be contexts. The scope of OR today is much more desirable. general, extending to numerous problems in science, engineering and medicine, and much of the subject Optimisation, which also appears in this report under overlaps, sometimes confusingly, with other areas. the heading of ‘operational research’ (Section 5.11), is OR methodologies range from conceptual problem seen internationally as a crucial part of problems at the structuring and formulation to mathematically and/ frontiers of science and engineering, which involve (for or computationally based methods, deterministic or example) emerging connections between optimisation stochastic. OR has always maintained a particularly and partial differential equations, probability, statistics strong practitioner base and a focus on applications; and discrete mathematics. For both analysis (Section the 2004 review of operational research commented
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‘[I]n no other country in the world is the orientation of UK work on hyper-heuristic methods is world-leading OR towards applications as strong as in the UK’ [21, and has had a significant international impact; these page 2]. methods address important mathematical problems from applications that cannot be solved today While traditional OR methods frequently have a by conventional exact techniques and are closely mathematical foundation, for historical reasons connected with computer science. the subject is located today in departments of management, business, industrial engineering, Much of the optimisation research in OR involves computer science and statistics, as well as applications to finance, data envelopment analysis, mathematics. In the UK the subject is most scheduling, multi-criteria decision-making and frequently represented in management and business decision-making under uncertainty, whereas departments, in contrast to the US where OR features optimisation on the international scene tends to be strongly in industrial engineering. Several OR-related viewed more broadly as an important approach to topics, such as probability, statistics and optimisation problems in the physical and biological sciences as well (both continuous and discrete) are considered in as engineering. An obvious suggestion, in the spirit of Sections 5.10, 5.12 and 5.13, emphasising the already- Section 3.1, is for optimisation researchers in OR and mentioned difficulty in assigning OR research to tidy numerical analysis to examine, together, the possible disjoint categories. connections between their separately developed approaches. As reported in the 2004 review of OR [21], at that time researchers in the field had achieved substantial Contributions in stochastic OR include simulation, progress in helping to solve important real-world risk, forecasting and revenue management, but these problems, but much of the community was pessimistic are not as strong and would benefit from further about the prospects for funding success. Since then, investment. In some cases the UK presence in these EPSRC has made significant investments to support areas depends on a small number of researchers and encourage foundational OR: who are approaching retirement. Strengthening is needed in research on supply chain problems and • DIMAP (Centre for Discrete Mathematics and Its applications in production and manufacturing; revenue Applications), mentioned earlier in Section 5.3, is a management, auctions pricing and market regulation; collaboration involving the Department of Computer and contributions to bioinformatics and data mining. Science, the Operational Research and Management Sciences group in the Warwick Business School, and Since OR is interdisciplinary by definition, researchers the Warwick Mathematical Institute; expressed concerns to the Panel about proposal • LANCS,16 a collaboration among Lancaster, evaluation (see Section 14.1.2). Nottingham, Cardiff and Southampton, was created by a Science and Innovation Award designed to 5.12 Probability strengthen foundational operational research; Probability is a diverse subject with research pursued • NATCOR17 (National Taught Course Centre in on both intrinsic foundations and applications. There Operational Research; see Section 16.2.2) was are many connections to other fields, as sophisticated established in 2006 as a collaboration among ten probabilistic methods are now pervasive and influential universities; through much of science and engineering, as well as other areas of mathematics. Research in the • STOR-i18 is a Centre for Doctoral Training (see fundamentals of probability and its applications is Section 16.2.2) in statistics and operational research, conducted at the highest international level in the UK. based at Lancaster University, with additional This is a historical UK strength and continues to have a funding from industry. vigorous community that includes a number of senior international leaders and a strong group of junior Today, UK researchers represent international researchers. There are extensive collaborations with the excellence in continuous, stochastic and combinatorial worldwide probability community. optimisation; some of this work overlaps with research in numerical analysis and probability. Especially 16 www.lancs-initiative.ac.uk. notable research includes creation of novel heuristic 17 www.natcor.ac.uk approaches in search and optimisation. In particular, 18 www.stor-i.lancs.ac.uk.
23 International Review of Mathematical Science Subfields of the Mathematical Sciences
The UK is one of the world leaders in stochastic analysis, including the topics of coagulation and fragmentation, rough path theory, stochastic differential geometry, stochastic partial differential equations, nonlinear filtering, Levy and Levy-type processes and numerical methods for stochastic equations. The UK is also an international leader in the study of probabilistic models related to mathematical physics and discrete probability including percolation, Markov chains, random graphs and random matrices. In applications of probability, the UK is an international leader in the analysis of probabilistic models for genetics, bioinformatics, communication and transportation networks, finance and epidemics.
While the UK probability community is strong in significant areas, a few very active areas worldwide such as stochastic Loewner evolution, random planar maps, Gaussian free fields, combinatorial optimisation and energy applications, are thinly represented.
Major examples of interdisciplinary activity occur in the interactions of probability, statistics and biology but should be beneficial for bringing probability PhD in genetics; probability, operational research and students in contact with researchers in related fields of computer science in the study of engineered networks; analysis, computational analysis and statistics. and probability, statistics, partial differential equations and numerical analysis in finance. There are many One area of concern is that the UK probability potential opportunities for further highly productive community is already experiencing retirements of some cross-disciplinary activities involving probability. In prominent probabilists and could experience more this domain, there is a need for support of in-depth before too long. Some excellent junior researchers engagement between highly trained probability have been appointed in recent years; however, quite researchers and first-class scientists. a few of these are from outside the UK and there are signs that some of these, as well as others in There is a strong demand for PhDs with knowledge mid-career, are being tempted by the availability of of probability from areas of application and industry. attractive ‘chairs’ in other countries. However, apparently (according to a rough estimate in the landscape documents provided to the Panel) 5.13 Statistics only about one-fourth of probability PhD students Statistics as a discipline, wherever it is found, is are from the UK, which is of potential concern. The rooted in research and ideas from the UK in the probability-focused residential weeks offered by the late nineteenth and early twentieth centuries. In Taught Course Centre NATCOR19 and by the probability the first part of the twentieth century the field was research centres at Bath, the Swansea node of the transformed when challenges from biology and Wales Institute of Mathematical and Computational agriculture stimulated insightful ideas with profound Sciences, and Warwick are important for enlarging implications from mathematicians at Rothamsted the base of PhDs with knowledge of probability and and University College London. Many innovations for exposing those specialising in probability to a wide in statistics still follow this pattern, whereby oncrete spectrum of probability topics that include those not questions arising in domains such as social science or well represented in the UK.
Two Centres for Doctoral Training20 – Mathematics and 19 21 See Sections 5.11 and 16.2.2. Statistics Centre for Doctoral Training at Warwick 20 See Section 16.2.2. 22 and Cambridge Centre for Analysis – have significant 21 www2.warwick.ac.uk/fac/sci/masdoc/. probability components. These are relatively new 22 www.maths.cam.ac.uk/postgrad/cca/.
International Review of Mathematical Science 24 Subfields of the Mathematical Sciences
medicine lead to the development of new statistical The 2004 IRM [13] gave separate consideration to methodology that can then be deployed much more the field of statistics because the UK’s international widely. Major UK contributions continue to the present position in research was seriously threatened then day; in the last forty years, new directions in both by structural and personnel issues (rather than by frequentist and Bayesian statistics have been pioneered gaps in research content per se). In response to by Cox and Lindley, figures of world stature. It is on these concerns, EPSRC took several major actions: these foundations, both early and more recent, that three Science and Innovation Awards were made in many of the UK strengths today are built. statistics at Bristol, Cambridge and Warwick; and three Taught Course Centres and two Centres for Areas in which UK statisticians are world-leading Doctoral Training,23 including elements of statistics, include Bayesian modelling, computational were established involving researchers from subsets statistics, spatial statistics, time series, the statistical of Aberdeen, Bath, Bristol, Cambridge, Dundee, study of shape, statistical methodology related to Edinburgh, Glasgow, Heriot-Watt, Lancaster, London, bioinformatics, multivariate and longitudinal data Nottingham, Oxford, Southampton, St Andrews, analysis, functional data analysis and extremal Strathclyde and Warwick. modelling. Research in these areas is an eclectic blend of theory, methods, computation and applications. Unfortunately, today the Panel finds once again that For example, recent contributions to Bayesian the UK statistics research enterprise is in a fragile modelling include novel computational algorithms, and weakened condition, despite all its areas of deep work on convergence properties, formulation excellence and the welcome measures taken during of new models for generic problems (especially those the intervening years to strengthen it. This worrying involving hierarchical structure) and applications to situation has arisen for several reasons, primarily fields ranging from engineering to economics, from structural, which are discussed in Section 15. medicine to machine learning, and from graphics to genomics.
A major feature of modern UK statistics is its strong motivation from, and enduring connection to, an extraordinary array of important applications in the sciences, industry, business and government. A sizeable part of this work, although not the whole, lies outside the area conventionally defined as the mathematical sciences. There are deep connections, however, between UK applied statistics and relatively theoretical contributions, particularly in areas such as methodology for dependent data, risk analysis and techniques for feature selection in high-dimensional data.
At the same time, the connections of modern statistics to mathematics remain strong and are growing. For example, both the theory and the methodology of functional data analysis rely on ideas and results from mathematical analysis. Even algebraic geometry, through its capacity for reducing complex relationships to properties of families of equations, and number theory, which in some statistical problems determines convergence rates of estimators, have important uses in statistics. Modern statistics has an ethos and foundation of its own, however, and statistical theory is today a large discipline in its own right, reaching out to other disciplines and finding new challenges from them. 23 See Section 16.2.2.
25 International Review of Mathematical Science 6. Applications Connected with the Mathematical Sciences
In this section we discuss, in alphabetical order, subfields in which the mathematical sciences are very closely connected with one or more disciplines in science, engineering or business. These topics are highly mathematical but their nature depends strongly on the application area. Industrial mathematics is considered in Section 7.
An essential common feature of these subfields is mathematical modelling, a process by which a real- world problem is represented in mathematical form. Mathematical modelling – a mixture of mathematics, science, engineering and art – inevitably involves an application-dependent combination of numerous mathematical areas. Mathematical expertise is needed to select the proper mathematical and computational approaches as well as the tools needed to satisfy sometimes ill-defined requirements. A thorough multidisciplinary understanding of a given application is also needed to understand the questions that the model is intended to answer. Further challenges in formulating and analysing mathematical models arise usage of ‘computational X’, where X can be any other both from fitting together advanced mathematical field. tools from heterogeneous disciplines and in developing novel mathematical theory as needed. The overall Modern computational and statistical methods are challenges are discussed in each subsection, along increasingly applied to areas such as archaeology, with Question E (multidisciplinary collaborations) in the architecture, art history and music that have previously Evidence Framework (Section 18) and for some areas been viewed as remote from computational science Question D (key societal/technological challenges). and engineering. Emerging areas like ‘Computational Humanities’ offer new challenges to several sub- 6.1 Computational science and disciplines of the mathematical sciences – for example, engineering in detecting novel patterns and concepts in historical, Throughout the world, ‘computational science musical, textual and artistic data.24 and engineering’ is interpreted as a tightly coupled multidisciplinary approach that combines research- A widely used definition of computational science level contributions from the mathematical sciences, and engineering includes all aspects of modelling computer science and one or more scientific and (formulation, analysis, calibration and validation) engineering disciplines. Unfortunate confusion along with computational methods, data analysis about this terminology arises for two reasons: its and numerical/symbolic simulation. Many researchers similarity with ‘scientific computing’, which is taken (but not all) regard high performance computing in many countries (including the US) as a synonym for ‘numerical analysis’ (see Section 5.10), and growing 24 staff.science.uva.nl/∼rens/CompHum2010.htm.
International Review of Mathematical Science 26 Applications Connected with the Mathematical Sciences
(HPC) as an essential part of computational science of stochastic analysis. A welcome development is that and engineering because of the close integration of the UK research field is being enlarged from purely hardware, software and numerical algorithms. financial products and markets to commodity markets, including resources like oil, gas, electric power and The 2004 IRM noted a concern that after pioneering agricultural products. In actuarial mathematics, which UK activities in the 1960s ‘the scale of activity [in applies insights and techniques from mathematical computational science and engineering] is small sciences research to assess risk in insurance, finance compared to its scientific importance’ [13, page 25]. and medicine (among other areas), the UK continues Thanks to EPSRC, progress has been made in recent as a world leader. This subject is becoming increasingly years toward supporting research in mathematical intertwined with financial mathematics through the sciences focused on advancing computational topics of insurance and risk management. science and engineering. In particular, a large Science and Innovation Award, ‘Numerical Algorithms and Two recently-founded innovative institutes in financial Software for the Evolving HPC Platform’, was made mathematics are discussed elsewhere in this report. in mid-2009 to a consortium of Edinburgh, Heriot- The Oxford-Man Institute (see Section 11.2) is Watt and Strathclyde. EPSRC has also supported entirely funded by industry; the Scottish Financial development of a ‘roadmap’ in high performance Risk Academy (see Section 10.4) is a consortium of numerical algorithms (involving Manchester, Oxford, academia and industry. The programmes of both Rutherford Appleton Laboratory and University College institutes will, the Panel believes, provide valuable London), to identify research areas for the next five information about ‘best practices’ in multidisciplinary years; further related programmes are ongoing or work and industrial collaborations (Section 14.3). planned. Several companies with interests in financial Because these activities are very recent, it is too mathematics were represented at the users’ meeting; early to assess their national or international their views related to Question F are discussed in impact. Nonetheless, the present Panel, like our Section 11. 2004 predecessor, believes that EPSRC should provide additional support and encouragement for 6.3 Materials science and engineering collaborative computational science and engineering New materials are often the driver of new research, subject to the requirement that research technologies. In the past, better materials have mostly teams must include mathematical scientists, preferably been found by experimentation, characterisation as co-principal investigators (see Section 14.1.1). and incremental improvement, sometimes guided In addition, UK programmes in this area should by empirical laws or simple continuum theories. be integrated as much as possible with related Dramatically increased computational capabilities and international networks. added insights about the fundamental mathematical equations on all levels offer the prospect of a much 6.2 Financial mathematics more systematic route to the discovery of new As a consequence of financial and economic crises materials. Key ingredients are a better understanding in recent years, quantitative methods for assisting of N-body quantum mechanics and its upscaling decision processes in these fields are in great demand. to relevant length scales, and of the role of The relatively new label of ‘financial mathematics’ microstructures (on a large variety of scales from applies to an inherently interdisciplinary subject atomistic to macroscopic) and their impact on the that contains extremely challenging problems and overall material behaviour. interfaces with econometrics, probability, statistics, partial differential equations and numerical analysis. In the application of new mathematical ideas to Because of the generality of the mathematical sciences materials science, the UK has a world-class group (see Section 3.2), progress in financial mathematics is in Oxford, with very significant contributions from a likely to lead to tools that can be applied to problems number of other institutions including Bath, Bristol, from other domains such as systems of stochastic Cambridge, Glasgow, Manchester, Nottingham and differential equations. Warwick.
