Annual Review 2019 | 2020 Annual Review | October 2019 – September 2020 Heilbronn Institute for Mathematical Research www.heilbronn.ac.uk CONTENTS Chair’s Report 1 Relationships 3 Research 4 Events 5 Personnel 7 Organisation 9 APPENDICES R1 Highlighted Papers 11 R2 Complete List of Papers 15 E1 Heilbronn Events 28 E2 Sponsored Events 33 E3 Focused Research Events 43 E4 Future Events 50 P1 Fellows Joining since September 2019 59 P2 Fellows Leaving since September 2019 62 P3 Fellows Moving with Extensions 64 P4 Fellows Joining in October 2020 65 P5 Sponsored PhD Studentships 68 M1 Career Development 71 Chair’s Report The Heilbronn Institute has, notwithstanding the challenges of the pandemic, enjoyed a remarkable and successful year as a national institute for mathematical research. It is commonly said that mathematicians need only pen, paper, and an internet connection to do their work. The pandemic has put the members of HIMR to the test, and the scientific outcomes have been very strong, achieved sometimes in difficult conditions. The external events and activities of HIMR have continued whenever possible, and the Institute’s mathematical output has been distinguished by its impact and breadth. This has been a big year for the Heilbronn Institute—our first complete year in an extensive suite of rooms within the newly renovated Fry Building of Bristol University, in cohabitation with the School of Mathematics; a change of leadership on both internal and external work; and then the challenges posed across the UK by the restricted working and living conditions of the COVID-19 pandemic. Members of the Institute have responded bravely and constructively to the ensuing changes in their environments, and HIMR is strengthened by a deepened feeling of shared commitment to excellence in mathematics. Our new accommodation in Bristol allows our organizational staff, for the first time, room to breathe. The hospitality of the University and School is gratefully acknowledged in this regard. We hope to be able to welcome all HIMR members on visits to Bristol in the near future. Annual Review | October 2019 – September 2020 Heilbronn Institute for Mathematical Research www.heilbronn.ac.uk P a g e | 1 The changes in leadership mark a progression for HIMR. Jon Keating’s successful and dynamic tenure as Chair has seen the evolution of its external activities into a mature operation that looks both within, to its Fellows and Students, and outwith, across the entirety of the UK mathematics community. The new Heilbronn Doctoral Partnership has accepted its first intake of 9 students, and our eyes are turning towards other cohorts of mathematicians including those studying at schools and on undergraduate courses. In addition, Daniel Shiu has retired from the Headship of HIMR after four successful years in post. We are especially concerned with issues around diversity. Our recent successes in hiring women to fellowships and studentships have been substantial, and our efforts will be intensified. The Heilbronn Doctoral Partnership aids our potential to attract women into the academic system who may not otherwise present themselves. While women are under- represented in mathematical research, the situation with other under-represented groups is more extreme, and we will support initiatives across the UK that tend towards increasing diversity in mathematical science. A major event of our year is the January appointment process. We made 14 appointments this year (including 3 women) to Heilbronn Research Fellowships (HRF). Since September 2019, 9 former Fellows have left HIMR, 8 for academic positions and 1 for industry. Details may be found in Appendix P2. Annual Review | October 2019 – September 2020 Heilbronn Institute for Mathematical Research www.heilbronn.ac.uk P a g e | 2 Relationships HIMR works closely with other major UK and international mathematics research institutes and organisations, including the American Institute of Mathematics, the Alan Turing Institute, the Clay Mathematics Institute, the International Centre for Mathematical Sciences, the Isaac Newton Institute, and the London Mathematical Society. We continue to run workshops with the Alan Turing Institute and to provide support for workshops at the ICMS in Edinburgh and the Isaac Newton Institute in Cambridge. Last year we entered into partnership with the Clay Mathematics Institute to establish a major new series of Postgraduate Summer Schools. Within this partnership, we provide support for two UK participants on the PROMYS Europe programme for highly gifted pre- university mathematicians. HIMR plays a leading role in the ‘STEM for Britain’ poster competition and exhibition that aims to encourage, support and promote Britain’s early-career researchers in Mathematics in Parliament and elsewhere. Annual Review | October 2019 – September 2020 Heilbronn Institute for Mathematical Research www.heilbronn.ac.uk P a g e | 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 offering opportunities for collaboration and