Annual Review 2017 | 2018

CONTENTS

1 Overview 1 2 Profile 4 3 Research 6 4 Events 9 5 Personnel 13 6 Mentoring 17 7 Structures 18 APPENDICES

R1 Highlighted Papers 20 R2 Complete List of Papers 23 E1 HIMR-run Events 29 E2 HIMR-sponsored Events 31 E3 Focused Research Events 39

E4 Future Events 54

P1 Fellows Joining in 2017|2018 59

P2 Fellows Leaving since September 2017 60

P3 Fellows Moving with 3-year Extensions 62

P4 Future Fellows 63

M1 Mentoring Programme 64

1. Overview

This has been another excellent year for the Heilbronn Institute, which is now firmly established as a major national mathematical research centre. HIMR has developed a strong brand and is increasingly influential in the UK mathematics community.

There is currently an outstanding cohort of Heilbronn Research Fellows doing first-rate research. Recruitment of new Fellows has been most encouraging, as is the fact that many distinguished academic mathematicians continue to work with the Institute.

The research culture at HIMR is excellent. Members have expressed a high level of satisfaction. This is especially the case with the Fellows, many of whom have chosen 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 29 Fellows, hosted by 6 universities. We are encouraged by the fact that of the 9 Fellows joining us this year, 5 are women.

The achievements of our Fellows this year again range from winning prestigious prizes to publishing in the elite mathematical journals and organising major mathematical meetings.

Annual Review | October 2017 – September 2018 Heilbronn Institute for Mathematical Research www.heilbronn.ac.uk Page|1

There has been a considerable increase over the past three years in the number of PhD students supported by HIMR. We now support 10, and are pleased that 7 are women.

Members of HIMR produced over 50 papers on their external research during the review period. This corresponds to roughly 1.6 papers per person, which compares favourably with expectations. 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. These included two major international meetings, one on Probability, Analysis and Dynamics and a second on the Riemann Hypothesis, which attracted the leading international researchers in their respective areas. The 2018 Annual Conference also featured a number of world-leading mathematicians. Last year we supported 37 events, taking place across the UK, more than ever before.

Annual Review | October 2017 – September 2018 Heilbronn Institute for Mathematical Research www.heilbronn.ac.uk Page|2

HIMR works closely with other major UK and international mathematics research institutes and organisations, including the American Institute of Mathematics, the Clay Mathematics Institute, the Alan Turing Institute, the International Centre for Mathematical Sciences, the Isaac Newton Institute, and the London Mathematical Society. In collaboration with the Clay Mathematics Institute we are currently establishing a new series of Postgraduate Summer Schools, which will start in 2019.

As other funding agencies are increasingly promoting applied and interdisciplinary research, and/or narrowing their focus, HIMR is playing a significant and visible role in supporting a broad spectrum of UK Mathematics and Early-Career Mathematicians. The academic community continues to value this highly.

HIMR is taking a leadership role with regard to several issues that are currently important to the UK mathematics community, including Knowledge Exchange and Impact. The Institute was held up as an example of best practice in the Independent Review of Knowledge Exchange in the Mathematical Sciences in the UK (The Era of Mathematics) led by Professor Philip Bond. One of the key recommendations of the review was that the idea of establishing more institutes based on the HIMR model should be explored.

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 contribute in a significant way to the Institute’s success by enhancing its attractiveness to the most able academic mathematicians.

Annual Review | October 2017 – September 2018 Heilbronn Institute for Mathematical Research www.heilbronn.ac.uk Page|3

2. Profile

HIMR’s reputation in the academic community is now well established. The successes of the Fellows and the quality of the external events supported by the Institute are widely appreciated. This is evidenced by the continuing increase in applications for Fellowships, participation in HIMR events, and requests for HIMR support, and by the quality of our partnerships and our involvement in major national mathematical initiatives.

The Focused Research Grant Scheme offers a distinctive funding opportunity that is highly valued. 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 highly successful.

Conversations across the UK academic mathematics community have indicated strong support for HIMR. In particular, the Institute received numerous approaches to partner in proposals to EPSRC to run Centres for Doctoral Training. We selected five bids to support.

The Institute was held up as an example of best practice in the Independent Review of Knowledge Exchange in the Mathematical Sciences in the UK (The Era of Mathematics) led by Professor Philip Bond. One of the key recommendations of the review was that the idea of establishing more institutes based on the HIMR model should be explored.

Annual Review | October 2017 – September 2018 Heilbronn Institute for Mathematical Research www.heilbronn.ac.uk Page|4

We have continued to collaborate with the American Institute of Mathematics, the Clay Mathematics Institute, the International Centre for Mathematical Sciences, the Isaac Newton Institute, the London Mathematical Society, and the Alan Turing Institute, for example in jointly running or co-funding events (see Section 4 for further details). In partnership with the Clay Institute we are establishing a major new series of Postgraduate Summer Schools, starting in 2019. We have also developed plans to collaborate with the Alan Turing Institute so that Heilbronn Fellows working in the area of Data Science can carry out their external research there.

HIMR has developed plans to establish a new facility in Manchester to support our collaborations with the university there and other universities nearby. We are encouraged by the way the University of Manchester has worked in partnership with us in this initiative.

We are increasingly involved in advocacy for UK Mathematics and have a unique vantage point from which to comment. For example, we play a lead role in the STEM for Britain poster competition in Parliament. We were also invited to have high-level involvement in the Review of Knowledge Exchange in the Mathematical Sciences referred to above, and we met with the Chief Executive of UKRI to discuss the HIMR model.

Annual Review | October 2017 – September 2018 Heilbronn Institute for Mathematical Research www.heilbronn.ac.uk Page|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 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 54 papers last year. This is a healthy average rate of production: over 1.6 papers per person per year. (The corresponding figure last year was roughly 1.8.). The papers identified by members as their best are listed in appendix R1. The complete set of papers is listed in Appendix R2.

In the year under review, members of the Institute have published papers in Biometrika, Communications in Mathematical Physics, Duke Mathematical Journal, the Journal of the American Statistical Association, the Memoirs of the American Mathematical Society, and Physical Review Letters. A paper published by one of the Heilbronn Fellows, solving a problem raised by Serre, was the subject of an article in Quanta Magazine in which Professor Kiran Kedlya, a highly distinguished US mathematician, described it as a “watershed moment”.

Annual Review | October 2017 – September 2018 Heilbronn Institute for Mathematical Research www.heilbronn.ac.uk Page|6

Citations represent a more objective but less reliable method for assessing research in Pure Mathematics. Whilst citation numbers do not really measure quality, they can be said to correlate (crudely) with visibility. In Pure Mathematics one cannot use citation counts to measure the performance of individuals, but they can be useful in picking out trends for groups of researchers. To this end, 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, especially those in London, 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, and in 2017 it was 16% higher than in 2016. It is too early to give a definitive citation count for 2018, but extrapolating current trends suggests that this growth will be maintained. 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.