The UK is among the world leaders in financial The 2004 IRM [13] described the UK as ‘not a player’ mathematics, with particular strength in applications in the key area of multiscale modelling. This situation
27 International Review of Mathematical Science Applications Connected with the Mathematical Sciences
has noticeably improved, partly due to EPSRC’s awards of Multidisciplinary Critical Mass Awards25 to the Bath Institute for Complex Systems (a collaboration between the departments of mathematical sciences and mechanical engineering) and the Oxford research programme in New Frontiers in the Mathematics of Solids. Nonetheless, mathematical research in materials science and solid mechanics is still largely under- represented in the UK, especially compared to the traditionally strong representation of fluid mechanics (Section 5.5).
6.4 Mathematical biology and medicine Connections between the mathematical sciences and life sciences arise in multiple ways and are rapidly expanding worldwide, with spectacular growth since the 2004 IRM [13]. Mathematical methods, computational simulation and statistical/quantitative analysis are essential components in life sciences research. Biomedicine has become internationally recognised as an area of research with potential for strong growth, driven by national and industrial metabolic modelling, is complemented by advanced priorities. approaches in network biology and virtual physiology modelling. Mathematical research groups cooperate It is impractical to make an exhaustive list of associated effectively with biology and medicine and the UK roles of the mathematical sciences, especially since publication track record in high-ranked journals is these are expected to continue increasing into the excellent. foreseeable future. A few examples (among many more) are: to improve understanding of cell processes, UK research in biomechanics, in particular biological cell interactions and formation of biological structures; fluid mechanics, is very strong and benefits from to automate and improve medical diagnosis; and to a long tradition of seminal work. Several major design and control therapeutic measures. In general, centres have recently been established, outstanding processes in biological systems are complex, which researchers have been newly appointed and, as a means that the derived models are typically nonlinear, result, the field has undergone rapid growth. This multiscale, often hybrid, discrete-continuous, involving discipline is certainly more active than in countries of high-dimensional dynamical systems. similar size in continental Europe. Although the influx of researchers at the interface between fluid dynamics UK excellence in mathematical biology (in which we and the biological sciences is not as massive as in the include mathematical medicine) is based on a long US, UK biomedical fluid mechanics is in a healthy and tradition, pursuing aims and concepts that now define vibrant state. A wide variety of topics are covered, systems biology and synthetic biology. The Centre over a large range of scales: blood flow in vessels for Mathematical Biology26 in Oxford, founded in and arteries, numerical simulations of flow in the 1983, acted as an important catalyst for a remarkable heart, pulmonary flows, cell biomechanics, collective development of this discipline. Excellent research dynamics of cells, mixing and transport in bacterial groups are distributed across the UK, located in a populations, and bioconvection phenomena. variety of universities and departments. Interdisciplinary biomathematics projects are often The research focus in the UK is broad, ranging from led by mathematical sciences researchers, who are medical applications (e.g. electrophysiology for supported in various ways from pharmaceutical and heart modelling) and strong biometry up to ‘hot’ areas such as biomarkers, genomics, proteomics and stem cell research. This position in established areas 25 www.epsrc.ac.uk/about/progs/maths/Pages/multi.aspx. of computational biology, including statistics and 26 www.maths.ox.ac.uk/groups/mathematical-biology.
International Review of Mathematical Science 28 Applications Connected with the Mathematical Sciences
biotechnology companies (AstraZeneca, Glaxo Smith Kline, Pfizer) and agrochemical companies (Syngenta), which have made significant, long-term investments in UK universities, including mathematics and statistics.
Although pharmaceutical companies tend to outsource off-the-shelf work to countries with lower salary levels, there are increasing needs for PhDs with substantial knowledge of the mathematical sciences. As we note in Section 16, because students produced by the UK’s traditional 3 + 3 model often have unacceptably narrow training, these companies tend to recruit outside the UK.
Mathematics is already well integrated into some existing systems biology centres but UK strength in mathematical biology would be increased if this integration were more systematic. Separate Research Councils administer grants and funding in biology, and the Panel’s site visits indicate a widespread perception that in medicine and the mathematical sciences funding structures are often hampered by conflicting remits and criteria of EPSRC and BBSRC, leading to workarounds by researchers that consume time and energy better devoted to research. It may be helpful to have specific ‘high-risk’ funding programmes for mathematical biology.
29 International Review of Mathematical Science 7. Industrial Mathematics
The primary focus of this Section is industrial An especially notable instance of an organisation that mathematics as an area of research capability links mathematical sciences research and industry (additional commentary on the interactions of is the Industrial Mathematics Knowledge Transfer mathematical sciences researchers with industrial Networkr27 (KTN), principally funded by the Technology users is given in Sections 11 and 14.2). Industrial Strategy Board with additional contributions from mathematics is treated separately from the topics of EPSRC, which has been highly effective in fostering Section 6 because industrial applications can, and industrial-academic partnerships. do, include literally every area of the mathematical sciences. In this regard, the Panel chooses to follow EPSRC has created several valuable programmes to the definition of ‘industry’ from a 2008 OECD connect mathematical sciences research and industry.28 report [19]: EPSRC also makes industrial Collaborative Awards in Science and Engineering (CASE) awards to fund The term industry . . . [is] broadly interpreted as any PhD studentships in which projects are arranged activity of economic or social value, regardless of between industry and an academic partner. The CASE whether it is in the public or private sector. awards, which serve as enabling tools for students to learn about industrial workflows and approaches to Industrial mathematics could be described in a problems, were highly praised at the Panel’s meeting lighthearted vein as ‘multidisciplinary squared’, in with industrial users (Section 11) and by PhD students that it typically includes more than one area of the who had received these awards (Section 16.3). mathematical sciences as well as more than one area of science and engineering, plus complex constraints The Panel is impressed by these important activities. (often imprecise and shifting) imposed by the business However, based on the Panel’s meeting with environment. industrial users, it is clear that the two-way transfer of knowledge could be further improved; see Sections 11 The UK is widely recognised to have had, for a long and 14.2. time, pioneering and innovative activities in industrial mathematics, based on a consistent view of industry as an important source of inspiration, reputation and funding. Institutions whose purpose is to further industrial mathematics have been founded by universities, industry and government; special activities have been introduced to enhance the transfer of knowledge and personnel. For example, Oxford Study Group workshops began more than 30 years ago to bring together academic and industrial researchers to work on problems defined by participating industries. 27 A Knowledge Transfer Network is a national network in a field of Many UK activities related to industrial mathematics technology or business application, intended to stimulate innovation today are imbedded in international cooperation, through knowledge transfer. The Industrial Mathematics KTN, e.g. within the European Consortium in Industrial managed by the Smith Institute for Industrial Mathematics and System Engineering, identifies and develops collaborative projects Mathematics. Here, the UK is providing important through programme delivery and partnership engagements that nodes in an international network in industrial create strategic collaborations. See https://ktn.innovateuk.org/web/ mathematics, influencing global development in this mathsktn. field. 28 www.epsrc.ac.uk/funding/business/schemes.
International Review of Mathematical Science 30 8. Institutes
The name of this section may be ambiguous because A further admirable property of the institutes is that the term ‘Mathematical Institute’ is applied at some their structures are sufficiently flexible to include UK universities to denote what might elsewhere be activities related to fast-breaking ‘hot’ topics at short called the ‘Mathematics Department’. Adding to the notice. confusion, there are ‘institutes’ and ‘centres’ of varying sizes and research directions in the mathematical The Panel makes two recommendations (R-3 and R-11, sciences throughout the UK. Section 2) for new roles for the institutes: creating connections within and outside the mathematical In this section we briefly discuss four mathematical sciences (Section 14.2), and encouraging women to sciences institutes that provided information during participate in mathematical sciences research (Section the Panel’s site visits: the International Centre for 16.5). Mathematical Sciences (ICMS), Edinburgh, created in 1990; the Isaac Newton Institute (INI), Cambridge, founded in 1992; the Wales Institute of Mathematical and Computational Sciences (WIMCS), established in 2006; and the Heilbronn Institute for Mathematical Research, established at Bristol in 2005. Both ICMS and INI are funded in (large) part by EPSRC. WIMCS was set up by the Welsh Assembly Government through the Higher Education Funding Council for Wales, and the Heilbronn Institute is a partnership between Bristol University and the UK Government Communications Headquarters (mentioned in Section 5.3).
Panel members were impressed by the range and excellence of activities organised and supported by these institutes. Several panel members had previously attended programmes at one or more of these institutes (most often at INI or ICMS) and hence had first-hand knowledge of their quality.
Top international researchers routinely form a part of institute workshops and programmes which means that the institutes make a substantial contribution to the international visibility of UK mathematical sciences research. Because distinguished international visitors very often spend time at other UK universities when they attend institute programmes, the benefits of these programmes include enhanced opportunities for UK collaborations with world-leading researchers from other countries.
31 International Review of Mathematical Science 9. Learned Society Activities
The Panel would be remiss if this report failed to out an in-depth investigation of a research topic and to mention the contributions to quality and capability learn about new and evolving links between different of UK mathematical sciences research made by the subfields of the mathematical sciences and other areas. six learned societies who nominated members of the Steering Committee – the Edinburgh Mathematical In the Panel’s opinion, these activities of the learned Society, the Institute of Mathematics and its societies strengthen the excellence of UK mathematical Applications, the Institute of Physics, the London sciences research. As with the institutes (Section 8), Mathematical Society (LMS), the Operational Research because eminent international researchers participate Society and the Royal Statistical Society (see Annex A). in some of these events, opportunities for international and multidisciplinary collaborations, as well as the UK’s Each of these organisations conducts a full programme visibility worldwide, are greatly enhanced. The Panel’s of activities for researchers in its particular area recommendations R-3 and R-11 (Section 2) involve of specialisation including conferences, symposia, potential roles for the learned societies to increase workshops and public lectures. For example, the connections within and outside the mathematical EPSRC/LMS Durham Symposia, established in 1974, sciences (Section 14.2), and to improve participation of provide a venue that allows invited researchers to carry women (Section 16.5).
International Review of Mathematical Science 32 10. Collaborations
Several questions in the Evidence Framework – The EPSRC staff who were present during the Questions D (key challenges), E (multidisciplinary sessions with collaborators could confirm the Panel’s research), F (interactions with industry) and G comments relevant to Question E-1, including the (economic benefits) – involve, in various ways, requested evidence. As described in Section 1.5.1, connections between the mathematical sciences, EPSRC provided the Panel with additional evidence in other science and engineering disciplines, medicine the form of interesting ‘case studies’, each of which and industry, as well as connections among sub- illustrates a multidisciplinary collaboration. disciplines of the mathematical sciences. Unfortunately, the answers do not separate neatly according to 10.1 Manufacturing the labelling of the questions. The Panel’s responses The Inkjet Research Centre29 carries out research accordingly appear in several sections of the report, into the foundational science for inkjet technology, starting with this one, which focuses on the outcomes with collaborating academics from Aberystwyth, of the Panel’s meetings with ‘collaborators’ at site Cambridge, Durham, Leeds and Newcastle as well visits. as industry partners CDT, Domino, FFEI, Inca, Linx, Sericol and Sunjet. The collaborator who described this As part of each site visit a selection of collaborators, work stated that new mathematical modelling was typically a mixture of academics and people from essential for understanding fluid flow at high rates industry, had been invited to participate in a session and drop/surface interaction, and that the prestige about multidisciplinary interactions. The format of of the affiliated mathematical sciences researchers these meetings was that each collaborator made brief was a key ingredient in attracting collaborators. This remarks about the nature of his/her collaboration (the centre, in the Panel’s view, is an excellent example of fields involved, the role of the mathematical sciences how mathematical sciences research benefits the UK and the nature of the results) and then answered economy (Question G-1), as is the spin-out company questions from the sub-panel. A general discussion mentioned in Section 10.4. followed with the sub-panel and all collaborators. 10.2 Energy As part of the Panel’s response to Questions D (especially D-1) and E-1 in the Evidence Framework, The Grantham Institute for Climate Change (Imperial) the remainder of this section highlights collaborations embodies interdisciplinary research that drives ‘the described during the site visits that are explicitly fundamental technological transformation needed addressing key challenges mentioned in the EPSRC to tackle climate change’. A key element in one of Delivery Plan [6], as well as improving the efficiency its research themes, sustainable futures,30 involves of the UK economy and global competitiveness. Only among other topics, mathematical analysis of different a small selection of these collaborations is presented energy generating and energy saving technologies, here, each representing a concrete instance of the along with the role of network technologies. An kinds of innovation that result from mathematical associated project uses a mathematical model based sciences research. A much more extended list could on fluid mechanics to predict the characteristics of a be provided if additional evidence (requested as ‘night purge’ (driving out accumulated warm air) that part of Question E-1) is desirable. Some of the is intended to reduce the energy needed for daytime broad challenges in increasing and enhancing cooling of buildings. multidisciplinary collaborations, including those with industry, are addressed in Section 14 to address 29 www.ifm.eng.cam.ac.uk/pp/inkjet/default.html. Question D-3. 30 www3.imperial.ac.uk/climatechange/research/sustainablefutures.
