Annual Review October 2016 – September 2017 Table of Contents Page 1. Overview 2 2. Profile 4 3 Research 6 4. Events 8 5. Personnel 11 6. Mentoring 14 7. Structures 15 APPENDICES R1 Highlighted papers 17 R2 Complete list of papers 20 E1 HIMR-run events 26 E2 HIMR-sponsored events 29 E3 Focused Research Events 39 E4 Future events 48 P1 Fellows joining in 2016 53 P2 Fellows leaving since September 2015 54 P3 Fellows moving with 3-year extensions 55 P4 Future Fellows 56 M1 Mentoring Programme 57 Annual Review | October 2016 – September 2017 Heilbronn Institute for Mathematical Research www.heilbronn.ac.uk P a g e | 1 1. Overview HIMR continues to go from strength to strength: there is currently an outstanding cohort of Heilbronn Research Fellows doing first-rate research, recruitment of new Fellows has been excellent, and those departing have gone on to attractive positions. Recruitment of other members has also gone extremely well. This is true in both Bristol and London. The research culture at the Institute is excellent. Members have expressed a high level of satisfaction with their experience at HIMR. This is especially the case with the Fellows, many of whom choose to continue their relationships with the Institute. Our new Fellows come from leading mathematics departments and have excellent academic credentials. Those who left have moved to high-profile groups, including several to permanent academic positions. We currently have 30 Fellows, which is a significant increase compared to the average over the previous 12 years. These Fellows are hosted in 8 universities. This is contributing to the emergence of HIMR as a national research institute that is increasingly influential in UK mathematics. The achievements of our Fellows this year range from winning prestigious prizes to publishing in some of the elite mathematical journals and organising major mathematical meetings. There has been a considerable increase over the past two years in the number of PhD students supported by HIMR. We now support 9 and are encouraged by the fact that 7 are women. Annual Review | October 2016 – September 2017 Heilbronn Institute for Mathematical Research www.heilbronn.ac.uk P a g e | 2 Members of HIMR produced nearly 70 papers on their external research during the review period, roughly two per person. Many of these papers are of a highly impressive quality. Publications appeared in a wide range of leading international journals. Work at HIMR is having a significant impact on Mathematics. The external events organised by the Institute have been extremely successful, with a number of exceptionally high quality Conferences, Workshops, and Focused Research Events. The 2017 Annual Conference featured a number of world-leading mathematicians and attracted a record number of participants. Last year we supported 35 events, more than ever before. HIMR works closely with the other major UK mathematics research institutes, including the Clay Mathematics Institute, the Alan Turing Institute, the International Centre for Mathematical Sciences, and the Isaac Newton Institute. There is also an increasingly close collaboration with the American Institute of Mathematics. We continue to sponsor Postgraduate Schools run by the London Mathematical Society. As funding agencies are increasingly promoting applied and interdisciplinary research, and/or narrowing their focus, HIMR is playing a more significant and visible role in supporting a broad spectrum of UK Mathematics and Early-Career Mathematicians. The academic community values this highly. HIMR is taking a leadership role with regard to several issues that are currently important to the UK mathematics community, such as Knowledge Exchange and Impact. The team at the University of Bristol that is responsible for HIMR’s external activities continues to make an outstanding contribution to the Institute’s development. The quality of HIMR’s external activities and the visibility given to the external achievements of HIMR members have contributed in a significant way to the Institute’s success by enhancing its attractiveness to the most able academic mathematicians. Annual Review | October 2016 – September 2017 Heilbronn Institute for Mathematical Research www.heilbronn.ac.uk P a g e | 3 2. Profile HIMR’s reputation in the academic community continues to grow. The successes of the Fellows and the quality of the external events supported by the Institute are widely appreciated. This is evidenced by the marked increase in applications for Fellowships, participation in HIMR events, and requests for HIMR support. Our Focused Research Grants offer a highly distinctive funding opportunity that is now well established. We received many excellent proposals again last year and were able to be highly selective. Those we funded are listed in Appendix E3. The reports we have received suggest that the events were successful. This is rapidly becoming a flagship scheme for HIMR and is viewed very positively in the academic