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 are underway to monitor Impact accruing from work at the Institute, in readiness for the next REF.

Annual Review | October 2017 – September 2018 Heilbronn Institute for Mathematical Research www.heilbronn.ac.uk Page|7

We note that members of HIMR produce a variety of research outputs, not just papers in academic journals. In particular, several members continue to make major contributions 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, and a grant from the Simons Foundation. The work of HIMR members in developing the LMFDB is, in international terms, a highly significant contribution to mathematical research.

In this context, Jonathan Bober is 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. He previously collaborated with Professor Ghaith Hiary in testing the Riemann Hypothesis for the Riemann zeta function at what is currently the record for the largest height up the critical line. Numerical computations of this kind are highly visible internationally and HIMR is now closely identified with the best work in this area. The first CMI-HIMR Summer School, to run in 2019, will be in the area of Computational Number Theory.

Annual Review | October 2017 – September 2018 Heilbronn Institute for Mathematical Research www.heilbronn.ac.uk Page|8

4. Events

The Heilbronn Institute organises a number of research events throughout the year. These include a two-day annual conference and several workshops, meetings and working groups. They are of a high quality, attracting leading mathematicians and contributing significantly to the research environment and the Institute’s reputation.

The Annual Conference is central to the programme and in 2018 continued the tradition of having excellent and distinguished speakers: Francis Brown (Oxford), Jacob Fox (Stanford), Mark Gross FRS (Cambridge), Martin Hairer FRS (Imperial), Chandrashekhar Khare FRS (UCLA), and Sarah Zerbes (UCL).

The Institute also ran a conference covering the broad area of Probability, Analysis and Dynamics that attracted many highly distinguished speakers (organised by M.Balazs, E. Crane, T. Jordan, J. Mackay and B. Toth), and a conference on Perspectives on the Riemann Hypothesis, which had a similarly distinguished cast of speakers, including Enrico Bombieri (IAS), Alain Connes (IHES), Nick Katz (Princeton), Peter Sarnak FRS (IAS/Princeton), Kannan Soundararajan (Stanford), Terry Tao FRS (UCLA), and Wei Zhang (MIT) (organised by B. Conrey, J. Keating, P. Sarnak and A. Wiles).

Annual Review | October 2017 – September 2018 Heilbronn Institute for Mathematical Research www.heilbronn.ac.uk Page|9

The Heilbronn Distinguished Lecture Series in 2018 was given by Professor Ingrid Daubechies (Duke). In 2019 there will be two Heilbronn Distinguished Lecture Series, given by Professors Jordan Ellenberg (Wisconsin-Madison) and Geordie Williamson FRS (Sydney). These lectures are organised by the University of Bristol in collaboration with HIMR.

Last year we again offered Focused Research Grants. This has become a distinctive and highly successful scheme, leading to a number of interesting and adventurous events that we see as promoting the Institute’s ethos. Our ability to move quickly has enabled us to support several important Focused Research Events that have played a key role in developing new avenues of research.

We now regularly partner with other major mathematics research institutes, co- sponsoring workshops and other research events. Over the summer we again partnered with the Clay Mathematics Institute, providing support for two UK participants on the PROMYS Europe programme for highly gifted pre-university mathematicians. The meeting on Perspectives on the Riemann Hypothesis was organised in cooperation with the Clay Institute and the American Institute of Mathematics, and it was also funded by the EPSRC and the NSF. 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. We are currently partnering with the Clay Institute to establish a major new series of Postgraduate Summer Schools, the first of which will be held in 2019.

HIMR also co-sponsors many events run throughout the UK, including the BMC, the Young Researchers in Mathematics conference, and various summer schools and smaller conferences. This support is increasingly popular, helped by our reputation for light-touch applications and quick decisions.

Annual Review | October 2017 – September 2018 Heilbronn Institute for Mathematical Research www.heilbronn.ac.uk Page|10

The increase in HIMR’s ability to support UK Mathematics is illustrated by the fact that between 2006 and 2015, HIMR supported around 35 events, i.e. roughly four per year; in 2015-16 we supported 26 events, in 2016-17 we supported 35 events, and in 2017-18 we supported 37 events.

To give one example of the way we can use our resources to benefit the mathematics community, last year the Women in Numbers Europe had to be moved from its intended venue at a very late stage. HIMR was able to support UK participation at the new venue and so ensured the success of this important event. This year we are supporting another Women in Numbers event, run by one of the HIMR-sponsored PhD students.

We have a policy that at least 20% of the speakers at HIMR-run events should, wherever possible, be women, and we press organisers on this matter. In fact, most events now do better than this.

Annual Review | October 2017 – September 2018 Heilbronn Institute for Mathematical Research www.heilbronn.ac.uk Page|11

For events run by HIMR, we offer to cover the costs of childcare for children up to 14 years of age. This is proving to be an important component of the support we offer.

More information and a complete list of HIMR run and co-sponsored events are given in Appendices E1-E4.

The feedback we have received from the community about the events we run and support has been extremely encouraging. As other funders and Institutes increasingly prioritise interdisciplinary and applied research in mathematics, HIMR is seen more and more as a partner of choice for activities in Pure Mathematics and Probability.

Our focus on advertising HIMR events and opportunities for funding more effectively appears to be succeeding: we are experiencing a considerable increase in requests for support. All funding calls are listed on our website.

Annual Review | October 2017 – September 2018 Heilbronn Institute for Mathematical Research www.heilbronn.ac.uk Page|12

5. Personnel

Amongst HIMR’s central goals are: to attract leading mathematicians to work as senior Consultants and Secondees, and to ensure that their experience of the research environment is a highly rewarding one; to appoint the best possible postdoctoral researchers to Fellowships and to ensure that they benefit from excellent opportunities and mentoring that will enhance their career development.

Recruitment went exceptionally well again in Bristol last year. We appointed 9 new Fellows and were encouraged that 5 of these are women.

Current Secondees report that they are enjoying the experience of working at the Institute; several have expressed a wish to continue.

The application pool for Fellowships was exceptionally strong again last year and we were able to be highly selective. In Bristol we received well over 100 applications.

We emphasize in our advertisements that we recruit Fellows from essentially all areas of Pure Mathematics, Probability and Statistics, and from areas involving theoretical Quantum Mechanics.

Details of current Fellows can be found on the Institute’s website. A list of new Fellows is given in Appendix P1, and a list of Fellows who have finished in the past year is given in Appendix P2.

Annual Review | October 2017 – September 2018 Heilbronn Institute for Mathematical Research www.heilbronn.ac.uk Page|13

At present we have Fellows in 6 Universities: Bristol, Imperial, King’s College London, Leicester, Oxford, and University College London. Most are based in Bristol. Having Fellows based in a larger number of institutions has the advantage of emphasizing HIMR’s role as a national institute, demonstrating the quality of the external research programme to a wider audience, and providing a broader experience base for the Fellows.