33 International Review of Mathematical Science Collaborations
10.3 Health and healthcare Researchers in the Infectious Diseases Consortium31 in the Cambridge Veterinary School are studying the dynamics at the heart of infectious diseases, which involve multiscale mathematical modelling as well as more traditional epidemiological approaches. While presenting this work, one of the collaborators stated that this area has been ‘completely transformed’ because of the insights gained from the mathematical sciences, including a ‘culture of precision’. This comment was echoed by the representative of a large biomedical research company during the Thursday morning meeting with industrial users (Section 11).
In Wales, an ambitious initiative32 has recently been announced to create a health modelling centre whose goal is to improve the quality and efficiency of healthcare by bringing together research in medicine, computational modelling, operations research, stochastic analysis, nonlinear partial differential equations, image processing and high performance computing.
10.4 Economic efficiency The Scottish Financial Risk Academy33 (SFRA), established in 2010, is a consortium of academia and industry, where the latter includes Aberdeen Asset Management, Barrie and Hibbert, and Lloyds Banking Group. Creation of SFRA was motivated by a recognition of the complexity of financial risks and the consequent importance to Scotland of connecting financial services with advanced mathematical modelling. A major part of SFRA’s activities involves knowledge exchange activities to improve interactions between mathematical sciences research and the financial services industry, such as a series of invitational ‘Risk Colloquia’.
At the operational level, efficient techniques for cutting and laying out materials such as glass, fabric and sheet or precious metal are important in many industries. Operational research experts at Nottingham who investigate cutting and packing have produced automatic algorithms that increase manufacturing efficiency by devising greatly improved layouts, thereby reducing cost and waste. Keeping Question G-2 in mind, the Panel notes that this research led to creation 34 of a spin-out company, Aptia Solutions, that has 31 www.vet.cam.ac.uk/cidc/. developed associated software products and services. 32 www.walesinternationalconsortium.com/news/N10_Model_ healthcareu.shtml. 33 www.sfra.ac.uk. 34 www.aptiasolutions.com/People.aspx.
International Review of Mathematical Science 34 11. Industrial Users
Because of the importance of connections between relation to Question G-1 of the Evidence Framework) the mathematical sciences and industry, the Panel that education is a large, albeit indirect, benefit of spent the morning of 9 December 2010 with sixteen mathematical sciences researchers to the UK economy. industrial (non-academic) ‘users’ from a variety of companies and agencies. These users individually Among the users who met with the Panel, there described the technical nature of connections between seemed to be no doubt about the importance, real mathematical sciences research and their companies, and potential, of the mathematical sciences as a and then offered commentary about how to improve key element in industrial applications, and the Panel relationships between industry and the mathematical heard numerous success stories from a wide variety sciences. The presenters were questioned by the Panel of areas. Of course, these particular users were in during and immediately after their presentations. some sense ‘self-selected’ in that they were willing Following a general discussion among all participants, to spend company time to meet with the Panel, but there were further opportunities at a sandwich lunch even so the Panel came away with a strong feeling for small-group conversations and follow-up. that mathematical sciences research is appreciated by and relevant to a significant cross section of UK The thoughts of the assembled users about the industry. One participant stated forcefully that “a relationship between industry and mathematical big mathematics push needs to happen in the long sciences research are covered in two places: the term”; another, representing a company that has remainder of this section and in Section 14 (for traditionally emphasised engineering, said, “moving ideas that apply in general to multidisciplinary forward, mathematics will be more important than collaborations). engineering”.
For completeness and to respond to Question G-1, 11.1 The range of interactions with the following varied and impressive list, in alphabetical industry order, includes the mathematical sciences topics It is common place to assert that there is an inherent that were mentioned as important to industry: mismatch between the long time scales of academic applied mathematics, combinatorics, computational research (see Section 3.2) and the immediate needs of mathematics, control, cryptography, data analysis, fluid industry. Based on the variations in length and content mechanics, geometry, mathematical modelling, of interactions described at the users’ meeting, this multiscale and risk modelling, networks, number view may be exaggerated. Although mathematical theory, numerical analysis, operational research, scientists seldom offer an immediate solution to optimisation, probability theory, risk assessment, industrial problems, a few users mentioned that this statistics, stochastic analysis and uncertainty kind of quick interaction can indeed happen, and is quantification. extremely gratifying when it does. For instance, one industrial participant cited, with a smile, an EPSRC/LMS In addition to considering collaborations with industry, Durham workshop at which a mathematician in the several participants mentioned the vital contribution audience exclaimed, during an industry presentation, of the mathematical sciences at UK universities to “you really don’t want to do it like that”. An obvious educating numerate citizens in all fields who can implication is that industry can receive high value from intelligently cope with the technological challenges structured short-term interactions with mathematical of modern society. This point is not directly related to scientists; hence it is reasonable to ask industry to the Panel’s charge, but it confirms the Panel’s view (in make an appropriate financial commitment to support
35 International Review of Mathematical Science Industrial Users
such activities, especially given the very large fees typically charged by external consultants.
In the most interesting cases, however, participants consistently observed that industry does not, and should not, expect its day-to-day needs to be addressed by a short conversation with a mathematical scientist. As one participant flatly stated, it“ is unreasonable for industry to expect academics to do industry’s job”.
A strong message from these users was that, almost by definition, any healthy industrial sector has long- term needs for transformative technologies and paradigm-changing processes. To address these needs, long-term collaborations with mathematical sciences research should be encouraged, preferably with involvement of mathematical scientists from the beginning. The policy of early inclusion of mathematical scientists was a major benefit from existence in the past of industrial and government research laboratories. It is widely felt that ‘many of these labs have decayed into near oblivion, and for multi-year research collaborations as well as pre- are becoming relics of the past’ [17], and that competitive academic-industry consortia. For example, opportunities for fundamental, adventurous research projects could focus on ‘quantum leap’ innovations at the few remaining labs are severely constrained. requiring new mathematical sciences research, not Industry and government must therefore turn to application of known techniques to a new problem. universities for genuine partnerships, not as consumers These efforts could involve one or more industrial who want to ‘buy mathematics’ on order. partners that should be required to demonstrate commitment by investing their own resources, plus 11.2 Strategies to enhance industrial public funding for at least one academic partner. connections A different approach is provided by the Oxford-Man As already mentioned in Section 7, several structures Institute of Quantitative Finance,35 established in exist for encouraging and creating collaborations 2007 and funded entirely by the Man Group.36 The between industry and mathematical sciences research. institute is academically independent, with associated The Panel hopes that the mathematical sciences faculty from economics, engineering science, statistics, community and industrial collaborators will develop mathematics, computing, business and law. Executives an increased awareness of these opportunities, for from the Man Group are seconded to a co-located example through workshops of the kind described in laboratory in order to pursue their own research Section 14.2. projects in quantitative finance. Examples of other structures requiring a financial commitment from Based on the informative session with users, the Panel industry that have been mentioned elsewhere in this concluded that even more encouragement is needed report are the Inkjet Research Centre (Section 10.1) for establishing fundamental research collaborations and the Scottish Financial Risk Academy (Section 10.4). driven by broad classes of industrial problems rather Certainly the track records of these organisations will than by the more frequent case studies of the past. be helpful in any future EPSRC evaluation of ‘best Recognising that CASE awards (Section 7) are likely to practices’ in academic-industry interactions (Section be too short and tightly focused for joint development 14.3). of transformative mathematical sciences research, it would be desirable for EPSRC to create mechanisms
35 www.oxford-man.ox.ac.uk. 36 www.mangroupplc.com.
International Review of Mathematical Science 36 Industrial Users
11.3 Issues in industrial connections Question F-1 asks about the movement of trained Despite the positive views of industrial users who people between industry and the research base, and met with the Panel about connections with the vice versa. The Panel heard that successful PhD or mathematical sciences, several impediments, some postdoctoral internships often lead to a ‘real job’ more serious than others, were discussed. in industry and there are visible examples of the movement of researchers from academia into industry With respect to graduate education, numerous users or government positions. In the other direction, in expressed a concern noted by the 2004 IRM [13]: much of the world (including the UK) the reduced UK PhD students are too narrowly educated and this number of industrial and government research issue is likely to become more pressing as globalisation laboratories means that people from industry may increases (see Section 16.2). Deep knowledge of well be unable to meet today’s academic standards for a research area in the mathematical sciences is publication. A positive development about which the essential but, since the problems faced by industry are Panel heard was that, in some instances, highly placed constantly changing, flexibility and adaptability are executives, engineers and scientists from industry equally important in the long run. have joined universities as ‘honorary faculty’ to teach courses, advise students and lead workshops. Such The Panel also heard about the inevitable difficulties arrangements, which appear to be mutually beneficial, in communication between experts in different fields, deserve further consideration on a national scale; see in particular the need to learn ‘new disciplinary Recommendation R-7. languages and culture’ [9, page 65]. One participant from industry commented that, in addition to misunderstandings caused by incompatible terminology, some researchers in the mathematical sciences, at all levels, struggle when faced with a poorly posed problem.
To reduce these difficulties for mathematical sciences researchers who are interested in involvement in multidisciplinary or industrial research, elsewhere in this report the Panel recommends (see Recommendation R-3 and the discussion in Section 14.2) institute or learned society workshops specifically designed to familiarise participants with multidisciplinary modes of operation. For PhD students who wish to work in industry (or to participate at some point in multidisciplinary research), training and experience in problem solving should play a key role in the offerings of Taught Course Centres and Centres for Doctoral Training (Section 16.2.2).
Participants from several larger companies described their established and growing programmes to build long-term strategic relationships with universities, including formal mechanisms for sponsoring PhD students, hiring interns, supporting faculty chairs and consulting with academics. Since programmes of this magnitude are not feasible for smaller companies, the Industrial Mathematics Knowledge Transfer Network was mentioned as having helped to make a variety of connections (see Section 7).
37 International Review of Mathematical Science 12. The Need for Increased EPSRC–Community Connections
This Panel consists of researchers, all of whom work This Panel is reluctant to suggest too many details, but outside the UK, who came together for one week (and urges consideration of the following general principles: have since exchanged many email messages) to do an arguably impossible task. Panel members are grateful • There should be some continuity to provide to EPSRC for placing confidence in their opinions, but institutional memory, allowing members to ‘learn it is far more important – indeed, it is essential – for the ropes’ while avoiding a self-perpetuating and EPSRC and the UK mathematical sciences community potentially self-serving body; to have a high-level of trust and confidence in each • There should be explicit opportunities for discussion other. of a wide range of topics affecting the mathematical sciences community. Ideally, EPSRC could ‘float’ The Panel is aware of the existence and valuable ideas that are being considered and representatives contributions of the EPSRC Mathematical Sciences of the community could comment on these ideas Strategic Advisory Team,37 as well as the regular before firm decisions are made. Examples of such meetings between the EPSRC Mathematical Sciences decisions are the nature of new calls for proposals Programme Team and the Council for Mathematical and selection of proposal review panels. The Panel Sciences (CMS).38 Unfortunately, numerous strongly understands that, because certain government worded comments made during the site visits clearly information is embargoed, EPSRC might be unable indicated to the Panel that, despite these structures, to reveal exact plans to the community group. there is, in the words of the 2009 International Review of Chemistry [2] a ‘tense environment for communication’, and that
It is precisely under such circumstances... that government and academia need to redouble their efforts to sustain open and clear communication. This communication is not one way but instead must engage both sides [2, page 33].
The present Panel similarly believes that an additional structure for regular conversations between EPSRC and the mathematical sciences community would be helpful in several ways – in particular, by complementing existing channels of communication and allowing a broader dialogue to inform the community and increase its comfort level. The Panel therefore strongly recommends (Recommendation R-2, Section 2) creation of a new structure, designed together by EPSRC and the mathematical sciences 37 www.epsrc.ac.uk/about/governance/sats. 38 research community, that will allow communication, The CMS contains representatives and observers from the mathematical sciences community and from the Edinburgh in advance rather than after the fact, about the most Mathematical Society, the Institute for Mathematics and its effective structures for funding, the nature of initiatives Applications, the London Mathematical Society, the Operational and other key issues. We regard this as an essential Research Society and the Royal Statistical Society. See www.cms. recommendation. ac.uk/activities.html.
International Review of Mathematical Science 38 13. The Need for Diverse Funding Structures
This section presents the Panel’s recommendations inappropriate for many leading researchers in the about funding structures and strategies, which rest on mathematical sciences, and was definitely not a recipe three consistent premises: for encouraging creative and adventurous research. The remainder of this section expands on that point. 1. Only internationally excellent research should be supported by EPSRC and other Research Councils; The enormous benefits to UK mathematical sciences research of diversity in research area, location and 2. It is reasonable and desirable for EPSRC and other institution have already been explained in Section 4. Research Councils to devise programmes that The EPSRC policy suggested above, if interpreted so encourage research in the mathematical sciences that large segments of the mathematical sciences associated with new areas and initiatives; and research community are likely to receive less funding, 3. Diversity and distributedness of the UK will be damaging to both excellence and capability. mathematical sciences research community are In addition, increasing the proportion of grants that an essential component of the UK’s strength in are restricted to teams of researchers working closely mathematical sciences research, as explained in together on a single focused research theme - such Section 4. as EPSRC’s `Programme Grants’ as currently defined (see below), or other similar funding programmes - Given these principles, the Panel strongly recommends would tend to produce an unhealthy concentration (Recommendation R-1) that EPSRC funding for of funding (and of leading researchers) in an ever- the mathematical sciences should contain a variety smaller number of universities. This unfortunate side of programmes designed to address the most effect would be exacerbated if (as is likely to be the important demands and challenges. Despite inevitable case) such large focused grants enable significant uncertainties about how future EPSRC budgets will be numbers of new faculty to be hired, to the detriment allocated, the Panel emphasises this recommendation of other universities (this situation has already arisen in now in the hope of influencing EPSRC’s definition of statistics; see Section 15). mathematical sciences funding structures during the next five years. An implementable solution – an essential recommendation of the Panel (Recommendation R-1) On the first day of the review, the Panel was informed – is for EPSRC to create a flexible model that permits about EPSRC’s admirable wish to support adventurous geographically distributed researchers working in a research with high impact. In this regard, a statement broad research area to qualify for funding at levels was made similar to one on EPSRC’s Programme Grant analogous to a ‘platform grant’ or ‘programme grant’. 39 website: The Panel heard repeatedly during the site visits that distributed groups of researchers working on a single The funding of longer, larger research grants is key broad topic are not eligible in practice for either to achieving EPSRC’s strategy to deliver greater platform or programme grants as they are presently impact than ever before. defined. Based on available information about these grants, the Panel agrees that neither type of grant It emerged from the ensuing discussion that the matches the Panel’s suggestion. intended strategy is to support teams of researchers who collaborate closely on a single research theme. Panel members immediately pointed out that a 39 www.epsrc.ac.uk/funding/grants/capacity/programme/Pages/ strategy of supporting large, close-knit groups was scopeofscheme.aspx
39 International Review of Mathematical Science The Need for Diverse Funding Structures
The EPSRC website describing platform grants40 states that they are intended to provide ‘underpinning funding to well established, world leading research groups’, and that ‘[applicants] should hold a substantial portfolio... of current EPSRC funding, typically over £2 million in value ...’