mathematics community. Meetings have been held with the Heads of several of the UK’s leading Mathematics Departments to explore their relationships with HIMR. These conversations have been extremely helpful; Heads have expressed strong support for HIMR in them. Annual Review | October 2016 – September 2017 Heilbronn Institute for Mathematical Research www.heilbronn.ac.uk P a g e | 4 In Mathematics Departments where soundings have been taken, the nature of the work done at HIMR is viewed positively and there is considerable support for the Institute. We now regularly receive approaches to discuss collaboration and partnership, especially around new Centres for Doctoral Training and from areas of the country where HIMR is less prominent. We have continued to explore opportunities to collaborate with the American Institute of Mathematics, the Clay Mathematics Institute, the International Centre for Mathematical Sciences, the Isaac Newton Institute, and the Alan Turing Institute, and are already jointly running or co-funding events (see Section 4 for further details). We are increasingly involved in advocacy for UK Mathematics and have a unique vantage point from which to comment. For example, we were invited last year to play a leading role in the STEM for Britain poster competition in Parliament, and will do the same again next year. We were also invited to have high-level involvement in the current Review of Knowledge Exchange in the Mathematical Sciences, and we met with the Government Chief Scientific Advisor to discuss how the HIMR model might inform similar initiatives in other areas. The Heilbronn website (heilbronn.ac.uk) continues to be a conspicuous success. It has considerably improved access to information about HIMR and plays an important role in attracting applications for Fellowships and in advertising funding opportunities for events. An abridged version of the Annual Report is posted there. Annual Review | October 2016 – September 2017 Heilbronn Institute for Mathematical Research www.heilbronn.ac.uk P a g e | 5 3. Research One of the primary aims of the Heilbronn Institute is to support the external research of its members by providing a stimulating environment and appropriate opportunities. We attract excellent mathematicians and aim to enable them to carry out excellent research. A natural measure of the Institute’s performance in relation to this goal is therefore the quality of the papers produced by its members. Members of the Institute produced 69 papers last year. This is a healthy average rate of productions: roughly 1.8 papers per person. The papers identified by members as their best are listed in appendix R1. The complete set of papers is listed in Appendix R2. The current portfolio of ‘best’ publications compares favourably with last year’s. Citations do not represent a reliable method for assessing research in Pure Mathematics, but they can be said to correlate (crudely) with visibility. We note that citations in 2015 to papers listing HIMR as the address of one or more authors (and some members do not to use this address, so inevitably a number of papers are missed) were 113% higher than in 2014. The corresponding citation count for 2016 was in turn 43% higher than in 2015. Citation performance looks like it is being maintained in 2017: it is too early to give a definitive citation count, but extrapolating current trends suggests that last year’s performance will be matched, and perhaps exceeded. Again, we remark that the numbers are relatively small and one should not read too much into their actual size, but the trend continues to be encouraging. Annual Review | October 2016 – September 2017 Heilbronn Institute for Mathematical Research www.heilbronn.ac.uk P a g e | 6 The inclusion of Impact in the 2014 REF, in which context work at the Institute made a significant contribution, and the fact that it will be an even larger component of next REF play to HIMR’s strengths. This is a significant advantage in recruitment and in the career progression opportunities of our Fellows. Arrangements have been made to monitor Impact accruing from work at the Institute, in readiness for the next REF. We note that members of HIMR produce a variety of research outputs, not just papers in academic journals. In particular, several members are major contributors to the development of the L-functions and Modular Forms Database (LMFDB). This is a high-profile new database of important functions in number theory. Its development in the past was supported by the NSF, and currently it is funded by a Programme Grant from the EPSRC run jointly by the universities of Bristol and Warwick. The work of HIMR members in developing the LMFDB is, in international terms, a highly significant contribution to mathematical research. In this context, members of the Institute are currently undertaking the first large-scale test of the Generalized Riemann Hypothesis for L-functions of degree >1 which do not come from elliptic curves.