EPSRC Review of Mathematical Sciences Infrastructure

Review Working Group

 Professor Alan Champneys, University of Bristol  Professor Ken Brown, University of Glasgow  Professor Paul Milewski, University of Bath  Dr Richard Pinch, GCHQ  Professor Sofia Olhede, UCL

EPSRC support for the review: Dr Christopher White, Dr Philippa Hemmings, Dr Laura Watkin, Dr Michael Ward, Dr Katharine Moore, Mr David O’Gorman

Summary

In 2014 a group was set up consisting of a subset of the Mathematical Sciences Theme Strategic Advisory Team and other relevant experts in the area to review the current UK mathematical sciences infrastructure. Throughout the evidence gathering stages of the review the working definition of mathematical sciences infrastructure was given as the following:

“Longer-term funding to enable collaboration and development of interconnections of the mathematical sciences community, current existing examples include but are not limited to the Isaac Newton Institute, LMS-Durham Symposium and Taught Course centres. Past examples include the Study Groups with Industry.”

The definition was purposefully broad to encourage a broad response to the survey questions. However currently, and over the period of the review, EPSRC funds four activities which are considered infrastructure in this context and form the focus of this review:

 Isaac Newton Institute  International Centre for Mathematical Sciences  Durham Symposia  Warwick Symposium

The main recommendations of the report are:

1. Mathematical infrastructure is fundamentally important for mathematical sciences research and should continue to be supported broadly at the current level.

2. The Isaac Newton Institute and International Centre for Mathematical Sciences are highly regarded and highly important activities which offer a suitable variety of high quality scientific and knowledge exchange activities.

3. We would like the funding for the named symposiums to achieve a more dynamic broader approach and to encourage more flexibility (e.g. length of activity and geographical

1 location). We would encourage more ambition, breadth and diversity, and a well-defined, consistent and well-advertised mechanism for funding these symposia.

4. Aspects of the current models which could be improved include support for the talent pipeline and better engagement with early career researchers, as hinted by the survey. Infrastructure facilities should have the explicit aim of improving diversity in participation, for example the current average female participation rate of 16% should be significantly increased.

5. The balance of longer term and shorter term programmes needs to be considered systemically and be effectively managed at the UK level.

6. If additional funding were available then a retreat in the style of Oberwolfach would be encouraged, but not at the expense of the current infrastructure in the UK.

7. EPSRC should consider options for how mathematical infrastructure is funded in the future whilst taking the above points into consideration.

Introduction

The review was initiated by a meeting of a sub group of the Strategic Advisory Team in June 2014 to discuss the value of mathematical sciences infrastructure to the UK. It became apparent that there had been no recent review or collective assessment of the mathematical sciences infrastructure in the UK. This meant that there were no specific indicators of the quality, importance and impact of the investment. Without this evidence it would be difficult to make informed strategic decisions on future investments. The review was initiated and the working group’s membership was expanded to better reflect the expertise supported by the Mathematical Sciences Theme, from the initial Strategic Advisory Team members, to include Professor Sofia Olhede. The review was carried out by EPSRC staff across several work streams and the synthesis of these was presented to the working group on the 29th June 2015. The data presented, conclusions and recommendations from this meeting are found within this document and the Annex.

Methodology

The meeting of the sub group of the Strategic Advisory Team in June 2014 identified four major themes to focus the review.

 What are the best ways to support connectivity/interactions across the mathematical sciences, and connections between mathematical sciences and other areas of science and engineering?  What is the current portfolio/landscape of connectivity/interaction activities in the mathematical sciences in the UK?  What models might exist for the longer term benefit of the UK?  What does success look like; and how do we measure it?

Following this initial meeting EPSRC carried out an options analysis for delivering the review. This was then presented to the Review Working Group, which met for the first time in December 2014. The decision was made to progress to an evidence gathering phase to address questions posed across several strands. The group met again to discuss the findings and make recommendations. The final meeting of the working group was on 29th June 2015 and following this, the draft conclusions and recommendations were shared with the broader Mathematical Sciences Theme Strategic Advisory Team in July 2015. The conclusions and recommendations were agreed; these are published in this document together with supporting data.

Explanation of the data and the information supplied to the working group

The following describes the different strands of evidence gathering and explains how this was presented to the working group.

Open Community Survey The survey opened on 14th April 2015 and closed on 18th May 2015. The link was publicised on the EPSRC website and in addition was circulated directly to the following groups:

 Review Working Group  EPSRC Mathematical Sciences Strategic Advisory Team  UK Heads of Department  EPSRC Mathematical Sciences Theme Early Career Forum  Council for Mathematical Sciences

Annex 4 contains a synthesis of the results of the survey. Overall 256 completed responses were received, as well as 111 blank responses, 138 partially completed responses and 7 duplicate responses.

Pro Forma The pro-forma was sent to representatives of the following existing components of the mathematical sciences infrastructure on 9th April 2015, with a deadline for completion of 21st May 2015:

 Isaac Newton Institute  International Centre for Mathematical Sciences  Durham Symposia  Warwick Symposium  Study Groups with Industry

Completed pro-forma documents were received from all. These confidential responses are not shared as part of this review. However the questions that were asked can be found in Annex 1.

Review of Overseas Infrastructure A desk exercise was completed to provide an overview of comparable mathematical infrastructure found in France, Germany, Canada and USA. The results are presented in Annex 3.

Summary of Current EPSRC Mathematical Sciences Infrastructure Annex 2 outlines the last 10 years of funding for each component of the EPSRC mathematical sciences infrastructure. It also gives some information regarding which panels considered the more recent grants, and includes a diagram of when the current grants finish.

Conclusions and recommendations of the working group

Conclusions

1. Mathematical sciences Infrastructure has been shown to be of great importance to UK Mathematics – it acts much like infrastructure features (labs etc) of other disciplines, in that it facilitates the creation of new mathematics & also is a vital mechanism for bringing together mathematical sciences and other disciplines. This is a core mechanism for linking mathematicians across the subfields of mathematical sciences, and also for connecting mathematical scientists with those working in other fields, including government and industry.

2. The EPSRC funded infrastructure is in two clear categories:

 The International Centre for Mathematical Sciences and the Isaac Newton Institute show clear, broad and deep engagement of and with the community as a whole, and an appropriate framework for broader impact.  With regard to the named symposia, Durham and Warwick, the degree of competitive testing of the delivered activities, and the range of potential activities from which they were selected, were not consonant with the level of Research Council funding being committed to them. Future funding for any such activities would benefit from more competitive tensioning against a wider selection of competing bids.

3. The primary aims of the Taught Course Centres relate to training rather than research and so were deemed out of scope for this review.

4. The Study Groups with Industry are not currently EPSRC funded. These are widely recognised as being valuable for industrial engagement with the mathematical sciences and for student training. There is only anecdotal evidence on the value of this activity for the generation of new mathematics and it was felt that more work is required to make the case for the benefits of the Study Groups to the core mathematical sciences community.

5. This review did not cover the Alan Turing Institute nor the Heilbronn Institute. These are considered as important parts of the research infrastructure landscape.

6. Given the challenging funding landscape, the amount of spend is felt to be about right (as a proportion of the budget of mathematical sciences at EPSRC). There are examples of good practice of bringing in matched funding of up to 100%.

7. The current balance of longer to shorter programmes would benefit from careful consideration. There is perhaps a need for more shorter to medium term activities.

8. There is a need to find more effective ways of enabling dialogue and communication between EPSRC and the UK mathematical sciences research community on how to create

and deliver infrastructure. Especially obtaining the view of younger researchers, and completing PhD students would be valuable, as they are less able to create their own infrastructure.

9. For our two international centres (International Centre for Mathematical Sciences and the Isaac Newton Institute) there needs to be longevity and continuity of funding.

10. The named symposia (Durham and Warwick) have a historic concentration in two geographical locations, which has been detrimental to diversity and agility.

11. The current model could do better as regards encouraging diversity of participation and in supporting the talent pipeline. There are a number of different aspects to diversity, including mathematical sciences research area; gender; career stages. Mechanisms for increasing diversity could include more support for early career researchers, funded childcare facilities etc. The UK’s funded mathematical sciences infrastructure should, for example, be performing better with respect to gender participation rates, currently between 13% – 30%.

12. The evidence showing the flow of industrial problems influencing mathematical sciences was patchy, and the working group would recommend initiating mechanisms to encourage a healthy two way flow. There is considerable scope to increase support in this area in partnership with other agencies; there is opportunity in particular areas such as data science as well as in specific industrial sectors. There needs to be deeper and wider community involvement, coordination and governance across this area.

13. The working group investigated existing international activities and concluded that the UK is overall doing well, with a range and quality of mathematical infrastructure that stands up well to international comparison.

Overall Conclusions and Next Steps

The process and feedback via the survey emphasised the great importance of infrastructure to the mathematical sciences community. The review has identified that there is a broad range of activities being undertaken by mathematical sciences infrastructure in the UK. While much of this is found to be excellent, well used and useful, the review has established that there are features, attributes and activities that can be improved upon.