Online information about the assessment criteria for Programme Grants includes the following four statements – (1) ‘[Programme Grants] are intended to support a suite of related activities focusing on one strategic research theme’, (2) ‘it is expected that most proposals will be interdisciplinary and collaborative in nature’, (3) ‘the principal investigator should have brought together a world-class team with complementary expertise so as to enhance the potential to achieve the vision’, and (4) ‘the proposal must demonstrate that there is a clear management plan’.41 These are highly unlikely to apply to a collection of leading researchers working independently on a major research theme (the kind of ‘programme’ needed in certain areas of the mathematical sciences). the panels were unhappy, more than a year ago, with strategies that might reduce community-initiated In the Panel’s view, flexible structures that provide proposals in favour of top-down management of long-term support for distributed excellence are research. essential to achieve EPSRC’s goal of supporting excellent research in the mathematical sciences. • The 2008 International Review of Materials Panel The activities of the Wales Institute of Mathematical stated, in response to a question in its Evidence and Computational Sciences (WIMCS) show that Framework, that: it is possible to build coherent and very effective More adventurous research will often require collaborations between geographically distributed longer term planning on the part of EPSRC. There institutions. The recommended new community group is concern that projects that do not mature in a 3–5 suggested in Section 12 should be able to provide year time horizon will not be provided for in the useful thoughts about how to define and manage future with responsive funding that emphasises new distributed grants. adventures... There is a concern among a number of Panel members and researchers that excessive Question B in the Evidence Framework asks about EPSRC top-down direction of research restricts high-risk, high-impact research. Almost by definition, innovation... [12, page 36]. all the areas in Sections 5 and 6 in which there is world-leading or world-class research include high- • Similarly, the 2009 International Review of UK risk, high-impact research. As for Questions B-2 and Chemistry Research stated ‘Current funding levels B-3 regarding more adventurous research, the Panel and implementation mechanisms are a significant believes that, as of today, research base funding barrier to adventurous research’ and formally (formerly ‘responsive mode’) offers the best chance for recommended that EPSRC should: optimally creative research in a wide array of sub-areas of the mathematical sciences. Increase the number of single PI-initiated grants to stimulate more adventurous research. ...Importantly, Similar views about the high importance of research such grants should not be in competition with very base funding in encouraging adventurous research large grants [emphasis added] [2, page 25]. were expressed by the two most recent international reviews conducted under the auspices of EPSRC. For 40 www.epsrc.ac.uk/funding/grants/capacity/platform. both fields under review (materials and chemistry), 41 www.epsrc.ac.uk/funding/grants/capacity/programme
International Review of Mathematical Science 40 14. Making Connections for the Mathematical Sciences
A defining role of mathematical sciences research should not be treated as an ‘optional extra’ within is its array of connections with other fields and initiatives involving scientific, engineering, societal and industry as well as within itself. This section considers technological challenges (see Section 3.2). several issues related to creating and strengthening multidisciplinary and industrial connections. Based on the Panel’s own experience and the comments from collaborators and industrial users 14.1 Multidisciplinary connections about the essential role of the mathematical sciences (Sections 10 and 11), major progress on ‘grand EPSRC has actively supported funding programmes challenge’ problems will almost certainly require to encourage multidisciplinary research, such as substantial involvement, from the beginning, by Multidisciplinary Critical Mass Centres,42 Programme mathematical sciences researchers. Otherwise, there is Grants43 (where funding was expected to be for a danger that the proposed research may boil down to multidisciplinary research) and Interdisciplinary applying standard mathematical sciences techniques Research Collaborations.44 Based on what the Panel to a new problem rather than seeking a fresh look learned during its site visits, these programmes have from the perspective of an expert. Thoughtful encouraged formation of large groups with a focus on advice from mathematical sciences researchers multidisciplinary topics. should be sought to ensure that proposed teams for multidisciplinary initiatives represent an appropriate Even so, multidisciplinary collaborations, including scientific balance. The Panel’s recommendation collaborations with industry, suffer from some well (see Recommendation R-3 and Section 14.2) for known difficulties identified in other countries that workshops intended to improve connections with also apply to the UK. An extensive 2004 US National other areas should accordingly be activated whenever Research Council study Facilitating Interdisciplinary new major initiatives or ‘grand challenge’ focus Research states: areas are contemplated or announced, to encourage Despite the apparent benefits of interdisciplinary mathematical scientists to think creatively about their research, researchers interested in pursuing it often role in potential collaborative proposals. face daunting obstacles and disincentives [9, page 1]. 14.1.2 Proposal review 14.1.1 Ensuring a substantive role for the The issue of appropriate proposal review came up mathematical sciences several times during the site visits and the Panel’s own The present Panel consists of mathematical scientists, discussion. Of particular relevance to EPSRC and the who (naturally) regard our common field as important, other Research Councils, there is a strong feeling in the and this view extends to the role of mathematical community, which the Panel regards as serious because scientists in research teams who tackle multidisciplinary it was expressed by very distinguished researchers, that and industrial problems. Because scientists and the peer review process for multidisciplinary proposals engineers have necessarily received training in is not working well. Similar concerns about proposal the mathematical sciences, they may relegate the review were expressed on behalf of mathematical mathematical sciences to a ‘service’ role, genuinely but wrongly believing that ‘we’ve already done the 42 www.epsrc.ac.uk/about/progs/maths/Pages/multi.aspx. mathematics’. Given that the mathematical sciences 43 www.epsrc.ac.uk/funding/grants/capacity/programme/Pages/ have a clear and consistent history of delivering widely default.aspx. useful, often transformative, theory and methods, they 44 www.epsrc.ac.uk/funding/grants/capacity/Pages/ircs.aspx.
41 International Review of Mathematical Science Making Connections for the Mathematical Sciences
biology (Section 6.4), operational research (Section In this direction, EPSRC has arranged ‘scoping’ 5.11) and statistics (Section 5.13), fields that combine workshops designed to engage UK researchers in a wide range of approaches and methodology. On societal themes such as energy or the digital economy. this topic, the US National Research Council report on The Panel urges an extension and generalisation of multidisciplinary research mentioned above notes: this idea to provide information and guidance for mathematical sciences researchers interested in making Reliable methods for prospective and retrospective new connections. In particular, short workshops evaluation of interdisciplinary research and education are a promising mechanism to provide guidance programmes will require modification of the for members of the community as well as academic peer review process to include researchers with colleagues from other fields and from industry. These interdisciplinary expertise in addition to researchers gatherings could be arranged at one of the institutes with expertise in the relevant disciplines [9, page 3]. (Section 8) or by a learned society (Section 9). With a well chosen set of topics and sufficient funding, Along these lines, the Panel recommends that review we believe that distinguished mathematical scientists panels for multidisciplinary proposals with substantial would agree to attend; their prestige would in turn mathematical sciences content should include attract junior people in the field. members with expertise in both multidisciplinary research and relevant areas of the mathematical Because of the language disconnect mentioned in sciences. For example, a proposal about future energy Section 11.3, great care would be needed in choosing options could well involve comparisons of technologies those invited to present multidisciplinary or industrial that are not yet fully developed or understood; in problems, but the present Panel’s positive experience such a context, judgements about the most promising with the collaborators who spoke at site visits and approaches can be made properly only with a subtle with the Industrial Mathematics KTN (which invited and advanced mathematical understanding of the attendees to the users’ meeting; see Section 11) implications of uncertainty. provides confidence that these potential workshops could be similarly successful. Because proposals in operational research and statistics typically involve an array of methodologies as well as 14.3 Assessing best practices application areas, the Panel recommends that they The Panel recognises and applauds the fact that should be reviewed by a separate panel covering both UK funding agencies, including EPSRC, have made areas. determined and successful efforts to encourage multidisciplinary research and industrial collaborations, 14.2 Broadening connections via as have individual academic institutions (including, workshops but by no means limited to, those mentioned in During the period of the Panel’s review panel members Section 10). Support has also come from industry, asked collaborators from other disciplines and industry as mentioned elsewhere in the report, and from how they met their mathematical sciences partners. other sources. For example, the Oxford Centre for To no one’s surprise, the almost universal answer was Collaborative Applied Mathematics45 is supported a random meeting, for example, at a seminar or social by the King Abdullah University of Science and gathering where a conversation led to recognition Technology Global Research Partnership. of common scientific interests. Even within the mathematical sciences, connections often result from Given this variety of centres and institutes within the chance meetings. UK using different strategies to initiate and encourage multidisciplinarity and industrial connections, the Panel In response to Questions E-3, F-2 and F-3, the Panel recommends that, after sufficient time has passed to believes that connections are so important for the make a reasonable judgement, EPSRC should assess mathematical sciences that they should not be left and analyse the associated ‘best practices’, as well as primarily to chance. During the site visits, panelists any less successful practices. were repeatedly told about an eagerness to connect and collaborate that was frustrated by not knowing how to begin. A similar theme was repeated at the Panel’s meeting with users (see Section 11.3). 45 www.maths.ox.ac.uk/occam/.
International Review of Mathematical Science 42 15. Structural Issues Specific to Statistics
This section follows up the mention in Section sounds the alarm about the difficulties encountered in 5.13 that the situation in the UK statistics research filling vacancies, warning that the situation will worsen community is of serious concern, even though its after the expected retirements. Without decisive members are doing outstanding research. The reasons action to enhance the ability of small departments to for this are primarily structural, involving the age compete on the international level for new faculty, a profile of statistics researchers, the unanticipated major decline seems likely, especially in the coming effects of large Science and Innovation Awards in constrained funding environment. statistics, and the position of statistics in school curricula. Evidence to support the statements in this 15.2 Diminution of statistics as a section was brought strongly to the Panel’s attention separately recognised field during the site visits by individual comments (which are This Panel has taken a consistent view that the not appropriate for inclusion in this report). mathematical sciences should be treated as a unity but this does not mean that we advocate ignoring 15.1 Weakening of small statistics real differences in culture and methodology. Some of departments the distinctive properties of statistics are described in At many universities where excellence is represented Section 5.13 and the Panel believes that it is highly by a relatively small number of researchers, research desirable for the UK to retain its international presence strength in statistics has been diminished by in statistics. In addition, the Panel favours having retirements, job moves by prominent statisticians and strong statistics research and teaching programmes at locally decided closures of statistics departments, a large number of UK universities, for two reasons: which tend (on average) to be small (in particular, there is now no free-standing statistics department in • For most school students, the study of statistics is Scotland or Wales). confined to descriptive procedures with a focus on application; only a small minority study it in any Although the science and innovation centres in depth as part of the school mathematics curriculum. statistics have had highly positive consequences for the Thus, many mathematics students first encounter institutions that received them, an unforeseen result is statistics as a mathematical discipline and begin to that their ability to offer attractive salaries and reduced appreciate its power, interest and usefulness only teaching inhibits the capacity of small departments, at university. Because of this lack of awareness by even those of high quality, to compete for new hires. entering undergraduates, a small number of high Thus far this decline of small departments has been profile centres, such as those funded by the science partially offset by junior appointments of young and innovation awards, are unlikely to attract many foreigners, but they may well leave if offers from of these students into statistics and to train them competitor countries become more attractive. first at the undergraduate level and then in research. Some researchers argue that the widespread In the fairly near future a generation of internationally omission of statistics at the school level is reasonable leading statistical researchers will retire; their potential because a solid basis in mathematics is essential to successors are not obvious, owing to a relative dearth study undergraduate statistics; hence schools should of people in their 40s. The absence of these renowned emphasise mathematics. However, this strategy senior figures will deny the UK access to internationally works countrywide only if mathematics students at outstanding statistical scientists who could train the most universities have access to stimulating modern next generation. The landscape document in statistics statistics courses given by experts in the field. The
43 International Review of Mathematical Science Structural Issues Specific to Statistics
increasing concentration of statistics in a few major departments means that this approach is less and less viable.
• Beyond the role of statistics as a discipline, it is a collaborative science whose presence is enormously beneficial to scientists and engineers, within universities of all sizes, who need statistical tools to advance their own research activities and to ensure their global competitiveness.
This potential marginalisation of statistics in the UK, with a diminished or non-existent recognisable presence in small universities, is in contrast to the situation in the US, where undergraduate statistics majors are increasing, especially in multidisciplinary applications.
15.3 Strategies for strengthening statistics To address the looming prospective fragility in small statistics departments, one idea (as suggested in Section 13) might be a flexible grant scheme that could provide support for excellence in statistics across a range of universities; see Recommendation R-1 (Section 2). Advice specifically about statistics should also be part of the community involvement described in Section 12 and included in Recommendation R-2. A third possibility is an in-depth study of structural issues in statistics.
Since postdoctoral training programmes in the statistics centres have been particularly successful, ideally they should be continued for a period beyond the point at which the centres would otherwise cease to function. Postdoctoral training is especially important to the profession in a number of ways, for example by giving young researchers stronger foundations for their early careers and by providing employment opportunities when regular statistics appointments are not available. Maintaining a strong cohort of excellent postdocs is crucial for UK statistics at the moment because of the factors mentioned earlier.
Finally, there are sound reasons for special procedures to assess research base funding (formerly ‘responsive mode’) grant proposals in statistics. Such proposals often include many different aspects, for example methodology, theory, applications and computational algorithms, all of which need examination by knowledgeable reviewers. This diversity of focus is less common in several of the fields with which statistics currently shares a review panel (see Section 14.1.2).