HIMR offers the opportunity for Fellows coming to the end of their first three years to extend their Fellowships, for either one year or three. A one-year extension is normally held at the same host university, and a three-year extension normally involves a move. Extending Fellowships in this way brings the benefit to HIMR of continuity of expertise; one concern is that it will diffuse the Fellows’ focus on their career development. All Fellows are invited to apply for an extension. Applications are assessed by a committee that includes the Chair and the Head of HIMR. A list of Fellows extending in this way is given in Appendix P3.

Annual Review | October 2017 – September 2018 Heilbronn Institute for Mathematical Research www.heilbronn.ac.uk Page|14

The quality of the Fellows appointed this past year is excellent, especially given that HIMR only appoints from a small subset of mathematicians. The strongest Fellows are comparable with typical Junior Research Fellows and their equivalents at leading universities. (This is evidenced, for example, by explicit comparisons made by referees, and by prizes gained by Fellows for their PhD theses. For example, this year one of our Fellows, Gene Kopp, won the SIAM Student Paper Prize.) The performance of the strongest Fellows and their career trajectories are also comparable with typical Junior Research Fellows. The website is a significant help in raising the Fellows’ visibility.

Fellows leaving HIMR continue to move on to good academic positions elsewhere, or to good positions outside academia. Over the past 10 years, most Fellows have stayed in academia, and the majority of those continuing now have permanent or tenure-track appointments. Former Fellows have in recent years gained permanent appointments in the mathematics departments at Durham, Exeter, Heriot Watt, Lancaster, Leeds, the Open University, Royal Holloway, Sheffield, UCL, and York. In the past year, Fellows have moved to either Lectureships or Senior Lectureships at Leeds and Leicester.

We have created a strategic fund to which members of HIMR can apply for support for specific research projects. A number were funded last year and we believe that this helped accelerate promising lines of research. The intention is to continue this scheme.

Increasing the number of female Fellows remains a major goal. We were pleased to appoint 5 this year and would like to see the number continue to increase. The referral reward scheme we introduced last year was a noteworthy success.

We have a scheme to support PhD study for women mathematicians who want to work at HIMR. This supported five women last year. HIMR currently supports 10 PhD students, 7 of whom are women.

Annual Review | October 2017 – September 2018 Heilbronn Institute for Mathematical Research www.heilbronn.ac.uk Page|15

HIMR funds students involved in three EPSRC Centres for Doctoral Training: the London CDT in Geometry and Number Theory (currently three students), the Bristol CDT in Quantum Engineering (currently one student), and the CDT associated with the EPSRC- funded Data Innovation Research Institute, led jointly by Cardiff University, the University of Bristol, and Swansea University (currently one student).

This year there has been another call for proposals to run EPSRC Centres for Doctoral Training. HIMR was invited by several institutions to partner bids. We chose five to partner and are currently awaiting the outcome.

Annual Review | October 2017 – September 2018 Heilbronn Institute for Mathematical Research www.heilbronn.ac.uk Page|16

6. Mentoring Programme

Three years ago we redesigned the mentoring arrangements for Fellows. A significant component of the new arrangements is that we have developed a programme of training events focusing on generic skills. This was led by Dr. Julia Wolf in her capacity as the Heilbronn Associate Chair in Bristol. Dr. Tim Burness recently took over the role from Julia. There is one event per month. Those that have taken place during the Review period are listed in Appendix M1. All Fellows are invited (i.e. not just those in Bristol). Feedback continues to be most encouraging.

Each Fellow also has an individual mentor with subject-specific expertise. The Fellows’ reports indicate that most of these relationships are working well.

One of the goals three years ago was to encourage closer collaboration between the Fellows and other members of their host departments. The Fellows’ reports this year give reason to believe that good progress continues to be made in this respect, with several listing joint papers.

The geographical spread of the Fellows has necessitated devolution of the monitoring of the quality of mentoring provided to the Fellows. We set out expectations and responsibilities concerning mentoring in a letter to the Heads of all Departments hosting Fellows. Heads are expected to monitor mentoring locally and send a brief annual report confirming that this has been done to their satisfaction. General guidance has been prepared on the points we feel would benefit from greater attention.

We believe that the mentoring provision now in place is providing excellent support for the Fellows.

Annual Review | October 2017 – September 2018 Heilbronn Institute for Mathematical Research www.heilbronn.ac.uk Page|17

7. Structures

The Heilbronn Institute has, over a short period of time, transformed itself from a research centre based almost entirely in Bristol (but drawing members from across the UK), to an institute with premises in both Bristol and London, staff employed by several universities across the South of England, and funding mathematical activities across the whole country. The planned expansion in Manchester will continue this trend.

In order to provide advice and challenge to the external programme, we established three years ago an External Advisory Board. The following have been members: Professors Keith Ball FRS (Warwick), Nathanael Berestycki (Cambridge), Joe Chuang (City), Andrew Granville (UCL), Ben Green FRS (Oxford), Frances Kirwan FRS (Oxford), Daniela Kuhn (Birmingham), Jens Marklof FRS (Bristol), Colin Sparrow (Warwick), and John Toland FRS (Bath/INI).

The External Advisory Board meets annually, in September.

We are currently reviewing the membership of the Board.

The admin team supporting the external programme, based at the University of Bristol, makes an outstanding and important contribution to the Institute’s success. The team is led by Chrystal Cherniwchan and Eleanor Machin, who share the role of Heilbronn Manager. It also includes Fran Blake, who is responsible for events, Chloe Biddle and Abla Hatherell, PA to the Chair.

Annual Review | October 2017 – September 2018 Heilbronn Institute for Mathematical Research www.heilbronn.ac.uk Page|18

The Associate Chair, Julia Wolf, made an exceptionally important contribution to the relationship with the University of Bristol, which is HIMR’s principal academic partner, establishing a number of new initiatives that proved extremely beneficial, in particular regarding the mentoring programme.

Recently Tim Burness has taken over the role from Julia, and he has made an excellent start, bringing fresh thinking to several key aspects of the partnership.