The outcomes of this review are envisaged to occur in two phases. The first is the communication of the principles outlined within this document, to encourage buy-in from the community. The second phase will involve EPSRC implementing changes to the mechanisms by which it supports the mathematical sciences infrastructure. EPSRC will begin to consult on this second phase shortly.

Annex 1 - 4

Contents Page:

Annex 1: Mathematical Sciences Infrastructure Pro Forma Questions (pages 2 – 3)

Annex 2: Summary of Current EPSRC Mathematical Sciences Infrastructure (pages 4 – 6)

Annex 3: Overseas Infrastructure Summary (pages 7 – 26)

Annex 4: Review of Mathematical Sciences Infrastructure Community Survey Summary (separate document)

1) Mathematical Sciences Infrastructure Pro Forma Questions

Existing mathematical infrastructure centres are encouraged to complete this form and answer all questions. Where questions are more fully answered elsewhere i.e. in annual reports, please reference or link to these documents and provide a brief summary on the pro-forma. We expect answers to take the last 5 years of funding/activity into consideration.

We ask that answers are provided under the heading below and submissions (including references) should not be more than 5 pages in length of reasonably formatted text and/or diagrams.

Q.1. How many person days are being funded per year? Can you provide an average per year breakdown of these participants by:

 Career stage  Geographic spread (Home institution/Other UK/International)  Place of work (Academic/government/industry)  Gender  Academic disciplines

Q.2. Please describe the types of activity that you support.

Q.3. How many applications for programmes do you receive in an average year? What is the rejection rate?

Q.4 What other funding over and above any core funding from the EPSRC/Research Councils have you attracted?

Q.5. What are your success criteria and how do you measure & assess yourself against them?

Q.6. What current methods do you use to measure Impact and how do you assess yourself against them?

Q.7. How do you engage non-academic users of research?

Q.8. How do you seek to enhance interactions between academic and non-academic user communities?

Q.9. What would help to enhance the delivery of the mathematical infrastructure in the UK? 3

Q.10. List three things you would like to engage in if you received significant additional funding.

2) Summary of Current EPSRC Mathematical Sciences Infrastructure

Submission Start Finish Amount Panel

Isaac Newton Institute GR/N09114/01 01-Mar-02 29-Feb-08 £1,842,750.00 GR/S31174/01 01-Mar-05 29-Feb-08 £1,322,891.00 EP/F005431/1 01-Mar-08 28-Feb-14 £9,733,806.00 Visiting Panel

EP/I016392/1 01-Sep-11 28-Feb-14 £443,221.00 Visiting Panel

EP/K032208/1 01-Mar-14 28-Feb-18 £5,957,239.00 Interview Panel

ICMS GR/T19827/01 01-Nov-04 31-Oct-08 £738,441.00 EP/F039522/1 14-Sep-07 01-Oct-08 31-Dec-12 £1,794,740.00 Visiting Panel EP/J018074/1 09-Nov-11 01-Oct-12 30-Sep-16 £1,629,559.00 Programme Grant Interview

Durham Symposia EP/D040027/1 30-Jun-06 29-Apr-07 £57,042.00 EP/E048676/1 18-Jun-07 17-Nov-07 £41,936.00 EP/E048595/1 18-Jun-07 17-Nov-07 £70,403.00 EP/F013914/1 19-Mar-08 18-Jan-09 £69,435.00 5

EP/F036477/1 10-Jun-08 09-Apr-09 £77,434.00 EP/F068751/1 29-Apr-09 27-Feb-10 £83,079.00 EP/G008485/1 19-Jun-09 18-Apr-10 £78,081.00 EP/G066736/1 11-Dec-08 01-Mar-10 28-Feb-14 £631,431.00 Responsive Mode Main List EP/K040154/1 13-Dec-12 01-Mar-14 28-Feb-18 £629,652.00 Responsive Mode Main List

Warwick EP/D075130/1 01-Sep-06 31-Aug-09 £121,775.00 EP/E060382/1 15-Aug-07 14-Aug-10 £164,568.00 EP/F032323/1 01-Sep-08 31-Aug-11 £206,853.00 EP/G021163/1 01-Sep-09 31-Aug-11 £243,956.00 EP/F032323/1 01-Sep-08 31-Aug-11 £206,853.00 EP/H022171/1 01-Sep-10 31-Aug-12 £190,078.00 EP/I014829/1 01-Sep-11 31-Aug-13 £206,586.00 EP/J009660/1 01-Sep-12 31-Aug-13 £135,360.00 EP/K015400/1 17-Aug-12 01-Sep-13 31-Aug-14 £148,681.00 Responsive Mode Main List EP/L018314/1 21-Aug-13 01-Sep-14 31-Aug-15 £159,849.00 Responsive Mode Main List EP/M003620/1 14-Mar-14 01-Sep-15 31-Aug-16 £161,542.00 Responsive Mode Main List

3) Overseas Infrastructure Summary: Trends and Observations

The document detailing the overseas infrastructure in mathematical sciences shows that throughout Europe and North America, a variety of funding routes are used for different institutes and centres in the mathematical sciences. In comparing maths infrastructure in Europe and North America, it can be said that although public funding is seen in all institutions/centres discussed, the European countries seem more heavily reliant on public funding than in North America. The infrastructure examined in North America seems to have funding from a wider variety of sources, in particular industrial funding and donations. For example, of the 5 examples of maths infrastructure in the UK discussed only two have financial support from industry. In France and Germany, this figure is one out of six. However, it should be mentioned that in Germany several of the institutions have funding from donations and generate their own revenue. In contrast, out of the 12 examples of maths infrastructure in the USA, half of them are partly funded by money from industry.

In the case where the NSF is not the major funder, a large proportion of mathematical activities in the USA are funded by donations such as the Institute for Advanced Study where a $100 million grant was given by two Foundations as an endowment. Another example is the Clay Institute which operates as a privately funded foundation. This type of funding mechanism, as well as substantial support from industry, is far less apparent in the UK and the rest of Europe.

In terms of the range of mathematical activities occurring in different countries, it is clear most countries discussed have infrastructure in place to support a variety of different mathematical activities. These include general research activities, workshops, networking events, summer programmes and symposia. However, in drawing out difference between the different countries it could be said that Germany tends to favour centres more focussed on mathematical research, due to its emphasis on Max Planck Institutes, in comparison to France, the UK, USA and Canada. As the USA has the greatest number of institutions/centres it is perhaps not surprising that they seem to have the greatest range of mathematical activities including research, networking, outreach, training, mathematical publications and summer programmes.

It is interesting to note that there seem to be a substantial number of collaborations between universities and institutions in mathematical infrastructure worldwide. For example, in Germany there is substantial overlap between the Max Planck Institute for Mathematics (Bonn) and other centres such as the Hausdroff Research Institute for Mathematics and the Bonn International Graduate School in Mathematics. In France, the Institut Henri Poincaré together with the INSMI organizes exchanges between networks through specific CNRS tools such as international joint units, international associated laboratories and international research networks. The Statistical and Applied Mathematical Sciences Institute in the USA is a partnership between Duke University, North Carolina State University (NCSU), the University of North Carolina at Chapel Hill (UNC) and the National Institute of Statistical Sciences (NISS), in 8

collaboration with the William Kenan, Jr. Institute for Engineering, Technology and Science. Finally, the Institut des sciences mathématiques (ISM) is a consortium of nine universities in Québec (Concordia University, HEC Montréal, Laval University, McGill University, the Université de Montréal, UQAM, UQTR, Université de Sherbrooke and Bishop's University) for training and collaboration in the mathematical sciences. This range of collaboration must be viewed positively in advancing mathematical research both within individual countries and globally.

Overseas Infrastructure in Mathematical Sciences

Contents 1. Germany ...... 10 1.1. Mathematisches Forschungsinstitut Oberwolfach ...... 10 1.2. Max Planck Institute for Mathematics in the Sciences (Leipzig) ...... 11 1.3. Hausdorff Centre for Mathematics ...... 12 1.4. Max Planck Institute for Mathematics (Bonn) ...... 14 1.5. Fachinformationszentrum Karlsruhe - Leibniz Institute for Information Infrastructure ...... 14 1.6. The Bethe Center for Theoretical Physics ...... 15 2. France ...... 15 2.1. Institut des Hautes Études Scientifiques (IHÉS) ...... 15 2.2. INSMI National Institute for Mathematical Sciences ...... 16 2.3. Institut Henri Poincare ...... 16 2.4. Centre International de Rencontres Mathématiques (CIRM) ...... 16 2.5. Toulouse Mathematics Institute ...... 17 2.6. The Foundation Sciences Mathématiques de Paris ...... 17 9