International Review of Mathematical Science 44 16. Training and Nurturing the Next Generation
At every site visit, panel members spent an extended undergraduates to become engaged in mathematical lunch period meeting early career researchers (a sciences research, and the Panel had no opportunity mixture of PhD students, postdocs and junior faculty). to learn about undergraduate research programmes in Panel members typically spread out, ‘working the the UK. Nonetheless, if (as suggested by the presence room’ in which lunch was served, each speaking of Question H-1 in the Evidence Framework) there is a at some length to one or more small groups. This wish for more undergraduates to become involved in format worked very well in providing the Panel with research, the Panel believes that there could well be a perspectives on the many sub-questions of Question H potentially damaging effect from the recently enacted in the Evidence Framework. Of course, any conclusions changes in funding of undergraduate education (see drawn from these conversations are based on a very Section 1.4); left to their own devices, undergraduates small sample of data. may be unlikely to regard ‘research’ as helpful to their future earning power. 16.1 Students seeking undergraduate degrees in mathematics 16.2 Education and support of PhD Question H-1 asks about the demand for UK students undergraduates to become engaged in mathematical The 2004 IRM [13] expressed serious concern about sciences research and requests a comparison with the short and narrow training received by UK PhDs other countries. under the traditional 3 + 3 model, which reduced their competitiveness for both academic and industrial In the US and Canada, undergraduate research is jobs. The next three subsections discuss several related regarded as extremely important to the point that issues. there is tremendous pressure on universities to establish programmes that encourage undergraduates 16.2.1 Doctoral Training Accounts across all disciplines to participate in research. Funding The information provided by EPSRC (Section agencies in those countries are deeply involved as 1.5.1) explains that most PhD assistantships in the well, offering support to undergraduates for summer mathematical sciences are funded by Doctoral Training internships either as part of a faculty research grant or Accounts (DTAs), which derive from awards made at a national laboratory. to institutions based on the results of a peer review panel convened by EPSRC. However, the Panel’s Although the Panel did not meet specifically with understanding, derived from the second LMS position undergraduate students, at several site visits the paper [16], is that although EPSRC informs institutions Panel was told that there is an ample supply, even about the earnings through research grants originating an oversupply, of students applying for admission in mathematical sciences departments, institutions to undergraduate programmes in the mathematical are not obliged to follow the associated division of sciences. The data in Section 4 of the London funds but rather are encouraged to think ‘strategically’ Mathematical Society position paper UK Mathematical about the internal allocation of DTA funds. As a result, Sciences – Research and Teaching in Symbiosis researchers in a mathematical sciences department [16] confirm that the number of undergraduates cannot count on receiving what might be considered at UK Higher Education Institutions studying the their ‘fair share’ of DTA money, since this is decided mathematical sciences has significantly increased by the local institution without review by EPSRC. In in the past five years. But this trend does not the Panel’s view, this policy about distribution of DTAs necessarily mean that there is sufficient demand from is likely to cause continuing harm to the pipeline of
45 International Review of Mathematical Science Training and Nurturing the Next Generation
PhD students in the mathematical sciences, especially A different approach to broadening the education of since, as announced on 6 January 2011, EPSRC will no UK PhDs more is represented by Centres for Doctoral longer support project studentships on research Training (CDTs), awarded to specific universities in grants.46 scientific areas within EPSRC’s remit (not just in the mathematical sciences). Fifty new CDTs were funded 16.2.2 Taught Course Centres and Centres for by EPSRC in 2009, each admitting about 10 students Doctoral Training per year. The students admitted to a CDT have access With the intent of improving the breadth of to taught courses and also complete a PhD dissertation PhD education, EPSRC has funded two different within the centre. programmes since 2004: Taught Course Centres (TCCs) in the Mathematical Sciences and Centres for Several concerns about CDTs were expressed during Doctoral Training (CDTs), whose scientific content must site visits – that they lead to an undue concentration of be aligned with EPSRC’s remit but is not limited to the funding in individual institutions and that the options mathematical sciences. for PhD research topics might be overly influenced by funding availability, where the latter concern arises The six Taught Course Centres were designed to because a relatively large proportion of the available encourage collaborations of universities, allowing PhD assistantships in a subfield might be available from each department to offer a broader education to its one institution. PhD students than would be possible with only its own faculty. Based on what the Panel heard during Based on these concerns (which the Panel sees as its site visits, TCCs seem to be fulfilling the purpose valid), the Panel strongly recommends that a consortia of increasing students’ knowledge of mathematical of universities be permitted to compete for Centres sciences areas outside their PhD topics. The secondary for Doctoral Training (or a similar programme with effects of TCCs have also been beneficial. For example, a different name); this is effectively impossible at a consequence of creating the Scottish Mathematical present because students must be trained together in Training Centre is that the faculty members from one place. If smaller universities without CDT funding Aberdeen, Dundee, Edinburgh, Glasgow, Heriot–Watt, cannot attract PhD students, the best faculty will either St Andrews and Strathclyde started to work together, leave the smaller institutions or else be hampered at first in preparing the lectures and then more in living up to their full research and educational generally on research. This result suggests an effective potential, in either case damaging the institutional collaboration mode that could be created elsewhere in diversity valued by the Panel (see Section 4 and the UK. Recommendation R-1).
Complaints were made about inadequate technology In response to Question H-7, it is too early to for remote transmission of TCC courses and about tell whether the measures taken will develop an access difficulties for students from outside institutions appropriate balance in UK PhDs between depth and but the Panel assumes that these problems can be breadth of knowledge in the mathematical sciences. fixed relatively easily as technology improves. However, the Panel was unhappy to learn that, for some TCCs, 16.2.3 Funding of PhD students policies about course assessment and PhD student A major change since the 2004 IRM has been attendance vary with participating departments, that EPSRC now funds PhD students, on average, with the result that the quality of the courses is not for 3.5 years rather than for only 3 years. This is reviewed and some students do not take advantage unquestionably an improvement in the effectiveness of the TCCs. A review47 of the TCCs commissioned of UK mechanisms for supporting talented individuals by EPSRC in the summer of 2010 had a favourable (Question H-3) and the Panel heard essentially impression but concluded, as does the present Panel, universal support for the extended time of PhD student that it is too early to determine whether TCC-trained funding. students are more competitive with respect to students trained outside the UK. The EPSRC review also noted with apparent disapproval the lack of a uniform policy 46 www.epsrc.ac.uk/newsevents/news/2011/Pages/ about TCC course attendance and assessment. projectstudentships.aspx. 47 www.epsrc.ac.uk/pubs/reports/Pages/maths.aspx.
International Review of Mathematical Science 46 Training and Nurturing the Next Generation
As to whether the length of EPSRC funding should be two-career couples). In the Panel’s view, UK-trained increased, comments at the site visits, as well as private PhDs should have adequate opportunities to pursue comments made to panel members, were mixed. Some careers that make good use of their training in people favoured moving to assured 4 year funding, research. while others argued that it was better to support more students for 3.5 years, asserting that their universities 16.4 Postdocs and junior faculty and departments could almost always find funding for Strikingly few of the postdocs and junior faculty whom an additional half-year if needed. the Panel met had received their PhDs in the UK (in a small number of cases, not a single postdoc or junior 16.2.4 A new kind of Master’s degree faculty member at the sub-panel lunch meeting had A system containing additional options for PhD received his/her PhD in the UK). It has already been student training is appealing to the Panel, and in this stressed that the Panel met with an unavoidably small spirit we recommend that UK universities consider number of postdocs and junior faculty. The Panel is not establishment of a PhD programme that begins with aware of hard data about the career goals of UK PhDs a 1 year research Master’s, followed by 3 years of when they finish their degrees or about their eventual PhD education and training. The special ‘Master’s’ career paths. Collection of this data would be useful. would contain advanced taught courses, appropriately assessed, and a project with a significant research During the review week, panel members spoke not component, to be carried out at a university or in only to postdocs and junior faculty, but also to heads industry. For students in such a programme who of mathematical sciences departments, to more senior decide not to pursue a PhD, an MSc degree could be faculty and to industrial participants. awarded. Such a structure is, in effect, a compromise with the Bologna agreement,48 usually described as Among academics, there was noticeable agreement 3+2+3. Its purpose is not simply to introduce early- that UK-trained PhDs were very often not the stage PhD students to taught courses but also to most highly ranked by the hiring departments. As provide a taste of research in either an academic already mentioned in Section 11, several industry or industrial setting to ensure that students are representatives expressed explicit concern about the committed (and able) to conduct research. frequent narrowness of training received by UK- educated PhDs. 16.3 PhD student concerns Stiff competition on the international job market for Based on information gathered in these contexts UK PhDs in mathematical sciences is a fact of life during the review week, the Panel’s response to today and it is too early to tell whether the changes Question H-6 is therefore that the UK’s process for discussed in Section 16.2.2 will lead to improved preparing and supporting early career researchers is prospects. In discussions with panel members at the not consistently producing PhDs who come out on top site visits, many PhD students said that they are very when competing with PhDs trained elsewhere. The worried about finding an academic job, in the UK or Panel attributes this problem almost entirely to the abroad, after completing their degree. These emphatic more mathematically rich preparation of PhD students comments added to the Panel’s view that UK-educated educated in other countries. PhDs are not, in general, as competitive as those from other countries. The only exceptions to concerns about When asked why they had come to the UK from finding a good job came from PhD students who had elsewhere, several postdocs stated vigorously that been supported by a CASE studentship (see Section 7), there are many more opportunities in the UK than who felt that they were likely to find a rewarding job in their home countries. This provides some (limited) in industry. evidence in response to Question H-5 that UK academic positions remain attractive in an international Several PhD students who plan to finish within the context. next year asserted that there are not enough suitable postdoctoral positions in the UK and that available The proportion of junior faculty from outside the UK, positions are limited in number and location (the which seemed to have increased since the 2004 IRM, is limited number of postdoctoral positions has, not surprisingly, a disproportionately negative effect on 48 www.hefce.ac.uk/learning/inter/
47 International Review of Mathematical Science Training and Nurturing the Next Generation
a worrying trend because it implies a dwindling supply The Panel was informed at some site visits about of top quality home-grown talent (Question A-5). If positive steps involving the London Mathematical other countries begin making a significant effort to Society – in particular, its Women in Mathematics attract leading mathematical sciences researchers at Committee and a March 2008 statement by the LMS all levels, the UK will no longer be able to count on its Council.49 In 2009, the LMS and the Committee of ability to hire the best researchers from abroad. The Heads of Departments on Mathematical Sciences Panel regards this fragility as a serious potential risk to established a Good Practice Award50 to help advance the UK’s future international standing. women’s careers in university mathematical sciences departments. The Panel observes with concern the apparent inconsistency of training PhDs under a system that, Nonetheless, the overall impression from data and in part by design, does not seem to prepare them the Panel’s experiences during the review week is that well for postdoctoral or academic positions in the UK, action about gender diversity is not a sufficiently high which go instead to PhDs educated in other countries. priority in the UK. Panel members believe that this lack A (presumed) goal of building a healthy pipeline is of attention will be damaging to the future research not, based on the Panel’s observations, satisfied by excellence of UK mathematical sciences research and the present system. The Panel encourages strong our experience suggests that significant changes will efforts to ensure that PhD training meets the highest happen only when the issue is taken seriously. international standards; it is in this spirit that the Panel recommends the ‘new’ Master’s described in Section In the US, seven NSF-funded mathematical sciences 16.2.4. institutes51 encourage outstanding women researchers (including early career women) in various ways. In the 16.5 Participation of women Panel’s view, a similar strategy should be followed in the UK via activities of the institutes and learned Question H-9 in the Evidence Framework involves societies (Sections 8 and 9), which could ensure diversity of the UK mathematical sciences research that excellent quality women at all levels attend community in terms of gender. (and, if appropriate, speak) at programmes held at UK institutes or organised by learned societies (see The Panel can state that, compared to other countries, Recommendation R-11, Section 2). the proportion of women is strikingly small. The gender data presented by EPSRC (in Sections 6.5.11 Concern about participation of UK women in science and 7.6 in Part I of Information for the Panel; see is not limited to the mathematical sciences. The 2008 Section 1.5.1) indicate that the proportion of women International Review of Materials Panel stated: principal and co-principal investigators is improving slightly (in younger researchers) but the overall The Panel strongly believes ...that there is an urgent numbers are not encouraging. need to improve diversity among groups designed as faculty leadership [12, page 37]. One-fourth of the present panel members are women, but during our site visits, no more than 10% In the same spirit, the present Panel agrees, with (sometimes much less than 10%) of those present special reference to the ‘Developing Leaders’ strategy were women and very few women made presentations in EPSRC’s Delivery Plan [6]; see Recommendation to the Panel. The only contexts in which there were R-11. more women were the lunch meetings with early career researchers; this is consistent with the trends in the data provided by EPSRC.
Possibly more worrying than the numbers was that, with a few notable exceptions, the people with whom we spoke did not seem to be particularly concerned about this issue. A typical attitude appeared to be, approximately, ‘it’s unfortunate, but there simply are 49 ftp.lms.ac.uk/activities/women_maths_com/index.html. very few women in the mathematical sciences’. 50 www.lms.ac.uk/content/good-practice-award. 51 mathinstitutes.org.