Annual Review | October 2017 – September 2018 Heilbronn Institute for Mathematical Research www.heilbronn.ac.uk Page|19

APPENDIX |R1 Highlighted Papers – 2017|2018

Individual testing is optimal for nonadaptive group testing in the linear regime. Aldridge, Matthew. IEEE Transaction on Information Theory, online first, 2018. ArXiv:1801.08590

Minimalist designs. Barber, Ben; Glock, Stefan; Kühn, Daniela; Lo, Allan; Montgomery, Richard; Osthus, Deryk. ArXiv:1808.06956

GCD sums and sum-product estimates. Bloom, Thomas; Walker, Aled. Arxiv 1806.07849

Twist-minimal trace formulas and the Selberg eigenvalue conjecture. Booker, Andrew R.; Lee, Min; Strömbergsson, Andreas. ArXiv:1803.06016

Steady state clusters and the Rath-Toth mean field forest fire model. Crane, Edward. ArXiv:1809.03462

An effective Chabauty-Kim theorem. Balakrishnan, Jennifer S.; Dogra, Neta. ArXiv:1803.10102

Explicit moduli spaces for congruences of elliptic curves. Fisher, T. ArXiv:1804.10195

Smooth values of polynomials. Bober, J; Fretwell, D.; Martin, G.; Wooley,T. ArXiv:1710.01970

A Classification of a family of maximum sets of equiangular lines in Euclidean space. Gillespie, Neil. ArXiv:1809.05739

Annual Review | October 2017 – September 2018 Heilbronn Institute for Mathematical Research www.heilbronn.ac.uk Page|20

Asymptotic Correlations in Gapped and Critical Topological Phases of 1D Quantum Systems. Jones, Nick; Verresen, Ruben. ArXiv:1805.06904

SIC-POVMs and the Stark conjectures. Kopp, Gene. ArXiv:1807.05877

The ℓ-modular local Langlands correspondence and local factors. Kurinczuk, Robert; Matringe, Nadir. ArXiv:1805.05888

On the unicity of types for tame toral supercuspial representations. Latham, Peter; Nevins, Monica. ArXiv:1801.06721

A McKean--Vlasov equation with positive feedback and blow-ups. Hambly, Ben; Ledger, Sean; Søjmark, Andreas. ArXiv:1801.07703

The p-width of the alternating groups. Malcolm, Alexander. ArXiv:1710.04972

On the structure of axial algebras. Sanhan, Khasraw; McInroy, Justin; Shpectorov, Sergey. ArXiv:1809.10132

On the few products, many sums problem. Murphy, Brendan; Rudnev, Misha; Shkredov, Ilya; Shteinikov, Yurii. ArXiv:1712:00410

Annual Review | October 2017 – September 2018 Heilbronn Institute for Mathematical Research www.heilbronn.ac.uk Page|21

Two converse theorems for Maass forms. Neururer, Michael; Oliver, Thomas. ArXiv:1809.06586

A statistical interpretation of spectral embedding: the generalised random dot product graph. Rubin-Delanchy, Patrick; Priebe, Carey; Tang, Minh; Cape, Joshua. ArXiv:1709.05506

Galois self-dual cuspidal types and Asai local factors. Anandavardhanan, U. K.; Kurinczuk, Robert; Matringe, Nadir; Sécherre, Vincent; Stevens, Shaun. ArXiv:1807.07755

Reducible subgroups of exceptional algebraic groups. Litterick, Alastair; Thomas, Adam. ArXiv:1801.09266

The multistep homology of the simplex and representations of symmetric groups. Wildon, Mark. ArXiv: 1803.00465

Annual Review | October 2017 – September 2018 Heilbronn Institute for Mathematical Research www.heilbronn.ac.uk Page|22

APPENDIX |R2 Complete List of Papers – 2017|2018

Individual testing is optimal for nonadaptive group testing in the linear regime. Aldridge, Matthew. IEEE Transaction on Information Theory, online first, 2018. ArXiv:1801.08590

Performance of group testing algorithms with near-constant tests-per-item. Johnson, Oliver; Aldridge, Matthew; Scarlett, Jonathan. ArXiv:1612.07122

Minimalist designs. Barber, Ben; Glock, Stefan; Kühn, Daniela; Lo, Allan; Montgomery, Richard; Osthus, Deryk. ArXiv:1808.06956

The Namer-Claimer game. Barber, Ben. ArXiv:1808.10800.

Logarithmic bounds for Roth's theorem via almost-periodicity. Bloom, Thomas; Sisask, Olof. Arxiv:1810.12791

GCD sums and sum-product estimates. Bloom, Thomas; Walker, Aled. ArXiv 1806.07849

Smooth values of polynomials. Bober, Jonathan; Fretwell, Daniel; Martin, Greg; Wooley, Trevor. ArXiv:1710.01970

A note on Maass forms of icosahedral type. Booker, Andrew R. ArXiv:1712.06876

Simple zeros of automorphic L-functions. Booker, Andrew R.; Cho, Peter J.; Kim, Myoungil. ArXiv:1802.01764

Twist-minimal trace formulas and the Selberg eigenvalue conjecture. Booker, Andrew R.; Lee, Minn; Strömbergsson, Andreas. ArXiv:1803.06016

Primitive values of quadratic polynomials in a finite field. Booker, Andrew R.; Cohen, Stephen D.; Sutherland, Nicole; Trudgian, Tim. ArXiv:1803:01435

New integral representations for Rankin-Selberg L-functions. Booker, Andrew R.; Krishnamurthy, Muthu; Lee, Minn. ArXiv:1804.07721

Quantitative estimates for simple zeros of L-functions. Booker, Andrew R.; Milinovich, Micah B.; Ng, Nathan. ArXiv:1806.01959

Annual Review | October 2017 – September 2018 Heilbronn Institute for Mathematical Research www.heilbronn.ac.uk Page|23

Functional large deviations for Cox processes and Cox/G/infinity queues, with a biological application. Crane, Edward; Dean, Justin; Ganesh, Ayalvadi. ArXiv:1808.04347

Steady state clusters and the Rath-Toth mean field forest fire model. Crane, Edward. ArXiv:1809.03462

Diffusion and superdiffusion in lattice models of colliding particles with stored momentum. Crane, Edward; Ledger, Sean; Tóth, Bálint. ArXiv:1809.03257

Explicit Chabauty-Kim for the split Cartan modular curve of level 13. Balakrishnan, Jennifer S.; Dogra, Neta; Müller, J. Steffen; Tuitman, Jan; Vonk, Jan. ArXiv:1711.05846

An effective Chabauty-Kim theorem. Balakrishnan, Jennifer S.; Dogra, Neta. ArXiv:1803.10102

Computing the Cassels-Tate pairing on 3-isogeny Selmer groups via cubic norm equations. Beek, M. van; Fisher, Tom. ArXiv:1711.02432

Explicit moduli spaces for congruences of elliptic curves. Fisher, Tom. ArXiv:1804.10195

Annual Review | October 2017 – September 2018 Heilbronn Institute for Mathematical Research www.heilbronn.ac.uk Page|24

A Classification of a family of maximum sets of equiangular lines in Euclidean space. Gillespie, Neil. ArXiv:1809.05739

2-neighbour transitive codes with small blocks of imprimitivity. Gillespie, Neil; Hawtin, Daniel; Praeger, Cheryl. ArXiv:1806:10514

Construction of the outer automorphism of S6 via a complex Hadamard matrix. Gillespie, Neil; O’Cathain, Padraig; Praeger, Cheryl. ArXiv:1805.01273

ℓ^p-improving for discrete spherical averages. Hughes, Kevin. ArXiv:1804.09260

Sparse bounds for k-spherical maximal functions: continuous and discrete. Anderson, Theresa and Hughes, Kevin.