3. USA ...... 17 3.1. The American Institute of Mathematics ...... 17 3.2. Institute for Advanced Study ...... 18 3.3. Clay Institute ...... 18 3.5. DIMACS – Centre for Discrete Mathematics & Theoretical Computer Science ...... 19 3.6. IPAM – Institute for Pure and Applied Mathematics ...... 19 3.7. Mathematical Association of America ...... 19 3.8. Mathematical Reviews ...... 20 3.9. MBI – Mathematical Biosciences Institute ...... 20 3.10. MSRI – Mathematical Sciences Research Institute ...... 20 3.11. SAMSI – Statistical and Applied Mathematical Sciences Institute ...... 21 3.12. Courant Institute of Mathematical Sciences ...... 21 4. Canada ...... 22 4.1. Fields Institute ...... 22 4.2. Centre de Recherches Mathématiques ...... 23 4.3. Banff International Research Station ...... 23 4.4. Atlantic Association for Research in the Mathematical Sciences ...... 24 4.5. The Institut des sciences mathématiques...... 24 4.6. Mathematics of Information Technology and Complex Systems ...... 24 4.7. Pacific Institute for the Mathematical Sciences ...... 25

1. Germany

1.1. Mathematisches Forschungsinstitut Oberwolfach Long-term decisions concerning funding are shared with the German federal government and the governments of the states of Germany; however the emphasis for funding is on the local state of Baden-Württemberg. Non-profit association Förderverein (Friends of Oberwolfach) provide support for the maintenance of the buildings, support for the library and travel support for participants of meetings. The Oberwolfach Stiftung (Oberwolfach Foundation) also provides support and financial assistance for projects and financing of infrastructural facilities of the MFO. A subsidiary of the Oberwolfach Foundation is the Horst Tietz Fund, which is dedicated to provide further financial support, targeting previous alumni and to guarantee its independence. Financial support was provided by the Volkswagen Stiftung (Foundation), Germany‘s largest private research funding foundation. Other funders include the Marga und Kurt Möllgaard-Stiftung, Carl Friedrich von Siemens Stiftung, Simons Foundation, Klaus Tschira Stiftung, Daimler-Fond, the European Union, Japan Association for Mathematical Sciences, Clay Mathematics Institute, European Science Foundation, Deutsche Forschungsgemeinschaft Bundesministerium für Bildung und Forschung, and the National Science Foundation.

The Mathematisches Forschungsinstitut Oberwolfach runs weekly workshops with about 45-48 participants. Sometimes there are two workshops of half the size (about 24 participants) taking place in one week. In addition, there are fixed weeks for mini-workshops (consisting of about 15-16 participants every year), study groups (arbeitsgemeinschaft) biannually and seminars. Recent events in the last month include Cohomology of Finite Groups: Interactions and Applications Tropical Aspects in Geometry, Topology and Physics, Multivariate Splines and Algebraic Geometry, Mirror Symmetry, Hodge Theory and Differential Equations, and the Mathematical Theory of Water Waves. “Research in Pairs” projects are undertaken at the institute, which involves small groups of researchers (between 2 and 4 people) lasting between 2 weeks to one month. Projects from all areas of mathematics can be supported by this programme; in particular, interdisciplinary co-operation is encouraged.

The Oberwolfach Foundation and the Mathematisches Forshungsinstitut Oberwolfach bestows the Oberwolfach Prize every three years to honour outstanding achievements in changing fields of mathematics, and the John Todd award is awarded every three years to mathematicians working in numerical analysis. 11

1.2. Max Planck Institute for Mathematics in the Sciences (Leipzig) Founded in 1996, the Max Planck Institute for Mathematics in the Sciences works closely with the University of Leipzig, and was set up to recognise the ‘mathematisation’ of the sciences and significant developments in mathematical analysis and geometry.

The German federal government together with the state governments each assume half of the funding for the budget of the Max Planck Society (budget A). The calculation of the financial contributions provided by the states is based on a distribution formula that is re-calculated each year as well as on the "home state quota", which has been steady at 50 per cent since the year 2000. In addition, all partners may agree to provide extra funding in addition to the specified quotas.

The exception to this is the Max Planck Institute for Plasma Physics, which is funded by the German government and the states of Bavaria and Mecklenburg Western Pommerania in a ratio of 90:10 (budget B) in accordance with regulations for major research institutions. In addition, this institute receives subsidies from EURATOM for a joint research program within the scope of association agreements.

In addition to the grants provided by the German federal government and its states for institutional support, the Max Planck Society receives project funding from the German government and state ministries, from the European Union, grants from private individuals, in the form of membership fees, donations and remuneration for services rendered.

Its special focus encompasses the following:

- Riemannian, Kählerian and algebraic geometry including their interrelation with modern theoretical physics - mathematical models in material sciences (microstructures, micromagnetism, homogenisation, phase transitions, refraction phenomena, interfaces and thin films) - continuum mechanics (the theory of elasticity and hydro- and gas dynamics) - many-particle systems in statistical physics and neural networks - general relativity theory and quantum field theory - problems of mathematical biology - scientific computing 12

A subsidiary of the Institute is the International Max Planck Research School Mathematics in the Sciences (IMPRS), which offers PhD fellowships for students with an excellent background in mathematics or related fields. It is a cooperation of the Max Planck Institute for Mathematics in the Sciences, the Mathematics and Computer Sciences, the Department of Physics and the Research Academy of the University of Leipzig.

Collaboration ties abroad exist with the ETH (Eidgenössische Technische Hochschule) in Zurich (Switzerland), IHES (Institut des Hautes Études Scientifiques, Bures-sur-Yvette, France), the Newton Institute in Cambridge (UK), the Courant Institute, New York (USA), and the IMA (Institute for Mathematics and its Applications) in Minneapolis, Minnesota (USA).

1.3. Hausdorff Centre for Mathematics Described as a cluster of excellence, the Hausdorff Centre for Mathematics was established in 2006 at the University of Bonn by the German federal and state governments, and has been renewed for a second funding period in 2012. Its work thematically comprises a broad spectrum of mathematics as well as mathematical economics: from topics from the classical core areas of mathematics through mathematical modelling and numerical simulation in the natural and social sciences to industrial applications in chip design. Bonn has internationally leading groups in pure mathematics, with foci on arithmetic and algebraic geometry, representation theory, global and harmonic analysis, differential geometry and topology, is strongly represented at the Mathematical Institute and the Max Planck Institute for Mathematics; applied mathematics is represented in applied and stochastic analysis at the Institute for Applied Mathematics, with numerical analysis and scientific computing at the Institute for Numerical Simulation, and with discrete mathematics in the strongly application oriented Research Institute for Discrete Mathematics; moreover, the Institute for Economics and Social Sciences has very mathematically oriented groups in game theory, econometrics, and mathematical finance.

The structure of the institute is shown below, consisting of two institutes (Hausdroff Research Institute for Mathematics and the Bonn International Graduate School in Mathematics. 13

Figure 1.1 - Structure of the Hausdorff Centre for Mathematics (from HCM website)

1.4. Max Planck Institute for Mathematics (Bonn) Belonging to the Max-Planck-Gesellschaft zur Förderung der Wissenschaften e.V (Max Planck Society), the MPI for Mathematics is a research institute for predominantly pure mathematics.

The working areas are: algebraic groups, arithmetic geometry, number theory, representation theory, algebraic and complex geometry, differential geometry and topology, algebraic topology, global analysis, non-commutative geometry, dynamical systems, and mathematical physics.

The guest program involves working at the institute for a fixed, a key concept of the MPI of mathematics, distinguishing the institute from other Max Planck Institutes. The time of stay ranges from weeks to several months. Scientists often combine their stay with e vents such as conferences and workshop activities. The graduate program of the Max Planck Institute for Mathematics in Bonn (MPIM), known as the International Max Planck Research School on Moduli Spaces (IMPRS), is jointly offered with the University of Bonn. It is part of the Bonn International Graduate School in Mathematics (BIGS-Mathematics). The IMPRS is sponsored by the Max Planck Society.

The academic training program of the IMPRS Moduli Spaces consists of courses, mini-courses, seminars and special activities in areas such as arithmetic geometry, modular forms, Riemannian geometry and topology. The institute forms part of the Hausdorff Centre of Mathematics in Bonn.

1.5. Fachinformationszentrum Karlsruhe - Leibniz Institute for Information Infrastructure The FIZ Karlsruhe is a non-profit corporation and the largest non-university institution for information infrastructure in Germany, with the aim of supplying scientists and companies with professional research and patent information as well as to develop innovative information services. As a ‘key player’ in the information infrastructure they pursue their own research program and also cooperate with leading universities and research associations. The FIZ Karlsruhe has been developing and operating databases and information for scientific communities, and has developed zbMATH, a reference service for mathematical research, compiled by a global network of academics.

Since its foundation, the FIZ Karlsruhe has jointly been funded by the German Federal Government and the Federal States. However, 78% of FIZ Karlsruhe’s budget is financed by its own revenues. The funding partners are the Federal Republic of Germany, Baden-Württemberg, the Max Planck Society for the Advancement of Science (MPG), Fraunhofer Society for the Advancement of Applied Research (FhG), German Physical Society (DPG), Association of German Engineers (VDI), Gesellschaft für Informatik (GI), and Association of German Mathematicians (DMV).