International Review of Mathematical Science 48 17. International Connections
The multipart Question C in the Evidence Framework sponsored by the learned societies; see Sections 8 asks for an assessment of collaborations between and 9. UK mathematical sciences researchers and world- leading researchers in other countries. Happily, this Question C-2 focuses on collaborations with specified question is straightforward to answer, based on the parts of the world. There is no question about the Panel’s own knowledge and the many consultation very high level of collaboration with the US and responses provided by EPSRC in Evidence for the Europe, and, as documented by multiple consultation Panel (Section 1.5.1). Research in the mathematical responses, collaborations with China, India and sciences lends itself more readily than perhaps any Japan are increasing. A difficulty with collaborations other area to international collaboration because in countries (including the latter three) that are far so much of its content represents general concepts removed geographically is that face-to-face meetings (in contrast to requiring, for example, a personal and visits are needed to strengthen collaborations visit to an experimental facility). Without doubt, but the associated expenses are high. In addition, as a significant element in the collaborations of UK mentioned in Section 1.4, concerns were expressed mathematical scientists with leaders from other to the Panel about funding for visits as well as recent countries is participation of the latter in programmes restrictions on visas. at the institutes and at conferences and workshops
49 International Review of Mathematical Science 18. Annotated Evidence Framework
This section contains the Evidence Framework B-1. What is the current volume of high-risk, high- annotated with the section numbers in which each impact research and is this appropriate? question is discussed. For some questions, the Panel Section 13. had no data or information on which to base an B-2. What are the barriers to more adventurous answer. research and how can they be overcome? Section 13. A. What is the standing on a global scale of the UK Mathematical Sciences research community B-3. To what extent do the Research Councils’ both in terms of research quality and the funding policies support/enable adventurous profile of researchers? research? All the subsections of Sections 5 and 6, and Section 13. Section 7. C. To what extent are the best UK-based A-1. Is the UK internationally leading in researchers in the Mathematical Sciences Mathematical Sciences research? In which engaged in collaborations with world-leading areas? What contributes to the UK strength researchers based in other countries? and what are the recommendations for Section 17. continued strength? All the subsections of Sections 5 and 6, and C-1. Does international collaboration give rise to Section 7. particular difficulties in the Mathematical Sciences research area? What could be done A-2. What are the opportunities/threats for the to improve international interactions? future? Section 17. All the subsections of Sections 5 and 6, and Section 7. C-2. What is the nature and extent of engagement between the UK and Europe, USA, China, A-3. Where are the gaps in the UK research base? India and Japan, and how effective is this All the subsections of Sections 5 and 6, and engagement? Section 7. Section 17.
A-4. In which areas is the UK weak and what are C-3. How does this compare with the engagement the recommendations for improvement? between the UK and the rest of the world? All the subsections of Sections 5 and 6, and Section 17. Section 7. D. Is the UK Mathematical Sciences community A-5. What are the trends in terms of the standing actively engaging in new research of UK research and the profile of UK opportunities to address key technological/ researchers? societal challenges? All the subsections of Sections 5 and 6, and Sections 3.2, 6, 7, 10 and 11. Section 7. D-1. What are the key technological/societal B. What evidence is there to indicate the challenges on which Mathematical Sciences existence of creativity and adventure in UK research has a bearing? To what extent is Mathematical Sciences research? the UK Mathematical Sciences research All the subsections of Sections 5 and 6; community contributing to these? Are there Sections 7 and 13.
International Review of Mathematical Science 50 Annotated Evidence Framework
fields where UK research activity does not the main barriers to effective knowledge match the potential significance of the area? and information flow and how can they be Are there areas where the UK has particular overcome? strengths? Sections 11 and 14. Sections 6, 6.2, 6.4, 7, 10 and 11. E-4. Have funding programmes been effective in D-2. Are there any areas which are under- encouraging multidisciplinary research? What supported in relation to the situation is the evidence? overseas? If so, what are the reasons Sections 7, 11 and 14. underlying this situation and how can it be remedied? F. What is the level of interaction between the Not answered. research base and industry? Sections 7 and 11. D-3. Does the structure of the UK’s mathematical science research community hamper its ability F-1. What is the flow of trained people between to address current and emerging industry and the research base and vice versa? technological/societal challenges? If so, what Is this sufficient and how does it compare improvements could be implemented? with international norms? Nothing in the structure of the research Sections 6.4, 11 and 11.3. community hampers its ability to address F-2. How robust are the relationships between current and emerging technological/societal UK academia and industry both nationally challenges, although improvements are, of and internationally and how can these be course, possible. Sections 7, 11, 14.1 and 14.2. improved? D-4. Are there a sufficient number of research Sections 7 and 11.3. leaders of international stature in the F-3. To what extent does the mathematical Mathematical Sciences in the UK? If not, sciences community take advantage of which areas are currently deficient? opportunities, including research council All the subsections of Sections 5 and 6. schemes, to foster and support this knowledge exchange? Is there more that E. Is the Mathematical Sciences research could be done to encourage knowledge base interacting with other disciplines and transfer? participating in multidisciplinary research? Section 11.3. All the subsections of Section 6; Sections 7, 10 and 11. F-4. Nationally and internationally, what is the scale of mathematical sciences research and E-1. Is there sufficient research connecting development undertaken directly by users? mathematical scientists with investigators What are the trends? Are there implications from a broad range of disciplines including for the UK mathematical sciences research life sciences, materials, the physical sciences, community and how well positioned is it to finance and engineering? What is the respond? Is there any way that its position evidence? could be improved? All the subsections of Section 6; Sections 7, Sections 7 and 11. 10 and 11.
E-2. Where does the leadership of multidisciplinary G. How is the UK mathematical sciences research research involving mathematical sciences activity benefiting the UK economy and global originate? In which other disciplines are the competitiveness? mathematical sciences contributing to major Sections 10 and 11. advances? G-1. What are the current and emerging major Sections 6, 7, 10, 11 and 14. advances in the mathematical sciences area E-3. Are there appropriate levels of knowledge which are benefiting the UK? Which of these exchange between the Mathematical Sciences include a significant contribution from UK community and other disciplines? What are research? Sections 10 and 11.
51 International Review of Mathematical Science Annotated Evidence Framework
G-2. How successful has the UK mathematical Sections 16.2, 16.3 and 16.4. sciences community (academic and user- H-7. Is the balance between deep subject based) been at wealth creation (e.g. spin- knowledge and ability to work at subject out companies, licences, etc.)? Does the interfaces and boundaries appropriate? community make the most of opportunities Sections 11.3 and 16.2. for new commercial activity? What are the barriers to successful innovation based on H-8. How is the UK community responding to advances in the mathematical sciences in the the changing trends in the UK employment UK and how can these be overcome? market? Sections 10 and 11.3. Not answered.
H. How successful is the UK in attracting and H-9. How diverse is the UK mathematical sciences developing talented Mathematical Sciences research community in terms of gender and researchers? How well are they nurtured and ethnicity and how does this compare with supported at each stage of their career? other countries? Section 16. Section 16.5.
H-1. Are the numbers of graduates (at first and higher degree level) sufficient to maintain the UK Mathematical Sciences research base? Is there sufficient demand from undergraduates to become engaged in Mathematical Sciences research? How does this compare to experience in other countries? Section 16.1.
H-2. Is the UK producing a steady stream of researchers in the required areas or are there areas of weakness in which the number of researchers should be actively managed to reflect the research climate? What adjustments should be made? Section 16.4.
H-3. How effective are UK funding mechanisms at providing resources to support the development and retention of talented individuals in the mathematical sciences? Sections 16.2 and 16.2.3.
H-4. How does the career structure for researchers in the Mathematical Sciences in the UK compare internationally? Not answered.
H-5. Is the UK able to attract international researchers in the Mathematical Sciences to work in the UK? Is there evidence of ongoing engagement either through retention within the UK research community or through international linkages? Section 16.4.
H-6. Are early career researchers suitably prepared and supported to embark on research careers?
International Review of Mathematical Science 52 References
1. www.aesops-fables.org.uk/aesop-fable-the- 12. International Perceptions of the UK Materials four-oxen-and-the-lion.htm. Research Base (2008), 2008 Materials International Review, EPSRC. 2. Chemistry for the Next Decade and Beyond Available from www.epsrc.ac.uk/pubs/ (2009), 2009 International Review of UK reports/Pages/internationalreviews.aspx. Chemistry Research, EPSRC. www.epsrc.ac.uk/research/ 13. International Review of UK Research in intrevs/2009ChemistryIR/Pages/default.aspx. Mathematics (2004), 2003 Mathematics International Review, EPSRC. 3. Citation Statistics (2008). Available from www.epsrc.ac.uk/pubs/ www.mathunion.org/fileadmin/IMU/Report/ reports/Pages/internationalreviews.aspx. CitationStatistics.pdf. 14. Lanczos, C. (1950). An iteration method for the 4. Comptop: Applied and Computational Algebraic solution of the eigenvalue problem of linear Topology. differential and integral operators, Journal of comptop.stanford.edu. Research at the National Bureau of Standards 45, 5. Deans, S. R. (1983). The Radon Transform and 255–282. Some of Its Applications, John Wiley and Sons, 15. Lessons from the First Six International Panel New York. Reviews (2005), EPSRC. 6. EPSRC Delivery Plan, 2011–2015 (2010), EPSRC. Available from www.epsrc.ac.uk/pubs/ www.epsrc.ac.uk/newsevents/news/2010/ reports/Pages/internationalreviews.aspx. Pages/deliveryplanfor20112015.aspx. 16. London Mathematical Society policy papers 7. EPSRC Funding Guide. (2010). www.epsrc.ac.uk/funding/apprev/basic/ UK Mathematical Sciences – Research and Pages/fundingguide.aspx. Teaching in Symbiosis. Doctoral Training in Mathematics in the UK. 8. The ‘Excellence Initiative’ in Germany. UK Government Funding for Mathematical See ’Research Landscape’ in www.research- Sciences Research. in-germany.de/52/home.html and www. Available from www.lms.ac.uk/content/ bmbf.de/en/1321.php. policy.
9. Facilitating Interdisciplinary Research (2004), 17. Noll, A. M. (2006). The industrial research lab: a National Research Council. relic of the past? Nature Materials 5, 337–338. www.nap.edu/catalog.php?record id=11153. www.nature.com/nmat/journal/v5/n5/full/ 10. Independent Review of Higher Education Funding nmat1639.html. and Student Finance (2010). 18. Report of the Senior Assessment Panel of the hereview.independent.gov.uk/hereview/ International Assessment of the US Mathematical report/. Sciences (1998), US National Science Foundation. 11. International Benchmarking of US Mathematics www.nsf.gov/publications/pub_summ. Research (1997), National Research Council. jsp?ods key=nsf9895. www.nap.edu/catalog/9089.html.
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19. Report on Mathematics in Industry, Organisation for Economic Co-operation and Development, 2008. www.oecd.org/dataoecd/47/1/41019441.pdf.
20. RAE 2008: the Outcome (2008). www.rae.ac.uk/pubs/2008/01/.
21. Review of Research Status of Operational Research in the UK (2004), EPSRC. Available from www.epsrc.ac.uk/pubs/ reports/Pages/internationalreviews.aspx.
22. entertainment.timesonline.co.uk/tol/ arts_ and_ entertainment/stage/theatre/ article7150115.ece.
International Review of Mathematical Science 54 Annex A
Steering Committee
Professor Tim Pedley (Chair) Professor Peter Green University of Cambridge Royal Statistical Society
Professor David Abrahams Professor Chris Hull Institute of Mathematics and its Applications Institute of Physics
Professor Janet Allen Dr Robert Leese BBSRC Industrial Mathematics Knowledge Transfer Network
Professor Sir John Ball Professor Lyn Thomas London Mathematical Society Operational Research Society
Professor Kenneth Brown Dr Lesley Thompson Edinburgh Mathematical Society EPSRC
55 International Review of Mathematical Science Annex B
Members of the International Panel – Brief Biographies
Professor Margaret Wright taking, in 1978, a position at the Australian National University. In November 2006 he moved back to the Professor Margaret H. Wright is Silver University of Melbourne. Professor of Computer Science and Mathematics in the Courant Institute His research interests range across several topics of Mathematical Sciences, New York in probability and statistics. He was elected to the University (NYU). She received her BS Australian Academy of Science in 1987 and the (Mathematics), MS and PhD (Computer Royal Society in 2000. Professor Hall is among the Science) from Stanford University. Her research world’s most prolific and highly-cited authors in both interests include optimisation, scientific computing and probability and statistics. He has made very substantial optimisation in real-world applications. and important contributions to non-parametric statistics, in particular for curve estimation and Prior to joining NYU, she worked at Bell Laboratories re-sampling: the bootstrap method, smoothing, (Lucent Technologies), where she was named as a Bell density estimation and bandwidth selection. He has Labs Fellow. She was elected to the National Academy worked on numerous applications across fields of of Engineering (1997), the American Academy of economics, engineering, physical science and biological Arts and Sciences (2001) and the National Academy science. Professor Hall has also made groundbreaking of Sciences (2005). During 1995-1996 she served as contributions to surface roughness measurement president of the Society for Industrial and Applied using fractals. In probability theory he has made many Mathematics (SIAM), and she has chaired advisory contributions to limit theory, spatial processes and committees for several mathematical sciences institutes stochastic geometry. and government agencies. Professor Anthony Davison In 2000, she received an honorary doctorate in Mathematics from the University of Waterloo and she Professor Anthony Davison is Professor was named as an honorary doctor of technology by of Statistics at the Ecole Polytechnique the Swedish Royal Institute of Technology in 2008. Fédérale de Lausanne, where he is also Director of the Institute of Mathematics. Professor Peter Hall After obtaining his BA in mathematics at the University of Oxford in 1980, he Professor Peter Hall is currently a obtained an MSc (1981) and PhD (1984) in statistics professor and ARC Federation Fellow from Imperial College London. Before moving to his at the Department of Mathematics current post in 1996 he worked at the University of and Statistics, University of Melbourne, Texas at Austin, at Imperial College London, and the and also has a joint appointment at University of Oxford, where he also held an EPSRC University of California Davis. Professor Advanced Research Fellowship. He has held visiting Hall was born in Sydney, Australia, and received his BSc professorships at various other universities. degree from the University of Sydney in 1974. His MSc and DPhil degrees are from the Australian National He is a fellow of the American Statistical Association, University and the University of Oxford, both in 1976. the Institute of Mathematical Statistics and the Royal He taught at the University of Melbourne before Statistical Society and an elected member of the
International Review of Mathematical Science 56 Annex B: Members of the International Panel – Brief Biographies
International Statistical Institute. In 2009 he was The Analysis of Cross-Classified Categorical Data are awarded a laurea honoris causa in statistical science by both Citation Classics and were recently reprinted by the University of Padova. Springer.