Asymptotic Correlations in Gapped and Critical Topological Phases of 1D Quantum Systems. Jones, Nick; Verresen, Ruben. ArXiv:1805.06904

Four dimensional Fano quiver flag zero loci (with an appendix by T. Coates, E. Kalashnikov, and A. Kasprzyk). Kalashnikov, Elana. ArXiv:1808.00311

SIC-POVMs and the Stark conjectures. Kopp, Gene. ArXiv:1807.05877

Galois self-dual cuspidal types and Asai local factors. Anandavardhanan, U. K.; Kurinczuk, Robert; Matringe, Nadir; Sécherre, Vincent; Stevens, Shaun. ArXiv:1807.07755

Annual Review | October 2017 – September 2018 Heilbronn Institute for Mathematical Research www.heilbronn.ac.uk Page|25

The ℓ-modular local Langlands correspondence and local factors. Kurinczuk, Robert; Matringe, Nadir. ArXiv:1805.05888

On the unicity of types for tame toral supercuspial representations. Latham, Peter; Nevins, Monica. ArXiv:1801.06721

Random walk on the randomly-oriented Manhattan lattice. Ledger, Sean; Tóth, Bálint; Valkó, Benedek. ArXiv:1802.01558

A McKean--Vlasov equation with positive feedback and blow-ups. Hambly, Ben; Ledger, Sean; Søjmark, Andreas. ArXiv:1801.07703

The p-width of the alternating groups. Malcolm, Alexander. ArXiv:1710.04972

Enumerating 3-generated axial algebras of Monster type. Sanhan, Khasraw; McInroy, Justin; Shpectorov, Sergey. ArXiv:1809.10657

On the structure of axial algebras. Sanhan, Khasraw; McInroy, Justin; Shpectorov, Sergey. ArXiv:1809.10132

Axial algebras, 28 pages, lecture notes and survey. McInroy, Justin. May 2018.

An expansion algorithm for constructing axial algebras. McInroy, Justin; Shpectorov, Sergey, ArXiv:1804.00587

Annual Review | October 2017 – September 2018 Heilbronn Institute for Mathematical Research www.heilbronn.ac.uk Page|26

Code algebras which are axial algebras and their Z2-gradings. Castillo-Ramirez, Alonso; McInroy, Justin. ArXiv:1802.03342

On the few products, many sums problem. Murphy, Brendan; Rudnev, Misha; Shkredov, Ilya; Shteinikov, Yurii. ArXiv:1712:00410

On the few products, many sums problem. Murphy, Brendan; Rudnev, Misha; Shkredov, Ilya; Shteinikov, Yurii. ArXiv:1712:00410

Popular products and continued fractions. Moshchevitin, Nikolay; Murphy, Brendan; Shkredov, Ilya. ArXiv:1808.05845

Two converse theorems for Maass forms. Neururer, Michael; Oliver, Thomas. ArXiv:1809.06586

A statistical interpretation of spectral embedding: the generalised random dot product graph. Rubin-Delanchy, Patrick; Priebe, Carey; Tang, Minh; Cape, Joshua. ArXiv:1709.05506

Choosing between methods for combining p-values. Heard, Nicholas; Rubin-Delanchy, Patrick. ArXiv:1707.06897

Meta-analysis of mid-p-values: some new results based on the convex order. Rubin- Delanchy, Patrick; Heard, Nicholas; Lawson, Daniel. ArXiv:1505.05068

Weights in a Benson--Solomon block. Lynd, Justin; Semeraro, Jason. ArXiv:1712.02826

Annual Review | October 2017 – September 2018 Heilbronn Institute for Mathematical Research www.heilbronn.ac.uk Page|27

Fusion systems on maximal class 3-groups of rank two revisited. Parker, Chris; Semeraro, Jason. ArXiv:1809.01957

Weights conjectures for fusion systems. Kessar, Radha; Linckelmann, Markus; Lynd, Justin; Semeraro; Jason. ArXiv:1810.01453

Galois self-dual cuspidal types and Asai local factors. Anandavardhanan, U. K.; Kurinczuk, Robert; Matringe, Nadir; Sécherre; Vincent, Stevens, Shaun. ArXiv:1807.07755

Reducible subgroups of exceptional algebraic groups. Litterick, Alastair; Thomas, Adam. ArXiv:1801.09266

A combinatorial proof of the Murnaghan–Nakayama rule. Kochhar, Jasdeep; Wildon, Mark. ArXiv: 1805.00255

The multistep homology of the simplex and representations of symmetric groups. Wildon, Mark. ArXiv: 1803.00465

Annual Review | October 2017 – September 2018 Heilbronn Institute for Mathematical Research www.heilbronn.ac.uk Page|28

APPENDIX |E1 HIMR Events

The Heilbronn Institute organises a two-day annual conference and a number of workshops, meetings and working groups n

4-6 April 2018 Probability, Analysis and Dynamics 2018 Bristol Organisers in Bristol| Marton Balazs, Edward Crane, Thomas 101 participants Jordan, John Mackay, Bálint Tóth Speakers | Viviane Baladi (Paris VI), Krzysztof Burdzy (Seattle) Sourav Chatterjee (Stanford), Laura DeMarco (Northwestern) Dmitry Dolgopyat (Maryland), Tatjana Eisner (Leipzig) Alison Etheridge (Oxford), Geoffrey Grimmett (Cambridge) Martin Hairer (Warwick), Mike Hochman (Jerusalem) Konstantin Khanin (Toronto), Antti Kupiainen (Helsinki) Jens Marklof (Bristol), Vladimir Markovic (Caltech), Felix Otto (Max Planck Institut), Steffen Rohde (Seattle)

11-13 April 2018 Distinguished Lecture Series 2018 Bristol Speaker | Ingrid Daubechies (Duke University) 84 participants 1| Wavelets, with image processing applications for Art History 2| Adaptive time-frequency localisation 3| Biologically relevant distances between surfaces

[Organised in cooperation with the School of Mathematics, University of Bristol].

15 May 2018 Heilbronn Colloquium Bristol Causal Inference for Treatment Effects: A Theory and 40 participants Associated Learning Algorithms Speaker| Michaela van der Schaar (Oxford)

[Organised in cooperation with the School of Mathematics, University of Bristol]

Annual Review | October 2017 – September 2018 Heilbronn Institute for Mathematical Research www.heilbronn.ac.uk Page|29

4-7 June 2018 Perspectives on the Riemann Hypothesis Symposium Bristol A meeting on the Riemann Hypothesis and on the theory of the 170 Participants zeta-function and other L-functions.