1.6. The Bethe Center for Theoretical Physics The Bethe Center for Theoretical Physics is a joint enterprise of theoretical physicists and mathematicians at various institutes of the University of Bonn, and fosters research activities, with the mathematical focus on mathematical physics, algebraic geometry and topology and partial differential equations. They provide short and long term visitors program, workshops on dedicated research topics, regular Bethe Seminar series and lectures for doctoral students. The centre has research groups in complex geometry, number theory, modular forms and moduli spaces, and string theory and mathematical physics.

2. France

2.1. Institut des Hautes Études Scientifiques (IHÉS) Founded in 1958, the IHES boasts significant achievements in mathematics and theoretical physics. Its mission is to encourage theoretical research in mathematics, physics, human sciences methodology and any other related theory based discipline.

The French Ministry has supported IHÉS since 1964 and today, the Ministry for Higher Education and Research awards the Institute an annual grant, representing about half of its budget. The Institute has also benefitted from support for major renovation and refurbishment work in offices and accommodation units. Funders of the renovation include Sénat – the upper house of the French Parliament, Conseil Régional Ile de France – the Greater Paris regional authority, and the Conseil Général de l’Essonne – the local departmental authority).The National Center for Scientific Research also supports the Institute by providing staff members based at IHÉS. The campaign committee sets IHES’s international fundraising strategy, and the ‘Friends of IHES’ public charity handles gifts for American tax residents. EPSRC has also provided funding since 1971.

Current residents of the institute include Misha Gromov (geometry, quantum field theory), Maxim Kontsevich (quantum theory, algebra), Laurent Lafforgue (galois theory, algebraic geometry), Alain Connes (algebra and geometry, number theory), Ofer Gabber (algebra and geometry), Christophe Soule (algebraic geometry) and Ahmed Abbes (algebraic geometry).

IHÉS regularly organises conferences, open days and receptions, which are open to the public. 16

2.2. INSMI National Institute for Mathematical Sciences The CNRS National Institute for Mathematical Sciences (INSMI) seeks to promote excellence in French mathematics by managing and coordinating a network of research units, national interest organizations and international laboratories. France's mathematics community boasts a number of tools solely or jointly managed by INSMI, including international centres (the Institut Henri Poincaré and Centre International de Rencontres Mathematiques in Luminy), documentary resources (the Bibliothèque d’Orsay (Orsay library), the Reseau National des Bibliothèques de Mathématiques (RNBM), the Cellule MathDoc), and networks such as the “Mathrice” network and the Calcul group.

2.3. Institut Henri Poincare Henri Poincaré Institute (HPI), created in 1928, is one of the oldest and most active international bodies dedicated to mathematics and theoretical physics, and regularly conducts seminars, exhibitions, conferences and working groups aimed at the wider community. More technical, specialised seminars in algebra, number theory, elliptical curves etc. are also undertaken, in collaboration with societies. A feature of the IHP is their ‘Thematic Quarters’ calls, to develop in-depth thinking on a cutting-edge research topic over a three-month period, and its support of PhD students. In addition to a large number of voluntary partnerships and collaboration agreements, INSMI organizes exchanges between networks through specific CNRS tools such as international joint units, international associated laboratories and international research networks.

2.4. Centre International de Rencontres Mathématiques (CIRM) Placed under the scientific administration of Société Mathématique de France (SMF) and of the Institut des Mathématiques et de leurs Interactions (INSMI) CNRS, CIRM receives yearly funding also from the French Ministry of Research and Higher education and from the contributions of conference participants. For exceptional projects, such as the construction of a new building, CIRM has received support from external sources such as local public authorities: the City of Marseille, the ‘Conseil Général des Bouches-du-Rhone’and the ‘Region Provence-Alpes-Côte d’Azur’.Funding is split between the daily running of the centre and grants awarded to subsidize conferences, workshops and other mathematical events held at CIRM.

CIRM supports various kinds of mathematical events throughout the year. These include large conferences/workshops and thematic sessions, which last about a week, with between 60 and 95 participants; CIRM subsidizes board and lodging for 40 people not based in the region. Large winter/summer 17

schools, lasting for one week host between 60 and 95 participants; mainly young researchers and Ph.D. students, which CIRM subsidizes board and lodging for 40 people not based in the region). The institute also hosts small groups (one week; up to 19 participants; self-funded), and research in pairs programs (2 to 3 researchers for 2 to 3 weeks), which CIRM subsidizes board and lodging for people not based in the region).

2.5. Toulouse Mathematics Institute The Toulouse Mathematical Institute, CNRS Research Laboratory, is comprised of three main teams: 1) Partial differential equations, numerical analysis and optimisation, 2) pure mathematics and 3) statistics and probability. The Laboratory of Statistics and Probability, the Mathematics for Industry and Physics Laboratory and the Emile Picard Laboratory, located at the University of Toulouse III, the Universities of Toulouse I and II, and the Institut National des Sciences Appliquees. It is host to long and short term foreign visitors from all over the world, and all mathematical backgrounds. The IMT is responsible for the Fermat Prize and the Annales de la Faculté des Sciences de Toulouse.

2.6. The Foundation Sciences Mathématiques de Paris The Foundation Sciences Mathematiques de Paris is a network of excellence created in 2006. Its members are large research institutions in the Paris area: the University of Pierre-et-Marie-Curie (UPMC), the University of aris-Diderot (UPD P7), the Ecole Normale Supérieure (ENS), the National Center for Scientific Research (CNRS), the University of Paris-Dauphine, the Collège de France, the INRIA, the University of Paris-Descartes and the University of Paris Nord. The foundation holds annual events, symposia, and lectures.

3. USA

3.1. The American Institute of Mathematics Established in 1994 by businessman and mathematics enthusiast John Fry, the American Institute of Mathematics is one of the NSF Mathematical Sciences institutes, located in San Jose, California, after recently moving from its original Palo Alto location. AIM receives major funding from the National Science Foundation, the PGA Tour and Fry's Electronics. AIM’s research program, known as Squares (Structured Quartet Research Ensembles) allow a dedicated group of four to six mathematicians to spend a week at the institute, with the option of returning in following years, with the research being carried out in 18

all areas of pure and applied mathematics, and hosts colloquiums, conferences, seminars and defences. AIM does not have a set budget, but in the past year it has spent about $300,000, all of it donated by Fry. AIM’s idea is to create a conference centre similar to the well-known one at Oberwolfach in the Black Forest in Germany.

3.2. Institute for Advanced Study The Institute is a private, independent academic institution located in Princeton, New Jersey. Work at the Institute takes place in four Schools: Historical Studies, Mathematics, Natural Sciences, and Social Science. The School of Mathematics is an international center of research and postdoctoral training in many diverse aspects of mathematics including pure mathematics, theoretical computer science, mathematical physics and applied mathematics. Currently, a permanent Faculty of approximately thirty academics guide the work of the Schools and each year awards fellowships to some two hundred visiting Members, from about one hundred universities and research institutions throughout the world. Dr. Robbert Dijkgraaf is the current Director of the Institute. The School of Mathematical Sciences holds conferences, workshops, seminars, and special programs. These special programs are Theoretical Computer Science and Discrete Mathematics, School of Mathematics 75th Anniversary Celebration, Women and Mathematics, and The Practice of Mathematics. Funders for the IAS includes the NSF and the Ambrose Monell Foundation, however the Institute received a $100 million unrestricted challenge grant from the Simons Foundation and the Charles and Lisa Simonyi Fund for Arts and Sciences in 2011 to strengthen the Institute’s endowment. Endowments contribute to 80% of the Institutes operating expenses, and funds can be donated as a gift, or to establish a special call/program.

3.3. Clay Institute The Clay Mathematics Institute (CMI) is a privately funded operating foundation dedicated to increasing and disseminating mathematical knowledge. The CMI supports the work of leading researchers at various stages of their careers and organizes conferences, workshops, and an annual summer school. Contemporary breakthroughs are recognized by its annual Research Award. The CMI is a tax-exempt charitable organization (private operating foundation) that can receive tax-deductible contributions from the public.

CMI may be best known for the seven Millennium Prize Problems announced at the Collège de France in Paris in June of 2000. The prizes were established by CMI to (i) recognize some of the arguably most difficult problems with which mathematicians were struggling at the turn of the millennium, (ii) to underline the importance of working on the really hard problems, and (iii) to spread the news that in mathematics hard, significant problems are still abound - the frontiers of knowledge are still wide open. The Millennium Prize Problems constitute but one of CMI's activities. Three of the largest, in terms 19

of both budget and importance, are the Clay Research Fellowships, the Clay Research Summer School, and the Clay Research Conference, the latter being the venue at which the Clay Research Awards are presented.

3.5. DIMACS – Centre for Discrete Mathematics & Theoretical Computer Science DIMACS facilitates research, education, and outreach in discrete mathematics, computer science theory, algorithms, mathematical and statistical methods, and their applications. DIMACS was founded in 1989 with a prestigious "science and technology centre" award from the National Science Foundation to create a centre for the advancement of science and technology with a national scope. DIMACS also receives significant funds from the six participating institutions and from partners at Avaya Labs, Georgia Institute of Technology, HP Labs, IBM Research, Microsoft Research, Rensselaer Polytechnic Institute, Stevens Institute of Technology, and Yahoo Labs as well as from other federal sponsors. DIMACS Activities include research conferences and workshops, visiting scientists, activities for high school teachers and students, special focus programs concentrating on specific topics, technical reports and other publications.