His research interests cover a wide range of topics in Professor Fienberg is a member of the US National statistical theory and methods, including statistics of Academy of Sciences and a fellow of the Royal Society extremes, likelihood theory and methods, resampling, of Canada, the American Academy of Arts and with applications principally to the biological and Sciences, and the American Academy of Political and environmental sciences. He is author of around 100 Social Science. journal publications and is author or co-author of several books. He is currently editor of Biometrika, Professor Andrew Granville and in addition to various other editorial roles has also been joint editor of Journal of the Royal Statistical Professor Andrew Granville is the Society, series B. Canadian Research Chair in Number Theory at the Université de Montréal. Professor Stephen Fienberg He obtained his first two degrees at Cambridge University, before moving Professor Stephen E. Fienberg is Maurice to Canada to obtain his doctorate in Falk University Professor of Statistics 1987 under the guidance of Dr Paulo Ribenboim. and Social Science at Carnegie Mellon Following several years as the Barrow Professor at the University, with appointments in the University of Georgia, he moved to his current position Department of Statistics, the Machine in Montréal in 2002. Learning Department, Cylab and i-Lab. He previously served as Dean of the College of Professor Granville’s primary research interest is Humanities and Social Sciences at Carnegie Mellon analytic number theory, though he has recently been and as Vice President for Academic Affairs at York interested in additive combinatorics. He also dabbles University in Toronto, as well as on the faculties of the in algebraic number theory, arithmetic geometry, University of Chicago and the University of Minnesota. combinatorics, harmonic and functional analysis and theoretical computer science. Professor Granville has He was founding co-editor of Chance and served received several awards for research including the as the Coordinating and Applications Editor of the Jeffery-Williams prize of the Canadian Mathematical Journal of the American Statistical Association. He is Society, for expository writing including the Chauvenet currently one of the founding editors of the Annals prize of the Mathematical Association of America, and of Applied Statistics and is co-founder and editor- for academic leadership including the (US) Presidential in-chief of the new online Journal of Privacy and Faculty Fellowship. Various honours include speaking Confidentiality, based in Cylab. He also co-chairs at the International Congress of Mathematicians and the National Academy of Sciences Report Review giving named lectureships in five different countries. Committee. Professor Granville is an associate director of Centre de He has been Vice President of the American Recherche mathématiques and has served on advisory Statistical Association and President of the Institute boards for this institute as well as for MSRI, the Fields’ of Mathematical Statistics and the International and Cryptography Research Institutes. He has been on Society for Bayesian Analysis. His research includes the the editorial boards of more than a dozen journals and development of statistical methods, especially tools several book series. He has served on various external for the analysis of categorical data, networks and review panels, most notably the NSF’s ‘Committee of privacy protection, from both likelihood and Bayesian Visitors’. He is the author of over 100 research articles, perspectives. Professor Fienberg is the author or more than 20 expository articles, several books, a play editor of over 20 books and 400 papers and related and is currently working on a (mathematical) graphic publications. His 1975 book on categorical data novel. analysis with Bishop and Holland, Discrete Multivariate Analysis: Theory and Practice, and his 1980 book
57 International Review of Mathematical Science Annex B: Members of the International Panel – Brief Biographies
Professor Gary Horowitz He was the founder and director of the Hydrodynamics Laboratory (LadHyX) at Ecole Polytechnique in the Professor Gary Horowitz is a Professor period 1990-2008. of physics at the University of California, Santa Barbara. He received his BA in He is President of the European Mechanics Society. He physics at Princeton University in 1976 was Associate-Editor of the Journal of Fluid Mechanics and PhD in physics at the University of (1999-2009) and Co-Editor in Chief of the European Chicago in 1979. He was a postdoc at Journal of Mechanics B/Fluids (1994-1998). He has the Mathematical Institute, Oxford, and a member of served on the Executive Committee of the American the Institute for Advanced Study, Princeton, before Physical Society, Division of Fluid Dynamics and on joining the faculty in Santa Barbara. several committees and panels in Europe and in the United States. Professor Huerre is a member of the Professor Horowitz is interested in both classical Académie des Sciences and received the Carnot Prize and quantum aspects of gravitational physics. His of the Académie des Sciences. He is a Fellow of the research mostly focuses on questions involving gravity American Physical Society and was the Batchelor under the most extreme conditions. These include lecturer at the University of Cambridge. He is Chevalier the big bang in cosmology and the spacetime inside de la Légion d’Honneur. black holes. According to general relativity, these are singularities – regions where Einstein’s field equation His areas of research interest cover a wide variety of breaks down. A deeper understanding of singularities hydrodynamic instabilities and transition phenomena requires a quantum theory of gravity and string theory in shear flows. His main research achievements include is a promising candidate for such a theory. Professor the effective use of absolute/convective instability Horowitz studies gravitational aspects of string theory, concepts to rigorously distinguish between amplifiers including black holes in higher dimensions, quantum and oscillators in fluid mechanics, the introduction of properties of black holes and especially quantum the notions of linear and nonlinear global mode and descriptions of singularities. associated frequency selection criteria to account for the dynamics of oscillators and the identification of Professor Horowitz is a member of the US National superdirectivity as a key mechanism for the production Academy of Science, a fellow of the American Physical of sound in shear flows. Society and member of the International Committee for the General Relativity and Gravitation Society. He Professor Willi Jäger participated in the National Research Council decadal review of gravitational physics in the US. Professor Professor Willi Jäger is a senior professor Horowitz has written over 150 research articles, at the University of Heidelberg. He including the most cited particle physics paper in the studied mathematics and physics 1980s (according to the CERN Courier). and received his PhD in 1966 at the University of Munich and his habilitation Professor Patrick Huerre in mathematics in 1969 at the University in Göttingen. He worked as a visiting member at Professor Patrick Huerre received Courant Institute (NYU) from 1969 to 1970. He was his Ingénieur’s degree from Ecole a full professor of Mathematics in Münster (1970-74) Centrale Paris in 1970 and his PhD in and has been professor in Heidelberg since 1974. Aeronautical Sciences from Stanford He was the founding director of the Interdisciplinary University in 1976. After postdoctoral Center for Scientific Computing (IWR). He is Director work at the University of Leeds with the of MATCH, Coordinator of BIOMS, Chairman of late Professor David Crighton, he joined the faculty the Gesellschaft für Mathematische Forschung of the Department of Aerospace Engineering at the Oberwolfach and Coordinator of the Junior Scientist University of Southern California (USC) in 1978. In Program WIN of the Heidelberg Academy of Sciences 1989 he was appointed Professor of Mechanics at and Humanities. He has been serving in many national Ecole Polytechnique. Since 1991 he has also been and international scientific committees and boards, Director of Research at the French National Center for e.g. as a chairman of the OECD-Global Science Scientific Research (classe exceptionnelle since 2003). Committee “Mathematics in Industry” or as chairman,
International Review of Mathematical Science 58 Annex B: Members of the International Panel – Brief Biographies
resp. member of the committees for Mathematics the chairman of the Graduate Degree Committee of in Industry and for the programme BioFuture of the Academy of Math and Systems Science (AMSS) since German government. 2007.
Professor Jäger’s main mathematical interests are Professor Ma was awarded the Max-Planck Research nonlinear dynamical systems, nonlinear partial Award in 1992 by the Max-Planck Society and differential equations, calculus of variation and Alexander von Humboldt Foundation, the First Class modelling, analysis and simulation of multiscale Prize for Natural Sciences in 1992 by the Chinese systems in natural sciences, medicine, economy Academy of Sciences, the Chinese National Natural and engineering and applications in industry, Sciences Prize in 1993, the Shing-Shen Chern image processing and applications in medicine and Mathematics Prize in 1995, the Qiu-Shi Outstanding humanities. He supervised more than 75 PhD theses. Young Scholars Prize in 1996, the He-Liang-He- Among his honours are 4 honorary doctorates and the Li Sciences and Technology Progress Prize in 1999 Bundesverdienstkreuz Erster Klasse (Cross of Merit, and the Hua Loo-Keng Mathematics Prize by the Federal Republic of Germany). Chinese Mathematical Society in 2005. He was invited to present a talk at the International Congress of Professor Zhi-Ming Ma Mathematicians in 1994, and present a Medallion Lecture at the 7th World Congress in Probability and Professor Zhi-Ming Ma is Professor Statistics in 2008. of Mathematics in the Academy of Math and Systems Science (AMSS), Professor Robert MacPherson Chinese Academy of Sciences (CAS). He graduated from Chongqing Normal Professor Robert MacPherson is currently University in 1978 and obtained his Hermann Weyl Professor of Mathematics PhD degree from the Chinese Academy of Sciences in at the Institute for Advanced Study in 1984. His major research interests include Probability Princeton. Previously, he was a Professor and Statistics, Stochastic Analysis, Markov processes of Mathematics at MIT, and before that, and Dirichlet forms and Applied Probability. at Brown University. He has had many visiting positions, spending four years in Paris, a year He has been at the Chinese Academy of Sciences each in Moscow and Rome, and semesters in Bonn since 1995, a Fellow at the Third World Academy and Utrecht. of Sciences since 1999 and at the Institute of Mathematical Statistics since 2007. He was the 8th His PhD thesis was in topology, but he has also worked President of the Chinese Mathematical Society (2000- in algebraic geometry, singularity theory, differential 2003) and has served as the 10th President since geometry, computer science, representation theory 2008. From 2003 to 2006 he was a member at large and in modular forms. He is currently doing applied of the Executive Committee of the International Math mathematics oriented to materials science. Union. Since 2007 he has been a Vice President of the Executive Committee of the International Math Union. Professor MacPherson is a recipient of the National Academy of Sciences Award in Mathematics, the Professor Ma has served in various academic American Mathematical Society’s Steele Prize, the committees. He was a council member of the Bernoulli Heinz Hopf Prize from the ETH Zürich, as well as Society for Math Statistics and Probability from 2003 honorary doctorates from Brown and from Lille. He to 2006. He was on the Committee for Conferences is a member of the National Academy of Sciences, on Stochastic Processes (2004-2007), the Committee the American Academy of Arts and Sciences and the of the National Natural Science Foundation of China American Philosophical Society. (2004-2006), and was a Co-chair of the Scientific Committee of IMS-China International Conference 2008. He served as the Chairman of the Organising Committee of the International Congress of Mathematicians held in Beijing in 2002. He has been
59 International Review of Mathematical Science Annex B: Members of the International Panel – Brief Biographies
Professor Dusa McDuff Professor Stefan Müller
Professor Dusa McDuff launched her Professor Stefan Müller was born in career while a graduate student at Wuppertal and studied mathematics Cambridge (where she earned her in Bonn, Paris and at the Heriot-Watt PhD in 1971) when she solved a well- University in Edinburgh during the years known von Neumann algebra problem, 1983 to 1989. He received a diploma constructing infinitely many different degree from Bonn in 1987 and a PhD factors of ‘type II-one’. She travelled to Moscow in from Heriot-Watt in 1989. During the academic year 1969-70 where she studied with Israel Gelfand, who 1989/90 he was the Zeev Nehari Assistant Professor at shared her view of mathematics as a kind of poetry Carnegie-Mellon University in Pittsburgh. Afterwards and encouraged her to study topology. She returned he returned to Bonn as a postdoc and after a visit to to Cambridge for a two year Science Research Council the IAS in Princeton in the fall of 1993, received his Fellowship. She was a Lecturer at the University of Habilitation in Bonn in 1994. He then moved to chairs York (1972-76) and then at the University of Warwick in Freiburg in 1994 and at ETH Zürich in 1995. In 1996 (1976-78), and spent 1974-75 at MIT. She was on he became a director at the newly founded Max Planck the faculty of the State University of New York at Institute for Mathematics in the Sciences in Leipzig. In Stony Brook from 1978-2008, first as an Assistant 2008 he accepted an offer for the first Hausdorff chair Professor then as a Distinguished Professor, along the in Bonn. way serving as department Chair and undergraduate Director. She moved to Barnard College in 2007 to For this work on the theory of partial differential take up the Kimmel Chair of Mathematics. equations and their applications to continuum mechanics and the mathematical theory of Professor McDuff has been involved in educational microstructures he received a number of awards issues at undergraduate and graduate levels, as including the prize of the European Mathematical well as actively encouraging more women to study Society for young mathematicians in 1992, the Max mathematics. She has worked in symplectic topology Planck research prize in 1993, the Collatz prize of since the 1980s, has written over 90 papers and CICIAM in 1999 and the Leibniz prize in 2000. He is a co-authored three books with Dietmar Salamon, member of the Berlin-Brandenburg Academy and of most recently J-holomorphic curves and Symplectic the Leopoldina, the national academy of Germany. Topology. She has held visiting positions at the Institute for Advanced Studies, UC Berkeley, MIT, Harvard and Professor Cheryl Praeger at MSRI, in addition to serving on MSRI’s Scientific Advisory Committee (1990-98, Chair 1993-96). She Professor Cheryl E. Praeger is Professor has served on the MSRI Board of Trustees (1998-2002) of Mathematics and an Australian and she was elected Chair (1998-2001). Research Council Federation Fellow at the University of Western Australia Professor McDuff has been awarded numerous (UWA). She is Director of the Centre honours including the Ruth Lyttle Satter Prize of the for the Mathematics of Symmetry and American Mathematical Society in 1991 and honorary Computation at the School of Mathematics and doctorates from the Universities of Edinburgh (where Statistics, UWA. Her research interests are Permutation she was an undergraduate) and York. She was elected and Computational Group Theory, Algebraic Graph a Fellow of the Royal Society in 1994 and a Fellow of Theory, Combinatorial Design Theory and Finite the American Academy of Arts and Sciences in 1995; Geometry. She has around 290 mathematical she became a member of the US National Academy of publications including four monographs. Sciences in 1999. She is an Honorary Member of the London Mathematical Society and a corresponding Professor Praeger graduated with BSc (Hons) from member of the Royal Society of Edinburgh. The University of Queensland in 1969 and completed
International Review of Mathematical Science 60 Annex B: Members of the International Panel – Brief Biographies
her DPhil in 1973 at the University of Oxford. She Papers to mark the 50th year of the publication of received a DSc from UWA in 1989, and has been the oldest OR journal. He has presented his work in awarded honorary doctorates from the Prince of many plenary lectures and was the IFORS Distinguished Songkla University (Thailand) in 1993 and Universite Lecturer at the 2002 INFORMS meeting in San Jose. de Bruxelles (Belgium) in 2005. Professor Praeger was At that meeting he was also awarded the INFORMS a Research Fellow at the Australian National University Prize for the Teaching of OR/MS Practice. In 2003 he (1973-75). She held a lecturer/senior lecturer position was elected as a Fellow of the Royal Society of New at UWA from 1976 and was appointed Professor there Zealand and in 2005 was also elected as a Fellow in November 1983. At UWA she has been Head of of the Institute for Operations Research and the the Department of Mathematics, inaugural Dean of Management Sciences in the US. In 2004 Professor Postgraduate Research Studies, Deputy Dean of the Ryan served as a member of the International Review Faculty of Engineering, Computing and Mathematics, Panel for EPSRC sponsored Review of Research in OR and an Australian Research Council Professorial in UK Universities. Fellowship before taking up the Federation Fellowship in December 2007. Professor Andreas Schuppert
Professor Praeger is a Fellow of the Australian Professor Andreas Schuppert is Academy of Science (FAA) and a member of the Order Professor for Data Based Modelling in of Australia (AM). She has been President of the Computational Engineering Sciences at Australian Mathematical Society and is currently Chair Aachen Institute for Advanced Studies of the Australian Council of Heads of Mathematical in Computational Engineering Sciences Sciences, and Member-at-Large of the Executive (AICES) at RWTH Aachen University. Committee of the International Mathematical Union. Additionally he serves as key expert for industrial mathematics at Bayer Technology Services GmbH in Professor David Ryan Leverkusen, the technology company of Bayer AG. He received his diploma in Physics and his PhD in Professor David Ryan is Professor of mathematics from University Stuttgart in 1984 and Operations Research in the Department 1988 respectively. Additionally he has a degree in of Engineering Science and Deputy economics with focus on operations research. In 1988 Dean of Engineering at the University he joined corporate research of the former Hoechst of Auckland. He also holds an Adjunct AG and in 1998 he moved to corporate engineering of Professorial appointment at the Danish Bayer AG. Technical University in Copenhagen. Professor Ryan graduated in Mathematics from the University of His research is focused on data-based modelling in Otago in New Zealand and completed his PhD material sciences, chemical engineering and systems in Mathematical Programming at the Australian biology. His main ambition is development of hybrid National University in 1971. From 1972 to 1974, he model structures combining artificial intelligence model was a Research Fellow in Operations Research at the components with mechanistic models and system Atomic Energy Research Establishment in the UK. He structure. The application focus was on modelling of returned to a lecturing position in the Department of reactive chemical processes and materials. Today the Mathematics at the University of Auckland in 1975 main focus is the development of hybrid mathematical and transferred his appointment to the Department of approaches which enable quantitative, predictive Engineering Science in 1980. From 1996 to 2002, he models for clinical applications in treatment of complex was Head of the Department. diseases as well as optimisation and control of cellular engineering. He has worked widely in real-world applications of Operations Research and the development of He was member of the scientific advisory board of the optimisation based methods for the solution of WIAS Berlin and is member of the DECHEMA working scheduling problems particularly associated with group “Systems Biology and Synthetic Biology”. He is airline crew scheduling. In 2000 the Journal of the also a member of the scientific organisation committee Operational Research Society selected his original 1992 of the European Science Foundation forward look publication on airline rostering as one of five Milestone project “Industrial Mathematics”.