Organised in Organisers| Brian Conrey (AIM/Bristol), Peter Sarnak (IAS, partnership with: Princeton), Andrew Wiles (Oxford) and Jon Keating (Bristol)

AIM | CMI | HIMR | Speakers| Keith Ball (Warwick), Enrico Bombieri (IAS Princeton), EPSRC | NSF | Andrew Booker (Bristol), Alain Connes (IHES), Alexandra Florea University of Bristol (Stanford), Henryk Iwaniec (Rutgers), Nicholas Katz (Princeton), Kaisa Matomaki (Turku), Philippe Michel (EPFL), Samuel Patterson (Göttingen), Maksym Radziwill (McGill), Christopher Skinner (Princeton), Kannan Soundararajan (Stanford), Wei Zhang (MIT)

6-7 September 2018 Heilbronn Annual Conference Bristol Speakers| Mark Gross (Cambridge), Jacob Fox (Stanford), Tamar 80 Participants Ziegler (Einstein Institute of Mathematics), Martin Hairer (Imperial College London), Francis Brown (Oxford), Shekhar Khare (UCLA), Sarah Zerbes (University College London)

Annual Review | October 2017 – September 2018 Heilbronn Institute for Mathematical Research www.heilbronn.ac.uk Page|30

APPENDIX |E2 Sponsored Events

The Heilbronn Institute supports mathematics in the UK through a programme of conferences, meetings and workshops n

27-28 November 2017 The London-Paris Number Theory Paris Organisers| Matthew Morrow (Jussieu), Olivier Fouquet (Orsay), 70 participants Michael Harris (Jussieu), Marc Hindry (Jussieu), Benjamin Schraen (École Polytechnique), Jacques Tilouine (Université Paris 13).

26-28 March 2018 British Colloquium for Theoretical Computer Science (BCTCS) Royal Holloway Organiser| Matthew Hague (Royal Holloway) 42 participants Speakers| John E. Hopcroft (Cornell University), Agata Ciabattoni (TU Wien), Marta Kwiatkowska (Oxford), Thomas Sauerwald 80 people attended (Cambridge), Alexandra Silva (UCL). John Hopcroft's public lecture. The British Colloquium for Theoretical Computer Science (BCTCS) is an annual event for UK-based researchers in theoretical computer science. A central aspect of BCTCS is the training of PhD students, providing an environment for students to gain experience in presenting their work, to broaden their outlook on the subject, and to benefit from contact with established researchers.

12 April 2018 Heilbronn Quantum Algorithms Meeting Cambridge Organisers| Steve Brierley (Cambridge), Ashley Montanaro 52 participants (Bristol), Sathya Subramanian (Cambridge) and Mithuna Yoganathan (Cambridge).

Annual Review | October 2017 – September 2018 Heilbronn Institute for Mathematical Research www.heilbronn.ac.uk Page|31

Speakers| Earl Campbell, András Gilyén, Stacey Jeffery, Damian Steiger

9-13 April 2018 Easter Probability Meeting 2018 on ‘Random Dynamics and Sheffield Other Recent Developments’ 60 participants Organiser| Nic Freeman (Sheffield) Speakers| Christina Goldschmidt (Oxford), Pierre Tarrès (NYU Shanghai), Robin Pemantle (Pennsylvania), Márton Balázs (Bristol), Elisabetta Candellero (Warwick) Sunil Chhita (Durham), Alexander Holroyd (Washington), David Leslie (Lancaster), Cécile Mailler (Bath), Matthias Hammer (Berlin), Balázs Ráth (Budapest), Frank Redig (Delft), Silke Rolles (Munich), Anja Sturm (Göttingen), Amandine Véber (École Polytechnique, France), Stanislav Volkov (Lund), Alex Watson (Manchester)

29-30 May 2018 The London-Paris Number Theory London Organisers| Yiannis Petridis (UCL), David Burns (KCL), Kevin 70 participants Buzzard (Imperial College), Fred Diamond (KCL), Alexei Skorobogatov (Imperial College), Andrei Yafaev (UCL), Sarah Zerbes (UCL)

Annual Review | October 2017 – September 2018 Heilbronn Institute for Mathematical Research www.heilbronn.ac.uk Page|32

11-14 June 2018 British Mathematical Colloquium (BMC 2018) St. Andrews Plenary Speakers| Laura DeMarco (Northwestern), Irit Dinur 172 participants (Weizmann Institute), Martin Hairer (Imperial College London), Nalini Joshi (Sydney), Paul Seymour (Princeton), Marcelo Viana (IMPA, Brazil) Morning Speakers| Jonathan Bennett (Birmingham), Clifford Cocks, David Conlon (Oxford), Charles Eaton (Manchester), Mike Fellows (Bergen), Victoria Gould (York), Daniel Král' (Warwick), Holly Krieger (Cambridge), Marta Mazzocco (Birmingham), Ian Morris (Surrey), Simon Smith (Lincoln), Hendrik Weber (Warwick). Public Speaker| Julia Wolf (Bristol)

25-29 June 2018 Stochastic Networks 2018 ICMS, Edinburgh Organisers| Sergey Foss (Heriot-Watt), Seva Shneer (Heriot- 85 Participants Watt), James Cruise (Heriot-Watt), Peter Taylor (Melbourne), Haya Kaspi (Technion - Israel Institute of Technology), Ilze Ziedins (Auckland), François Baccelli (Texas, Austin and INRIA), Kavita Ramanan (Brown), Philippe Robert (INRIA), R. Srikant (Illinois, Urbana-Champaign) Speakers| Jose Blanchet (Stanford), Sem Borst (Technical University of Eindhoven and Nokia Bell Labs), Jim Dai (Cornell),

Annual Review | October 2017 – September 2018 Heilbronn Institute for Mathematical Research www.heilbronn.ac.uk Page|33

Ken Duffy (National University of Ireland, Maynooth), Pablo Ferrari (Universidad de Buenos Aires), David Gamarnik (Massachusetts Institute of Technology), Bruce Hajek (Illinois, Urbana-Champaign), Stella Kapodistria (Technical University of Eindhoven), James Martin (Oxford), Andreea Minca (Cornell), Peter Moerters (Koeln), Amber Puha (California, San Marcos) Justin Salez (Université Paris Diderot), Sasha Stolyar (Illinois, Urbana-Champaign), Tolga Tezcan (London Business School), Ngoc Tran (Texas, Austin), Remco van der Hofstad (Technical University of Eindhoven), Ruth Williams (California, San Diego), Bert Zwart (CWI, Amsterdam).

17-19 July 2018 20th Postgraduate Group Theory Conference (PGTC) St. Andrews An annual conference organised by PhD students for PhD 32 Participants students in group theory and related areas. Organisers at St. Andrews| Mun See Chang, Fernando Flores Brito, Nayab Khalid, Matt McDevitt, Adán Mordcovich.