3.6. IPAM – Institute for Pure and Applied Mathematics IPAM was founded in 2000 as an NSF Mathematical Sciences Institute with a grant from the NSF Division of Mathematical Sciences. Over 2,000 visitors per year attend its workshops, long programs, student research programs, summer schools, and other programs. Long programs bring together researchers from mathematics and other disciplines, or multiple areas of mathematics, with the goal of facilitating collaborative, cross-disciplinary research. The long program opens with a week of tutorials, which are followed by several (usually four) workshops on topics related to the overall theme of the program, and a culminating workshop at UCLA’s Lake Arrowhead Conference centre. Between the workshops, the participants organize a seminar series and other activities. IPAM offers housing and travel support to participants of long programs.

3.7. Mathematical Association of America The Mathematical Association of America is the largest professional society that focuses on mathematics accessible at the undergraduate level. Their members include university, college, and high school teachers; graduate and undergraduate students; pure and applied mathematicians; computer scientists; statisticians; and many others in academia, government, business, and industry. 20

The MAA provides a range of programs and resources that foster professional skills and enrich the broader mathematical community. These include collaboration and networking opportunities, discussion groups, books and publications, and grants - the MAA administers programs funded by public and private sources to support activities that help advance their goals.

The Greater MAA Fund provides support for organizational priorities. Membership dues account for 15% of their annual budget. Other forms of donations can be made to the MAA, and campaigns such as the ‘Second Century Campaign” raised a further $3.9 million.

3.8. Mathematical Reviews Since 1940, Mathematical Reviews (MR) has served researchers and scholars in the mathematical sciences by providing timely information on peer- reviewed articles and books. MathSciNet, the electronic version of MR, presents a fully searchable database with many tools designed to help navigate the mathematical sciences literature, including reviews written by a community of experts, bibliographic listings dating back to the early 1800s, links to articles, journals, and publishers, linked reference lists, citation information on articles, books, and journals.

3.9. MBI – Mathematical Biosciences Institute The mission of MBI is, in their words is “to foster innovation in the application of mathematical, statistical, and computational methods in the resolution of significant problems in the biosciences, to foster the development of new areas in the mathematical sciences motivated by important questions in the biosciences; to engage mathematical and biological scientists in these pursuits; and to expand the community of scholars in mathematical biosciences through education, training, and support of students and researchers”.

3.10. MSRI – Mathematical Sciences Research Institute The Mathematical Sciences Research Institute was founded in 1982, and is an independent non-profit mathematical research institution whose major funding source includes the National Science Foundation, and more than 90 Universities and institutions. Other corporate sponsors include CME Group, IBM, Mathematics Association of America, Texas Instruments, Google, Pacific Journal of Mathematics, Akamai Partner, Intel, Meyer Sound, Microsoft, and Torchlight Investors. There has also been funding supplied by Foundations. MSRI organizes and hosts term duration programs in the leading edge in that 21

field of study, including classical fundamental mathematics, modern applied mathematics, statistics, computer science and other mathematical sciences. The institute also holds workshops, colloquia and seminars.

3.11. SAMSI – Statistical and Applied Mathematical Sciences Institute SAMSI is a partnership of Duke University, North Carolina State University (NCSU), the University of North Carolina at Chapel Hill (UNC), and the National Institute of Statistical Sciences (NISS), in collaboration with the William Kenan, Jr. Institute for Engineering, Technology and Science. It is part of the Mathematical Sciences Institutes program of the Division of Mathematical Sciences at the National Science Foundation, the latter providing major 5 year funding renewal in 2014. Corporations that provide funding include AIG, GlaxoSmithKline, Merck Research Laboratories, MetaMetrics, PepsiCo, Quintiles, RTI International, and the SAS Institute.

SAMSI’s research programs are large-scale efforts focusing on interfaces among statistics, applied mathematics and other disciplinary sciences. Visiting researchers are resident at SAMSI for periods of a month to a year. Graduate and upper level undergraduate students are provided unique insight into the formation of research areas and collaborations. Every SAMSI program conducts workshops in statistical and applied mathematical sciences. Selective outreach programs to undergraduate and graduate students, high-school teachers and faculty from teaching institutions extend SAMSI’s impact still further. SAMSI holds regular year-long programs, and shorter summer programs, as well as an extensive education and outreach program. Some research programs focus on particular scientific problem areas, while others are defined by statistical and mathematical themes that cut across multiple scientific contexts. Each is led by national and international leaders in the statistical and applied mathematical sciences, coupled with strong involvement of disciplinary scientists.

3.12. Courant Institute of Mathematical Sciences The institute is an independent division of New York University (NYU) under the Faculty of Arts & Science that serves as a centre for research and advanced training in computer science and mathematics. The Department of Mathematics at the Courant Institute offers training in mathematics and applications of mathematics in the broadest sense. The department has leading research groups in many areas, including partial differential equations, probability and stochastic processes, geometric analysis, metric geometry, scientific computation, mathematical biology, and fluid dynamics. A special feature of the Institute is its highly interdisciplinary character — with courses, seminars, and active research collaborations in areas such as materials science, visual neural science, atmosphere/ocean science, cardiac fluid dynamics, plasma physics, financial mathematics, and mathematical genomics. Another special feature is 22

the central role of analysis, which provides a natural bridge between pure and applied mathematics.

3.13. Institute for Computational and Experimental Research in Mathematics (ICERM)

ICERM conducts research on topics at the interface of mathematics and computation. ICERM has partnered with Google, IBM and Microsoft, whose representatives serve on the Institute's Scientific Advisory Board. ICERM actively works with regional, national and global research institutes and companies to create workshops, conferences, and unique research opportunities that are relevant to both. The ICERM looks to expand the use of computational and experimental methods in mathematics, to support theoretical advances related to computation, and address problems posed by the existence and use of the computer through mathematical tools, research and innovation. A large part of ICERM's activities take place in the context of semester long thematic programs together with their associated workshops. Each such program hosts a number of long-term visitors (15-20 senior personnel, 5-10 postdoctoral fellows, and 8-12 graduate students) in addition to workshop participants. ICERM hosts 1-4 topical workshops each year. They focus on topics of current interest in the mathematical sciences. To apply, please submit the online application form for workshop participants. Decisions about online applications are typically made 1-3 months before the workshop. It also hosts special events, public lectures and outreach activities.

4. Canada

4.1. Fields Institute The primary activities at the Institute are its thematic programs, each lasting one or two semesters. They involve participants from Canada and around the world, including graduate students, post-doctoral fellows, and more senior and well-established scientists. The primary activities of the Fields Institute are Thematic and Focus Programs, ranging from one to six months in length. These involve long- and short-term visitors, postdoctoral fellows and students, and include workshops and seminars, distinguished lectures, and graduate courses. In addition, the Institute supports a wide range of programs of shorter duration such as workshops and conferences, mini-courses, summer schools, seminar series, and public lectures. Major funding is provided by the Ontario Ministry of Training, Colleges and Universities and the federal Natural Sciences and Engineering Research Council (NSERC). The eight principal sponsoring universities are; Carleton University, McMaster University, Queen's University, the University of Ottawa, the University of Toronto, the University of Waterloo, Western University, and York University. In addition there are sixteen affiliate universities, and the Corporate Affiliate Members of the Fields 23

Institute are: IBM Canada, CANNEX. S&P Capital IQ, Sigma Analysis and Management, Synchrony Consulting Services Inc., Maplesoft, and Waterfront International Ltd.

4.2. Centre de Recherches Mathématiques The CRM is mainly financed by NSERC (Natural Sciences and Engineering Research Council Canada), the Fonds FQRNT (Le Fonds québécois de recherche sur la nature et les technologies), NSF (National Science Foundation), the Clay Institute, and NATO's Scientific Affairs division. The CRM also receives support from its partner universities: Université de Montréal, McGill University, UQAM, Concordia University, Université Laval, Université de Sherbrooke and University of Ottawa. The CRM's scientific activities fall into two principal categories: research projects undertaken by teams, and thematic activities organised on a national or international scale. These thematic activities are open to all disciplines and involve researchers from the Centre and from other universities. In order to assure the widest possible diffusion of the participants' research results, the CRM launched, in 1989, a publication programme. The CRM has nine research laboratories, one in each of: mathematical analysis, number theory and symbolic computation, differential geometry and topology, discrete mathematics and combinatorics, applied mathematics, neuroimaging, mathematical physics, statistics, and quantum computing. It has programs connecting universities to industry, postdoctoral and educational programs, four publications series, including two published in collaboration with the American Mathematical Society, and one with Springer in mathematical physics.

