International Review of Mathematics
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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;