Annual Review | October 2017 – September 2018 Heilbronn Institute for Mathematical Research www.heilbronn.ac.uk Page|34

9-20 July 2018 Building Bridges: 4th EU/US Summer School and Workshop Budapest Organisers| Jim Brown (Occidental College, Los Angeles), Gergely 75 Participants Harcos (Budapest), Jay Jorgenson (The City College of New York)), Árpád Tóth (Budapest), Lynne Walling (Bristol).

9-13 July 2018 Non-Associative Algebras and Applications Lancaster Organisers| Yuri Bahturin (Memorial University of 47 participants Newfoundland), Georgia Benkart (Wisconsin-Madison), Murray Bremner (Saskatchewan), Alberto Elduque (Zaragoza), Rolf Farnsteiner (Kiel), Pavel Kolesnikov (Sobolev Institute of Mathematics), Ottmar Loos (FernUniversität in Hagen), Consuelo Martinez (Oviedo), Justin McInroy (Bristol), Jacob Mostovoy (Cinvestav IPN), Alexander Premet (Manchester), Susanne Pumpluen (Nottingham), Ivan Shestakov (Sao Paulo), Sergey Shpectorov (Birmingham), Efim Zelmanov (UC San Diego).

Annual Review | October 2017 – September 2018 Heilbronn Institute for Mathematical Research www.heilbronn.ac.uk Page|35

9-13 July 2018 LMS-CMI Research School | Homotopy Theory and Arithmetic Imperial College Geometry: Motivic and Diophantine Aspects 40 participants Organisers| Frank Neumann (Leicester) and Ambrus Pál (Imperial College).

24-27 July 2018 41st Research Students Conference in Probability and Statistics Sheffield (RSC 2018) 130 participants Organisers in Sheffield| Mark Yarrow, Jane Candlish, Christopher Griffiths, Sofia Karadimitriou, Alison Parton, Fiona Turner, Yi-shan Wang.

23-26 July 2018 Young Researchers in Mathematics (YRM 2018) Southampton Speakers| James Anderson (Southampton), 73 participants Andrew Brooke-Taylor (Leeds), Brita Nucinkis (Royal Holloway), Helen Ogden (Southampton), Melanie Rupflin (Oxford), Jamie Vicary (Oxford), Lynne Walling (Bristol), Claude Warnick (Cambridge), Sarah Whitehouse (Sheffield).

13-17 August 2018 LMS-CMI Research School | New Trends in Analytic Number Exeter Theory 56 participants Organiser| Julio Andrade (Exeter) Lecturers | Steve Gonek (Rochester), Andrew Granville (UCL), Jon Keating (Bristol), Zeev Rudnick (Tel-Aviv), Trevor Wooley (Bristol) Distinguished Lectures | Chris Hughes (York), James Maynard (Oxford), Damaris Schindler (Utrecht), Caroline Turnage- Butterbaugh (Duke).

Annual Review | October 2017 – September 2018 Heilbronn Institute for Mathematical Research www.heilbronn.ac.uk Page|36

29-31 August 2018 Simple Groups: New Perspectives and Applications Bristol Organisers| Tim Burness (Bristol) and Adam Thomas (Bristol) 75 participants Speakers| Inna Capdeboscq (Warwick), Pierre-Emmanuel Caprace (Université catholique de Louvain), David Craven (Birmingham), Tom De Medts (Ghent), Robert Guralnick (Southern California), Martin Liebeck (Imperial College), Gunter Malle (TU Kaiserslautern), Ben Martin (Aberdeen), Eamonn O’Brien (Auckland), Gerhard Röhrle (Ruhr-Universität Bochum), Colva Roney-Dougal (St Andrews), Aner Shalev (Hebrew University), Donna Testerman (EPFL), Pham Tiep (Rutgers).

3-7 September 2018 Groups, Representations and Geometry | Celebrating Dan Segal Oxford and Aner Shalev 70 participants Organisers| Inna Capdebosq (Warwick), Martin Liebeck (Imperial), Nikolay Nikolov (Oxford), Ben Klopsch (Dusseldorf), Martin Bridson (Oxford), Alex Lubotzky (Jerusalem), Efim Zelmanov (San Diego).

Annual Review | October 2017 – September 2018 Heilbronn Institute for Mathematical Research www.heilbronn.ac.uk Page|37

10-13 September 2018 Arithmetic Ramsey Theory (ART) Manchester Organisers| Sean Prendiville (Manchester), Julia Wolf 53 participants (Cambridge) and Jacob Fox (Stanford). Speakers| Ben Barber (Bristol), Thomas Bloom (Bristol), Jacob Fox (Stanford), Ben Green (Oxford), Oliver Janzer (Cambridge), Nina Kamčev (ETH Zürich), Sofia Lindqvist (Oxford), Joel Moreira (Northwestern), Peter Pach (Warwick), Sarah Peluse (Stanford), Tom Sanders (Oxford), Maryam Sharifzadeh (Warwick), Xuancheng Shao (Kentucky), Katherine Staden (Oxford), Benny Sudakov (ETH Zürich), Caroline Terry (Chicago).

Annual Review | October 2017 – September 2018 Heilbronn Institute for Mathematical Research www.heilbronn.ac.uk Page|38

APPENDIX |E3 Focused Research

Heilbronn Focused Research Workshops, formed with the aim of facilitating research groups to work on adventurous and challenging mathematical problems n

7-13 October 2017 Non-Signalling Correlations Belfast Organiser| Ivan Todorov (Belfast). 7 participants As originally planned, the event did not feature formal talks. The 6 Report out of the planned 7 participants were present in these dates. The 7th participant - Prof. Andrew Winter - was not able to join the main group, but a separate visit was organised with him and took place in February 2018.

The participants of the Focused Research Meeting concentrated their research on the topics that were planned originally. In the first part of the meeting, one publication of the team was completed entirely. This paper, entitled ‘Perfect strategies for non-signalling games’ was later submitted for publication to a leading journal in mathematical physics (decision is still pending). https://arxiv.org/abs/1804.06151

In the second part of the workshop, discussions in several directions took place, and another paper, by M. Lupini, L. Mancinska and D. Roberson, on quantum permutations, was initiated and later completed (preprint is still to be posted on the arXiv). A first draft on product games was also completed during the worksop, by V. Paulsen and I. G. Todorov. During the follow- up visit of Andreas Winter, discussions were held between him, myself and my student G. Boreland, which led to new advances on the Lovasz theta number of a non-commutative graph (the last draft of the paper has not however been completed yet).

Annual Review | October 2017 – September 2018 Heilbronn Institute for Mathematical Research www.heilbronn.ac.uk Page|39

4-5 January 2018 Lagrangian Mean Curvature Flow: Progress and Problems UCL Organisers: Jason D. Lotay (UCL) and Felix Schulze (UCL). 11 participants Speakers| Jingyi Chen (UBC), Dominic Joyce (Oxford), Ben Lambert (UCL), Jason Lotay (UCL), Knut Smoczyk (Hannover), Mu-Tao Wang (Columbia/CUHK).