4.3. Banff International Research Station BIRS embraces all aspects of the mathematical, computational and statistical sciences from the most fundamental challenges of pure and applied mathematics, theoretical and applied computer science, statistics, and mathematical physics, to financial and industrial mathematics, as well as the mathematics of information technology, and the life sciences. BIRS also frequently accommodates two-day events, suitable for promoting industry- academic collaborations, and research in teams/focused research groups, who are given the opportunity to live and to do research together in a non- workshop/non-conference style setting for periods of 1 to 2 weeks. BIRS furthermore hosts summer schools and graduate training camps. BIRS receives funding from the federal government of Canada, through the Natural Sciences and Engineering Research Council (NSERC), the provincial government of Alberta, through Alberta Science and Research Authority (ASRA), the U.S. National Science Foundation (NSF) and Mexico’s National Science and Technology Council, (CONACYT). The Pacific Institute for the Mathematical Sciences (PIMS), the Mathematics of Information Technology and Complex Systems Network (MITACS), the Mathematical Science Research Institute Berkeley (MSRI) and The Instituto de Matemáticas at the Universidad Nacional Autónoma de México (UNAM) provide support for workshops. 24

4.4. Atlantic Association for Research in the Mathematical Sciences Since its inception, AARMS has played an important role in research activities in the Atlantic region, sponsoring or co-sponsoring numerous meetings and workshops. AARMS exists to encourage and advance research in mathematics, statistics, computer science, and mathematical sciences, in the Atlantic region. AARMS receives donations from the Province of New Brunswick, and the Province of Nova Scotia to support their activities. Canada's three mathematical institutes, the Centre de Recherches Mathématiques, the Fields Institute, and the Pacific Institute for the Mathematical Sciences also provide support to the AARMS. AARMS sponsor a Collaborative Research Group Programs (CRG). CRG typically organize intensive workshops, share Post-Doctoral Fellowship appointments, coordinate graduate training programs, propose and assist in AARMS summer school programs, jointly supervise graduate students, and carry out other activities supporting their research programs.

4.5. The Institut des sciences mathématiques The Institut des sciences mathématiques (ISM) is a consortium of nine Québec universities (Concordia University, HEC Montréal, Laval University, McGill University, the Université de Montréal, UQAM, UQTR, Université de Sherbrooke and Bishop's University) for training and collaboration in the mathematical sciences. The ISM organizes the Quebec Mathematical Sciences Colloquium where well-known mathematicians known for the communications skills, give talks for a general mathematical audience. In addition, more highly specialized seminars are organized on a regular basis by the research groups. Students are also involved in organizing various activities, including several student seminars. Every year, a group of ISM graduate students organizes the ISM Graduate Student Colloquium, open to graduate students from everywhere and hosted by one of the ISM member departments. The ISM also contributes to the Séminaire de mathématiques supérieures, an annual summer school in pure and applied mathematics that has taken place for more than fifty years on the campus of the University of Montréal. The Carl Herz Foundation is a non-profit organisation that serves to fund ISM activities; however the Institute also relies on funding from the public.

4.6. Mathematics of Information Technology and Complex Systems Mitacs is a national, not-for-profit organization that has designed and delivered research and training programs in Canada. Mitacs was founded in 1999 as a Canadian Network of Centres of Excellence, dedicated to supporting applied and industrial research in mathematical sciences and associated disciplines. 25

Fully independent since 2011, Mitacs remains committed to its core vision of supporting research-based innovation and continues to work closely with its partners in industry, academia and government. Mitacs funding comes from Federal grants (39%), Provincial grants (25%), and Partner funds (31%). Smaller contributions to the institution include Networking and Foreign partners.

The Institute split to form Mprime, which brings together academia, industry and the public sector to develop cutting edge mathematical tools vital to our knowledge-based economy focusing on five key sectors of the economy: Biomedical & Health, Environment & Natural Resources, Information Processing, Risk & Finance, Communication and Networks & Security.

4.7. Pacific Institute for the Mathematical Sciences The Pacific Institute for the Mathematical Sciences (PIMS) was created in 1996 by the community of mathematical scientists in Alberta and British Columbia, and subsequently extended to both Washington State and Saskatchewan. The mandate of the institute is to promote research in and applications of the mathematical sciences, to facilitate the training of highly qualified personnel, to enrich public awareness of and education in the mathematical sciences, and to create mathematical partnerships with similar organizations in other countries (with a particular focus on the Pacific Rim). PIMS funds Collaborative Research Groups, Post-Doctoral Fellowships and individual events on a competitive basis. The institute provides scientific, educational and industrial outreach events that increase public awareness of the importance of mathematics in the community. The most intensive research activities of PIMS are the Focus Periods, each covering a specific but substantial area of research in the mathematical sciences, with participants ranging from students to world experts. The PIMS receives funding from NSERC, provincial governments and in 2007 became a Unité Mixte Internationale of the French Centre National de la Recherche Scientifique.

EPSRC MATHEMATICAL SCIENCES REVIEW OF MATHEMATICAL SCIENCES INFRASTRUCTURE

COMMUNITY CONSULTATION

Survey Data

OFFICIAL-SENSITIVE Review of Infrastructure: Community Survey

1. Sample Demographics

There were 259 completed responses to the survey and a further 121 incomplete responses. The data in this document refer to the completed responses only.

a. Gender

Question: Please select an option from the list (Male, Female, Prefer not to disclose)

Female Male Not Disclosed All respondents 16.6% (43) 76.8% (199) 6.6% (17) Excluding non-disclosed 17.8% 82.2% -

b. Career Stage

Question: How would you describe your career stage?

New Other Senior Reader Lecturer Lecturer Emeritus Professor Professor Academic Early Career Postdoctoral Not Disclosed All 5.4% 0.4% 3.9% 10.4% 11.2% 10.8% 46.7% 5.4% 3.5% 2.3% Respondents (14) (1) (10) (27) (29) (28) (121) (14) (9) (6)

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Number of of Number Respondents 20

Career Stage

Other responses included one respondent who identified their career stage as senior management, two who mentioned industry without specifying a career stage, three postgraduate students and three retirees (of which one retired from a reader position, one from a senior lecturer position and one from a lecturer position). One respondent mentioned identified as an associate professor in Canada was reallocated to the senior lecturer category as the UK equivalent.

OFFICIAL-SENSITIVE Review of Infrastructure: Community Survey

c. Sector

Question: Please describe the stakeholder type which best describes you.

Sector Academic Academic Industry Government Other (UK) (International) All respondents 56.8% (147) 37.8% (98) 1.9% (5) 1.5% (4) 1.9% (5)

160 140

120 100 80 60 40 Number of of Number Respondents 20 0 Academic (UK) Academic (Int) Industry Government Other Sector

None of the five respondents who identified their sector as “Other” provided any further information. Two respondents identified their sector as “Academic (International)” but indicated in their additional comments that they were currently based in the UK. These responses were therefore reallocated to “Academic (UK)”.

The most commonly mentioned locations for international academics were the United States (20), Germany (12), France (7), Italy (6) and Canada (5). Other countries identified were Norway (2), Russia (2), Australia (1), Austria (1), Denmark (1), Poland (1), Switzerland (1) and Turkey (1). Of the 98 respondents who identified themselves as international academics, 38 did not identify their location.

40 35 30 25 20 15 10 5 0 Number of of Number Respondents

Country

OFFICIAL-SENSITIVE Review of Infrastructure: Community Survey

2. Key UK Mathematical Sciences Infrastructure

Question: What do you consider to be the key Mathematical Sciences Infrastructure activities in the UK? (Industrial Study Groups, International Centre for Mathematical Sciences, Isaac Newton Institute, LMS-EPSRC Durham Symposium, Taught Course Centres (TCCs), Warwick Symposium, Don’t Know, Other). Tick all that apply. Groups Study Industrial Sciences (ICMS) Mathematical for Centre International Institute (INI) Newton Isaac LMS Symposium Durham (TCCs) Centres Course Taught Symposium Warwick Don’t know Other - EPSRC EPSRC

All 14.7% 82.6% (214) 79.9% 35.1% 27.0% 20.5% 8.5% 6.6% respondents (38) (207) (91) (70) (53) (22) (17) International 4.0% (4) 86.0% (86) 66.0% 18.0% 7.0% 14.0% 15.0% 7.0% (7) Academics (66) (18) (7) (14) (15) Only

100.0% 90.0% 80.0% 70.0% 60.0% 50.0% 40.0% % Int 30.0% % All 20.0% 10.0% 0.0% % of Respondents Selecting Option Each Selecting Respondents % of Ind. Study ICMS INI Durh. TCCs Warw. DK Other Groups Symp Symp Activity / Organisation

Other organisations or activities identified included BAMC/BMC, the Edinburgh Mathematical Society, the Alan Turing Institute, the Maths in Medicine Study Group and the Industrial Maths KTN Community.

OFFICIAL-SENSITIVE Review of Infrastructure: Community Survey

3. Attendance

Question: In the last 5 years, have you ever attended a Mathematical Sciences Infrastructure event in the UK?