61 International Review of Mathematical Science Annex B: Members of the International Panel – Brief Biographies
Professor Ruth Williams at the University of Minnesota. She chaired the Scientific Program Committee for the World Congress Professor Ruth Williams is Distinguished in Probability and Statistics held in Singapore in 2008. Professor of Mathematics at the She was recently nominated to be the next President- University of California at San Diego. elect of the Institute of Mathematical Statistics, an She received her BSc (Honours) and MSc international professional society for the development degrees at the University of Melbourne and dissemination of the theory and applications of in 1977 and 1979 respectively and probability and statistics. she earned her PhD in Mathematics from Stanford University in 1983. She was a postdoctoral visiting member of the Courant Institute of Mathematical Sciences in 1983-84.
Professor Williams’ research interests are in probability theory, stochastic processes and their applications. As dynamic models for systems subject to random perturbations, stochastic processes are used in a wide variety of applications in science, engineering and economics. Professor Williams’ research includes foundational work on reflecting diffusion processes in non-smooth domains, co-development of a systematic approach to proving heavy traffic limit theorems for multiclass queuing networks, and the development of fluid and diffusion approximations for the analysis and control of more general stochastic networks. Her current research is focused in the latter area and includes work on stochastic networks models arising in Internet congestion control and systems biology.
Professor Williams is an elected member of the American Academy of Arts and Sciences, a Fellow of the American Association for the Advancement of Science, a Fellow of the Institute of Mathematical Statistics and a Fellow of the Institute for Operations Research and the Management Sciences. She has been a US National Science Foundation (NSF) Presidential Young Investigator (1987-93), an Alfred P. Sloan Fellow (1988-92), a Guggenheim Fellow (2001-2002) and was an invited speaker at the International Congress of Mathematicians held in Berlin in 1998.
She has served as an Associate Editor for the Annals of Probability, Annals of Applied Probability, SIAM J. on Applied Mathematics, Electronic Communications in Probability, Electronic J. of Probability, Probability Surveys, Bulletin of the American Mathematical Society, Mathematics of Operations Research and Stochastic Systems. She has served on a wide variety of committees for the University of California and the profession, including the UCSD Committee on Academic Personnel, the US National Committee on Mathematics and the Board of Governors of the Institute for Mathematics and Its Applications located
International Review of Mathematical Science 62 Annex C
Review Week Itinerary
Date Institution Participants Hosted by
Sunday 5 December 2010 Welcome / Briefing session
Sub-Panel A Monday 6 December 2010 University of Durham Durham, Leeds, Newcastle, York
Sub-Panel B Keele, Lancaster, Liverpool, Manchester, Queen’s University University of Manchester Belfast, Sheffield
Sub-Panel C University of Warwick Birmingham, Leicester, Loughborough, Nottingham, Warwick
Sub-Panel A Tuesday 7 December 2010 Aberdeen, Dundee, Edinburgh, Glasgow, Heriot-Watt, University of Edinburgh St Andrews, Strathclyde, ICMS
Sub-Panel B University of Bristol Bath, Bristol, Exeter, Reading, Southampton
Sub-Panel C University of Cambridge Cambridge, INI
Sub-Panel A Wednesday 8 December 2010 Oxford, Rutherford Appleton Laboratory, WIMCS and Welsh University of Oxford Universities
Sub-Panel B University College London Brunel, East Anglia, Kent, Surrey, University College London
Sub-Panel C Imperial College London Imperial College, King’s College, Portsmouth, Queen Mary
Full Panel met with high level industry representatives and then Thursday 9 December 2010 London convened at a venue near Heathrow
Agreed main findings and recommendations for future actions; Friday 10 December 2010 presented these to Steering Committee
Saturday 11 December 2010 Panel departed
63 International Review of Mathematical Science Annex D
Supporting Evidence and Information Provided
A range of supporting evidence and information was • ICMS provided to the Review Panel both before and during Keith Ball the review. This included: • Imperial College, London Overview: Funding of Science and Innovation in Ari Laptev the UK: This described the key developments that had • INI taken place concerning public funding arrangements David Wallace for science and innovation in the UK and provided a high-level overview of how the science budget • Keele University was secured and distributed. It also contained broad Rama Thirunamachandran descriptions of various Research Council mechanisms for supporting research and training. • King’s College London David Burns Background Data: This provided research council related grant and studentship data and information • Lancaster University about relevant activities and information on other Paul Fearnhead potential funders and collaborators. It was prepared as • a companion to ‘Funding of Science and Innovation in Loughborough University Chris Linton the UK’ to give more detailed contextual data relevant to Mathematical Sciences research in the UK. • Newcastle University Ian Moss Consultation Responses: As part of the preparation for the review a public consultation was held to gather • Queen Mary College evidence for the Panel. Responses were specifically David Arrowsmith invited from the institutions who visited the Panel, from others who did not visit the Panel and from any • Queen’s University Belfast other interested person/organisation via a public call Tony Wickstead on the EPSRC website. A standard template was used to ensure that submissions addressed the Evidence • Rutherford Appleton Laboratory Framework agreed by the Steering Committee. The Jennifer Scott Panel was provided with both a summary and the full • University College London text of all responses received. Responses were received Valerie Isham and Dimitri Vassiliev from: • University of Aberdeen Institutions/individuals: Dominic Houlihan • Brunel University • University of Bath Tony Rawlins Alastair King • Durham University • University of Birmingham Paul Mansfield David Needham • Heriot-Watt University • University of Bristol James Howie Guy Nason
International Review of Mathematical Science 64 Supporting Evidence and Information Provided
• University of Cambridge • University of Surrey Peter Haynes Mark Roberts
• University of Dundee • University of Warwick Mark Chaplain Colin Sparrow
• University of East Anglia • WIMCS David Evans Terry Lyons
• University of Edinburgh • University of York Michael Singer Stephen Donkin
• University of Exeter Other Stakeholders: Peter Ashwin • Aberystwyth University • University of Glasgow John Gough Nick Hill • The Acturial Profession • University of Kent Ruth Loseby Peter Clarkson • Bangor University • University of Leeds Ronald Brown Frank Nijhoff • Bangor University • University of Leicester D Shepherd Alexander Gorban • The British Academy • University of Liverpool Nigel Vincent Ian Jack • University of Cardiff • The University of Manchester Graham Hutchings Peter Duck • CORDIS Consulting European Commission • University of Nottingham Eduard Babulak Oliver Jensen • Defence Science and Technology Laboratory • University of Oxford Alan Robinson Christopher Voyce • Edinburgh Mathematical Society • University of Portsmouth Penny Davies David Wands • Ben Aston • University of Reading • Government Communications HQ (GCHQ) Simon Chandler-Wilde Confidential • University of Sheffield • Institute for Animal Health John Greenlees Simon Gubbins • University of Southampton • Institute of Food Research (BBSRC) James Vickers Jozsef Baranyi • University of St Andrews • Institute of Mathematics and its Applications Nik Ruskuc David Youdan • University of Strathclyde • K W Morton Stephen Wilson
65 International Review of Mathematical Science Supporting Evidence and Information Provided
• The London Mathematical Society Research Group submissions: Mathematical Sciences Fiona Nixon Research Groups at each institution with which the Panel met were requested to prepare in advance brief • London School of Economics details of their strategic plans and individual research Stuart Corbridge activities. A standard template was used to ensure that submissions addressed the Evidence Framework agreed • The Operational Research Society by the Steering Committee. The following Institutions/ Edmund Burke Consortia submitted details relating to the projects/ • Professor Peter Grindrod CBE CMath groups listed below:
• Royal Astronomical Society • Brunel University Robert Massey Mathematical Sciences
• Royal Holloway, University of London • Durham University Adam Tickell Mathematical Sciences
• Royal Statistical Society • Heriot-Watt University Martin Dougherty School of Mathematical and Computer Sciences
• Smith Institute • ICMS Keith Winters International Centre for Mathematical Sciences
• Swansea University • Imperial College, London Niels Jacob Mathematics
• UK Computing Research Committee • INI Ursula Martin Isaac Newton Institute for Mathematical Sciences
• University of Edinburgh • Keele University Andrew Ranicki Mathematics
• University of Oxford • King’s College London Andy Watham Mathematics
• University of Plymouth • Lancaster University Phil James Mathematics and Statistics, Management Science (OR group), Division of Medicine (CHICAS) • University of Salford Matt Boswell • Loughborough University Mathematical Sciences • University of Stirling Ian Simpson • Newcastle University School of Mathematics and Statistics • University of Sussex Robert Allison • Queen Mary College School of Mathematical Sciences • University of Sussex Omar Lakkis • Queen’s University Belfast Pure Mathematics Research Centre
• Rutherford Appleton Laboratory Numerical Analysis Group within the Computational Science and Engineering Department
International Review of Mathematical Science 66 Supporting Evidence and Information Provided
• University College London • University of Reading Mathematics; Statistical Science Mathematics and Statistics
• University of Aberdeen • University of Sheffield Institute of Mathematics School of Mathematics and Statistics
• University of Bath • University of Southampton Mathematical Sciences School of Mathematics
• University of Birmingham • University of St Andrews School of Mathematics School of Mathematics and Statistics
• University of Bristol • University of Strathclyde School of Mathematics; Engineering Mathematics Management Science; Mathematics and Statistics
• University of Cambridge • University of Surrey Pure Mathematics and Mathematical Statistics; Mathematics Applied Mathematics and Theoretical Physics • University of Warwick • University of Dundee Statistics; Operational Research & Management Division of Mathematics Sciences; Mathematics Institute
• University of East Anglia • WIMCS School of Mathematics Institute of Mathematics and Physics, Aberystwyth University; Cardiff School of Mathematics, Cardiff • University of Edinburgh University; Mathematics and Statistics, University of School of Mathematics Glamorgan; Mathematics, Swansea University
• University of Exeter • University of York Mathematics Mathematics
• University of Glasgow The following international and UK collaborating School of Mathematics and Statistics bodies made representatives available to the Panel during their meetings with the institutions and • University of Kent at a separate meeting with the Panel for user School of Maths, Statistics & Actuarial Science representatives: • University of Leeds School of Mathematics Arup
• University of Leicester BAE Systems Mathematics; Computer Science Biomathematics and Statistics Scotland (BioSS) • University of Liverpool Blizard Institute of Cell & Molecular Science, Barts & Mathematical Sciences The London School of Medicine & Dentistry • The University of Manchester Defence Science and Technology Laboratory Mathematics Department for Business, Innovation and Skills • University of Nottingham School of Mathematical Sciences GlaxoSmithKline
• University of Oxford John Innes Centre Mathematical Institute, Statistics JP Morgan • University of Portsmouth Institute of Cosmology and Gravitation Lloyds Banking Group
67 International Review of Mathematical Science Supporting Evidence and Information Provided
Marine Scotland – Science
The Meterological Office
National Air Traffic Control Service (NATS)
National Grid
Numerical Algorithms Group (NAG)
Ocado
Pfizer
RSPB
Scottish Financial Risk Academy
Syngenta
University of Alberta
Vodafone
Willis Research Network
International Review of Mathematical Science 68