personal development. We attract excellent mathematicians and support them in carrying out excellent research. A natural measure of the Institute’s performance in relation to this goal is the quality of the papers produced by its members. In October 2020, members of the Institute submitted reports (37 in all) on their external research. They were invited to list papers produced in the twelve-month period from October 2019, to identify which of these papers they considered their best, giving reasons for their choice, and to list papers appearing in print during this period. The papers identified by members as their best are listed in Appendix R1, and the complete set of papers may be found in Appendix R2. HIMR’s publications find homes in mathematical journals including many of the highest ranked. Mention is made of two papers, in algebra and dynamical systems respectively, written by current fellows that have appeared recently in Inventiones Mathematicae. Classified work at HIMR is proving a rich and popular source of high-quality impact cases for submission to the 2020 Research Excellence Framework. There are about 18 HIMR cases under consideration for 12 UK universities. COVID-19 has inspired members of HIMR to harness their science to good cause. They participated in a COVID working group hosted by the Isaac Newton Institute, and contributed to modelling for the Cabinet Office. Annual Review | October 2019 – September 2020 Heilbronn Institute for Mathematical Research www.heilbronn.ac.uk P a g e | 4 Events A series of research events is offered throughout the year under the auspices of the Heilbronn Institute. These include the two‐day Annual Conference and several workshops, meetings and working groups. These events are of a high quality, and attract leading mathematicians from around the world. They contribute significantly to the research environment and reputation of the Institute. The regular Heilbronn Colloquia were a lively source of inspiration and discussion, until their forced postponement from around mid-March. A series of frequent events in Data Science took place between October 2019 and March 2020, namely 7 seminars and a workshop on hypocoercivity. Mention is made of the one-day meeting in February in memory of Elmer Rees, Founding Director of HIMR. Elmer was a leading individual in geometry and topology, who spent much of his career in Oxford and Edinburgh before moving to Bristol. He was greatly respected and loved by those close to him, and his friends enjoyed his company and his unpretentious sense of humour. Sadly, all events scheduled for mid-March and later had to be postponed, including Amie Wilkinson’s planned Distinguished Lecture Series. Annual Review | October 2019 – September 2020 Heilbronn Institute for Mathematical Research www.heilbronn.ac.uk P a g e | 5 HIMR has entered into an agreement with the Clay Mathematics Institute to jointly sponsor a series of Postgraduate Summer Schools. The first of these took place last year in Bristol in the area of computational number theory and this year’s summer school took place online in July, on the topic of integrable probability. The third (on hyperbolic geometry/dynamics) is planned for two weeks in Bristol during June/July 2021. Our 2020 flagship event was the Annual Conference, which took place remotely from 10–11 September. We were grateful to our eight speakers for their willingness to move their lectures online. Stimulating talks were given by Maria Chudnovsky (Princeton), Adam Harper (Warwick), Özlem Imamoglu (ETH Zurich), Kurt Johansson (KTH Royal Institute of Technology), Ailsa Keating (Cambridge), Hendrik Lenstra (Universiteit Leiden), Ulrike Tillmann (Oxford), and Ronald de Wolf (CWI & Universiteit van Amsterdam). When the questions dried up after Hendrik Lenstra’s closing lecture, he embarked upon his own quiz of the audience. The Institute is proud to have been able to offer part funding for a large number of significant scientific events held across the UK. Details may be found in Appendix E2. A distinctive element of HIMR’s research profile is its programme on Focused Research Events, of which we funded 14 during the year. Of these, 3 took place between October 2019 and January 2020 and 11 have been postponed until next year due to the COVID-19 pandemic restrictions. These events, which are listed in Appendix E3, enable groups of researchers and students to gather and discuss topical problems in mathematics. The competition for funds is fairly fierce and HIMR was able to fund only about one half of the deserving applications that it received this year. Annual Review | October 2019 – September 2020 Heilbronn Institute for Mathematical Research www.heilbronn.ac.uk P a g e | 6 Personnel Jon Keating resigned as Chair from 31 July 2020, following his 2019 election to the Sedleian Professorship of Natural Philosophy at Oxford University. He was succeeded on 1 September by the incoming Chair, Geoffrey Grimmett, Professor Emeritus of Mathematical Statistics at Cambridge University.