91.5% of respondents have attended a Mathematical sciences Infrastructure event in the last 5 years. Respondents were asked to list events attended and this can be broken down as follows:

Table: Frequency of Infrastructure attendance by activity type

Industrial ICMS INI LMS- Taught Warwick Other study Durham Course Symposium Groups Symposium Centres 9 209 114 24 14 21 21 *Please note that this is the frequency of events attended, i.e. the total is could be greater than the number of participants as an individual may have attend a number of events at a given activity over the last 5 years. Where an events was not attributable to a specific activity it was not included in this data, similarly proposed future events were also not included.

Using this as a proxy for usage of Mathematical Infrastructure over the last 5 years, comparison with perceptions of what is key infrastructure in the UK reveals a different profile.

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0 Indu. Study ICMS INI Durh. Symp TCCs Warw. Symp Other Groups

What is key infrastructure in UK (count data) Attended in last 5 years (frequency data)

Using attendance as a proxy of behaviour, the below graph shows the proportion of people who felt that a given activity was key against attendance of an event in the last 5 years, this gives an indication of perceived importance versus observed behaviour.

OFFICIAL-SENSITIVE Review of Infrastructure: Community Survey

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0 Indu. Study ICMS INI Durh. Symp TCCs Warw. Symp Groups

Key and Attended Key but not attended in last 5 years Not key but have attended in last 5 years

There is no correlation between perceiving as key but not attending in the last 5 years and stakeholder type, i.e. not due to being overseas etc.

Question: How frequently do you try to attend one of these events?

Once every Once a year Twice a More than When Don’t Know 2 – 3 years year twice a year relevant activities are available Respondents 16.9% (41) 13.2% (32) 5.8% (14) 7.9% (19) 55.4% (134) 0.8% (2) who have attended an event in the last five years

60.0%

50.0%

40.0%

30.0%

20.0% % of Respondents % of

10.0%

0.0% Once every 2- Once a Year Twice a Year More than When Don't Know 3 years Twice a Year relevant activities are available

OFFICIAL-SENSITIVE Review of Infrastructure: Community Survey

Question: How important is it to attend these type of events? (1 = not at all important, 5 = very important)

Very Important Neither Unimportant Not at all Important important nor important unimportant Respondents 45.0% (109) 49.2% (119) 5.0% (12) 5.0% (1) 5.0% (1) who have attended an event in the last five years

60.0%

50.0%

40.0%

30.0%

20.0% % of Respondents % of

10.0%

0.0% Very important Important Neither important Unimportant Not at all nor unimportant important

OFFICIAL-SENSITIVE Review of Infrastructure: Community Survey

4. Motivation and Drivers

Question: What motivates you to attend these events? Please rank in order of importance, where 1 is the most important. If not relevant please leave blank.

Times The Opportunity Staying Opportunity Time to Other ranked in topic of to highlight up to to discuss think position… the your date with your about event research research research your of others with others research ideas All 1 173 23 36 52 13 5 respondents 2 18 36 101 73 18 1 3 24 39 57 56 30 1 4 11 66 27 34 44 1 5 7 47 7 8 83 0

To produce the following graph, each option was allocated a score of 5 for a ranking in position one, 4 for a ranking in position two, 3 for a ranking in position three, 2 for a ranking in position four and 1 for a ranking in position five. The scores for each option can therefore be considered a measure of their relative importance in motivating attendance.

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Score Based on All All on Rankings Based Score 200

0 The topic of Staying up to Opportunity to Opportunity to Time to think Other the event date with discuss your highlight your about your research of research with research research ideas others others

Although eight respondents chose to rank “Other”, only one other motivation was identified by one respondent. This was the quality of the event.

OFFICIAL-SENSITIVE Review of Infrastructure: Community Survey

Question: What do you gain by attending these events? (Please tick all that apply)

New New New Visibility in Interaction Other research collaborators collaborations the with end ideas / contacts in /contacts Community users your field outside your field All 87.6% 83.8% (217) 44.0% (114) 68.7% (178) 18.9% (49) 2.3% (6) respondents (227) International 95.0% (95) 89.0% (89) 36.0% (36) 69.0% (69) 10.0% (10) 1.0% (1) Academics Only Respondents 95.2% 91.2% (208) 48.2% (110) 75.4% (172) 20.6% (47) 0.0% (0) answering (217) “Important” or “Very important” to Q4. Respondents 71.4% (10) 64.3% (9) 28.6% (4) 42.9% (6) 14.3% (2) 0.0% (0) answering “Neither important nor unimportant”, “Unimportant” or “Not at all important” to Q4.

100.0% 90.0% 80.0% 70.0% 60.0% 50.0% 40.0% 30.0% 20.0% 10.0% 0.0% % of Respondents Selecting Option Selecting Respondents % of

% International % Total

OFFICIAL-SENSITIVE Review of Infrastructure: Community Survey

Of the six “Other” responses, three (including the one international academic respondent) identified interaction with other researchers as being an important benefit of attending such event or activities, whilst the remaining three respondents identified high quality research time as a key benefit.

100.0%

90.0% 80.0% 70.0% 60.0% % Total 50.0% % Important 40.0% % Unimportant 30.0% 20.0%

% of Respondents Selecting Option Selecting Respondents % of 10.0% 0.0%

OFFICIAL-SENSITIVE Review of Infrastructure: Community Survey

5. Outcomes and Benefits

Question: Thinking back to the events of this nature you have attended in the last year how significant an impact have they had on: - (1= Not at all significant, 5= Very significant)

Significance Your research Your research Your network of Your career direction progress collaborators 1 15 12 13 35 2 32 26 16 35 3 47 51 51 72 4 94 85 74 52 5 34 47 67 16 Average 3.45 3.58 3.75 2.90 Standard Deviation 1.12 1.11 1.14 1.18

100 90

80 70 60 Your research direction 50 Your research progress 40 Your network of collaborators 30 Your career Number of of Number Respondents 20 10 0 1 2 3 4 5 Significance

1 Average Significance Score Significance Average 0 Your network of Your research progress Your research Your career collaborators direction

*The error bars represent the standard deviation.

OFFICIAL-SENSITIVE Review of Infrastructure: Community Survey

Question: What are the key features that existing Maths infrastructure offer in the UK? Please tick all that apply.

Networking with Funded Other (please Time and space key researchers sabbaticals specify): All Respondents 177 206 35 8

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Number of of Number Respondents 50

0 Time and space Networking with key Funded sabbaticals Other (please specify): researchers

Question: Thinking about your current experiences and future needs, to what extent does the current provision of Mathematical Sciences Infrastructure meet your needs? (1 = Not at all, 5 = Completely meets all needs).

Extent that Current Provision Meets Needs Number of Respondents 1 6 2 23 3 65 4 109 5 33 Not responded 23

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0 1 2 3 4 5 Not Responded

OFFICIAL-SENSITIVE Review of Infrastructure: Community Survey

Question: Please explain your answer to the previous question.

Responses were coded into 9 topics; distribution by response to Q9 is shown below

Graphs shows extent to which current infrastructure meets needs by reasons

80 70 60 50 40 30 20 10 0 1 2 3 4 5

Topic Connectivity Logistics Funding Participation Need new Opportunities Adminstration Overseas No changes need

The table below indicates the breakdown of sub-groups within these topics.

OFFICIAL-SENSITIVE Review of Infrastructure: Community Survey

Coding Topics Description 1 Topic Not enough in area (1) Funding Lack of funding to attend (1) Need new Opportunities Need for change to current infrastructure (1) Administration Lack of advertising (1) 2 Topic Unusual to get in area (1), infrequent coverage in my area (1), not accessible to non-mathematicians (1) Connectivity Too much focus on networking Logistics Timing not convenient (4), Requires large time commitment (2), Ease of travel in UK Funding Can’t get funding unless invited (1), lack of funding to attend (1), need more funding for this type of activity Need new opportunities Need for change to current infrastructure (2), need more opportunities (2), need shorter programs/smaller activities (1) Overseas factors Better provision overseas (1) 3 Topic Not enough applied topics (3), unusual to get a topic in my area (3), infrequent coverage of my area (3) Connectivity Keeps abreast of developments in field (4), exposure to international community (1) Logistics Ease of UK in difficult (1), timing not convenient (1), difficult to attend due to family commitments (1) Funding Need more funding for this type of activity Participation Need to broaden participation Need new Opportunities More retreat style activities (2), Shorter programs/Small activities (4), More opportunities (3), More work with industry (1), More interaction with other disciplines/challenges (1) Administration Better advertising (1) Overseas Better funded activities overseas (1) 4 Topic Not enough applied topics (1), Good range of topics (3),Unusual to get in my area (1), infrequent coverage in my area (3) Connectivity Keeps up to date with field (12), Exposure to international community (8), helps meet collaborators (2) Logistics Requires large time commitment Funding Lack of funding to attend (3), More funding need for these activities (2) Participation Broaden participation (2), Allows retired academics to participate (2) Need new Opportunities More retreat style activities (3), More challenges from maths/other disciplines (1), Funded sabbaticals (2), more TCC style activities (1), More shorter/ smaller activities (1) Administration Better provision overseas (1), Better topics (2) 5 Topic Good topics available (1) Connectivity Keeps up to date of development in field (5), Exposure to international community (5), Networking opportunity (1) Logistics Not easy locations to travel to (1), Issues with family commitments (2) Funding Cant go unless funding given (1)

OFFICIAL-SENSITIVE Review of Infrastructure: Community Survey

6. Organisation and Involvement

Question: In the last 5 years, have you ever been an organiser of a UK event supported by Mathematical Infrastructure? An organiser is defined as someone who has been involved in the planning and administration of an infrastructure event, it does not include keynote speakers.

Infrastructure Yes No International Centre for 28 Mathematical Sciences Isaac Newton Institute 21 Durham Symposium 2 175 Study Groups with Industry 2 Taught Course Centres 2 Turing Gateway to 1 Mathematics

200 180

160 140 120 100 80 60

Number of of Number Respondents 40 20 0 None ICMS INI TCCs Warwick Durham Study TGM Group

OFFICIAL-SENSITIVE Review of Infrastructure: Community Survey

Question: If you have been an organiser of a Mathematical Sciences Event in the past, please could you highlight any additional motivations you may have had and list any additional benefits that you feel you gained.

0 People Resources Topic Personal Science Community University Motivations Benefits No response

Motivations Benefits No response

Topic Description People Desire to bring people together (13), Desire to serve the community (3), Desire to bring researchers to the UK (7) Resources Ease of organisation due to infrastructure available (11) Topic Desire to shape future research directions (7)

Personal Raised academic profile (8), Advanced career (4) Contribution to UK Mathematics (2), Gained experience/skills (4), Increased network of contacts (7), Dissemination of research result (2) Science Advanced the Science involved (5), Produced a tangible scientific outcome (e.g. paper) (4), New research perspective developed (6) Community Meeting new people (1), Bringing people together (3) University Raised the reputation of University/Department (4)

OFFICIAL-SENSITIVE Review of Infrastructure: Community Survey

7. International Landscape

Question: In the last 5 years, have you attended an infrastructure event overseas?

10.81%

30.89% 58.30%

Yes No Don’t know

The Word Cloud below shows this attendance by facility

OFFICIAL-SENSITIVE Review of Infrastructure: Community Survey

Questions: What were your motivations for attending these events?

Topic Description People in attendance Speakers, Organisers and networking opportunities. Disseminate research opportunity to showcase research, get feedback on research Time and space for learning, keeping up to date in field, research progress, generating new ideas Same as the UK responded with “same reasons as the UK” International international infrastructure higher calibre (1), better provision internationally (1), opportunity to promote UK maths (2)

OFFICIAL-SENSITIVE Review of Infrastructure: Community Survey

Question: Considering all the opportunities available internationally, which would be your top three to participate in over the course of your career (your choice may include UK based infrastructure)? Please outline the reasons behind your choices

70 60 50 40 30 20 10 0

1 2 3

Question: Using the three choices selected above, what are the key features that make them particularly attractive to you? Please explain why you value these features and what benefits they yield?

Nil responses = 12

Key features 40 35 30 25 20 15 10 5 0

OFFICIAL-SENSITIVE Review of Infrastructure: Community Survey

Benefits 35 30 25 20 15 10 5 0

Question: Based on your selected three choices are these opportunities unique or are there other infrastructure events that are similar in nature? If so, why is your choice your preferred option?

Nil responses= 130

30 25 20 15 10 5 0 Topics Location Best in UK Best location features Administration No reason given No reason Well established No given Reason Most prestigious Programme style Best combination Best Best topics for me Has unique individual unique Has Is the best the best Is example(s) Best in my experience Yes No Don’t know

Yes No Don’t Know

OFFICIAL-SENSITIVE Review of Infrastructure: Community Survey

8. Resources and Support

Question: How important is it to support (in terms of resources not attendance) Mathematical Sciences Infrastructure? (1= not at all important, 5= very important).

Importance Number of Respondents 1 7 2 3 3 14 4 51 5 184

200 180

160 140 120 100 80 60 Number of of Number Respondents 40 20 0 1 2 3 4 5 Importance

Question: In your opinion, what proportion of funding should be allocated to the following activities? Please ensure totals add up to 100% and outline the reasons behind your choice in the comments box below.

Proportion Fellowships Infrastructure Research Training Average 23 22 36 18 Standard 13 11 15 11 Deviation

OFFICIAL-SENSITIVE Review of Infrastructure: Community Survey

Proportion / % / Proportion 20

0 Fellowships Infrastructure Research Training

*Error bars represent the standard deviation.

A Sample of comments received “The main aim of EPSRC should be to fund research. However, infrastructure and fellowships are very important too (I include doctoral fellowships here too). Since learning by doing and interacting with others is the best way in my opinion to learn the skills needed for research in mathematical sciences I don't see the benefit of devoting resources directly to training” “General research funding has greatest impact on the morale of the UK mathematics community”

“I think that all these aspects are equally important.”

“Supporting young people is the best way of nurturing mathematical talent. The institutes themselves usually recognise this too, but without a significant cohort of local mathematical researchers the Institutes would lose part of their national role.” “The bottom line is that research trumps everything. - Fellowships are valuable, training our PhDs for the future is important - but infrastructure is really a bit of a luxury unless it is really delivering something really outstanding?” “I think fellowships are the least important because the money is better placed supporting PhD students (I assume that is what is meant by training). I also think maintaining infrastructure is very important because it enables the UK to compete internationally.” “All research depends on the People (fellowships), infrastructure and training”

“I really have no idea.”

“One shouldn't have to trade one for the other - funding is important for all these activities”

“I really do not know how much places like the Newton Inst actually cost. But I certainly feel one should support them in preference of the other areas…” “All activities are equally important for a healthy discipline with sustained support.”

“Build it and they will come! Most people should expect to pay their own travel.”

OFFICIAL-SENSITIVE Review of Infrastructure: Community Survey

9. Current and Future Provision

Question: What are the key elements that Mathematical Sciences Infrastructure in the UK offer that maintain/enhance the health of the discipline?

No response: 95 80 70 60 50 40 30 20 10 0

Topic Description Connectivity People interactions (60), Virtual connectivity (1), Connections with other disciplines/users (9), Connections with early career academics (1) International Interaction with International community (14), Attracts international leaders (20) Environment Positive environment for research (10), Prestigious environment (5), Has the facilities to easily deliver (16) Time Provide uninterrupted time and space (18) Organisation Mixture of short and long term programmes (10), Need for geographical diversity (3, Not have too many activities (1), Diversity of topics (2), More participation for younger mathematicians (3), More funding provision (2), Broaden participation (1) UK Maintains to health of the UK (14), Keeps the UK competitive (8) Research Generates new collaborations (12), Generates new projects (3), generates interesting programmes (1), Allows exchange of ideas (27) Impact Encourages impactful thinking (3) No key elements Participants highlighted no key elements:

“They might be offering something to some mathematical disciplines but not to mine. It seems impossible to get support, and after a few strange experiences, no point applying. I get opportunities all around the world, but not in my home country.”

“there are no such key elements - - essentially, it is rather waste of time of EPSRC and other funding sources, since the quality of the events supported is becoming lower and lower”

OFFICIAL-SENSITIVE Review of Infrastructure: Community Survey

Question: What would be your top three aspirations for Mathematical Sciences Infrastructure of the future? A number of responses were related to fellowship and training provision thus were removed.

70 60 50 40 30 20 10 0

First Choice Second Choice Third Choice

Topic Description Continue and expand Continue- general (16), Continue INI (12), Continue ICMS (14), Continue Study Groups (3), Continue LMS-Durham symposium (1), Continue TCCs (4), Continue Warwick symposium (1) Access Wider participation (16), More younger people involved (26), More support for women (5), Support new talent (4) Science Cover emerging research (12), Engage with other disciplines (16), Promote exchange of ideas (5), Focus on pure maths (5), Focus on impact (3), Support new research areas (2), Not focus on fashionable areas (2) Organisation Have dedicated research staff (2), ease of organisation (5), More time for own research (4), Great facilities (6), Have a procedure for disseminating results (3), Be flexible in style (10), New Infrastructure Retreat style institute (5), Inter University infrastructure (1), Shorter program style (8), Have a more diverse portfolio (5), Offer permenant research positions (1), Have longer programmes (1), MRC style workshop (1), Partner with international infrastructure (1) Funding Stability of Funding (8), Support to attend overseas infrastructure (2), Increased funding (9), Reverse concentration of funding (2) International Be internationally excellent (15), Involve international leaders (5), Be more internationally aware (1) Connectivity Bringing people together (4), Networking (8), new collaborations (5) Geographic Involve more universities (1), Regional centres (3), Remote participation facilities (3), Northern Centre (2), Better locations for infrastructure (1), Better support For individuals (3), For existing infrastructure (1), For PDRAs (1), For retirees (1), From Universities (1), More local activities (1) Time Time and space for research (4), Time for attendance (2) Interactions Better integration between infrastructure in UK (3)

OFFICIAL-SENSITIVE Review of Infrastructure: Community Survey

Individual decision routes from first to second to third choice (see below), highlight the diversity in responses. Choice maps are group by primary choice.

OFFICIAL-SENSITIVE Review of Infrastructure: Community Survey