Report This meeting brought together world leaders in Lagrangian mean curvature flow with new and young researchers in the subject. There was a combination of formal talks, surveying recent exciting progress in the field, and informal discussion sessions, focusing on open problems and potential future research directions. There were 11 participants, including 6 speakers. The meeting was stimulating and productive, leading to new research projects for both established and more junior researchers. In particular, the research leading to the article below arose directly out of discussions at the workshop. Jason D. Lotay, Felix Schulze; Consequences of Strong Stability of Minimal Submanifolds, International Mathematics Research Notices, 2018, https://doi.org/10.1093/imrn/rny095

Annual Review | October 2017 – September 2018 Heilbronn Institute for Mathematical Research www.heilbronn.ac.uk Page|40

19-23 February 2018 Automorphic Forms, Equiangular Lines and Kac - Moody Groups Bristol Organisers| Tom Oliver (Oxford), Neil Gillespie (Bristol). 13 participants

Report Our workshop explored two mechanisms by which automorphic forms could be connected to Kac--Moody groups and attempted to establish a relationship between them. We had a relaxed talk schedule covering background and peripheral material, including one popular colloquium talk from Prof. Cohn. The remaining time was spent working collaboratively. There were 13 participants, including researchers from the fields of number theory, representation theory and string theory. The visitors all enthusiastically engaged with the research problems and have stayed in contact with the organisers since the workshop. Tom is currently writing a paper with Prof. Lee, and Neil began a project with Prof. He.

Annual Review | October 2017 – September 2018 Heilbronn Institute for Mathematical Research www.heilbronn.ac.uk Page|41

10-12 January 2018 Dispersive Equations with Random Initial Data Bristol Organisers| Tamara Grava (Bristol), Sean Ledger (Bristol). 15 participants Participants| Herbert Spohn (Munich), Christian B. Mendl A joint University of (Stanford), Anne Sophie de Suzzoni (Paris), Nikolay Tzvetkov Bristol and Heilbronn (Cergy-Pontoise), Benedek Valk ́ (Wisconsin Madison), Sergey Focused Research Nazarenko, (Warwick), Miguel Onorato, (Turin), Pierre Suret, Workshop. (Lille), Kennet McLaughlin, (Colorado), Gennadi El, (Loughborough), Tadahiro Oh (Edinburgh), Oana Pocovnicu (Heriot-Watt).

Report The workshop gathered together mathematicians and physicists working in the field of nonlinear dispersive equations with random initial data. The following main topics were presented. Construction of well-defined probability measures for infinite- dimensional Hamiltonian systems, in particular the nonlinear wave equation. There are two approaches to this problem. One can construct a well-defined non-invariant measure, and then the main issue is to describe the evolution of the measure in time. For example, in the talk of N. Tzvekov it was showed that if one chooses as a probability measure the invariant measure of the linear part of the equation, then the Fourier coefficients remain independent random variables for all times. Another approach is to construct an invariant measure (Gibbs measure) for the nonlinear system. For infinite-dimensional systems whose Hamiltonian is unbounded from below, invariant

Annual Review | October 2017 – September 2018 Heilbronn Institute for Mathematical Research www.heilbronn.ac.uk Page|42

measures are mathematically ill defined. For this reason, one needs to change the equation via renormalization techniques, as originally introduced by physicists in quantum field theory. T. Oh gave a nice overview of these results and the mathematical techniques needed to develop them. Open questions | Given a non-invariant measure for a PDE, what can be said about its evolution for long times? Given an invariant measure, what is the behaviour of correlation functions (such as space-time correlation) for long times? These kind of questions seem to be out of reach from the mathematical point of view, however they were addressed numerically in several talks by physicists. Several nonlinear wave systems were presented, with both continuous and discrete distributions on the random Fourier coefficients. The remarkable feature of these numerical results is that the evolution of the system seems to saturate very quickly in time. Regarding correlation functions, interesting scaling laws in small temperature regimes were presented. The workshop was a fantastic source of inspiration and gave an opportunity to researchers working in this area to learn about results from other communities.

Annual Review | October 2017 – September 2018 Heilbronn Institute for Mathematical Research www.heilbronn.ac.uk Page|43

28 May – 1st June 2018 Axial Algebras Workshop Bristol Organisers| Justin McInroy (Bristol) and Sergey Shpectorov 13 participants (Birmingham). Participants| Mashaer Alsaeedi (Birmingham), Tom De Medts (Ghent), Clara Franchi (UNICATT), Jon Hall (Michigan State), Sasha Ivanov (Imperial), Vijay Joshi (Birmingham), Mario Mainardis (Udine), Justin McInroy (Bristol), Yoav Segev (Ben-Gurion), Sergey Shpectorov (Birmingham), Vladimir Tkachev (Linkoping), Michiel Van Couwenberghe (Ghent), Madeleine Whybrow (Imperial)

Report We had thirteen participants of which ten gave talks. The workshop was very successful, with several participants interested in having future such workshops. Of particular interest was one of the participants and speaker who is from a different background (geometry connected to PDEs) to the rest of the participants background in algebra. He gave a very different perspective and several people had productive talks about, for example, the geometry of idempotents in axial algebras and Bernstein algebras.

Progress was made in several areas. In particular, some further generalisations from axial algebras to decomposition algebras and the categorical description which this then allows. Prompted by discussions at the workshop, the minimal $3$-generated axial algebras and the $3$-generated $4$-transposition have been calculated. A simplification of the treatment of idempotents in

Annual Review | October 2017 – September 2018 Heilbronn Institute for Mathematical Research www.heilbronn.ac.uk Page|44

axial algebras of Jordan-type $\frac{1}{2}$ was discussed and Bernstein algebras were considered as candidates for additional new examples in this case. Was also had discussions on the future direction of research in the area and a harmonisation of terminology.

11-13 June 2018 Parallelizing Monte Carlo Algorithms Bristol Organiser| Nick Whiteley (Bristol) 9 participants Participants| Louis Aslett (Durham), Pierre Jacob (Harvard), Kari Heine (Bath), Maria Lomeli Garcia (Cambridge), Catalina Vallejos (UCL), Lawrence Murray (Uppsala), Christophe Andrieu (Bristol), Anthony Lee (Bristol), Mathieu Gerber (Bristol).

Report This meeting was a valuable opportunity to bring together experts with complementary skills in Monte Carlo algorithms and parallel computing. Two particular highlights derived from the diverse academic backgrounds of the participants were:

1. Dr. Lawrence Murray’s on-going work on probabilistic programming languages. This topic stimulated discussion of connections to graphical models and formulation of stochastic process models for probabilistic programming languages. These models are being fed in to a paper Murray is currently writing and the open-source Birch software he is currently developing (http://birch-lang.org/).

Annual Review | October 2017 – September 2018 Heilbronn Institute for Mathematical Research www.heilbronn.ac.uk Page|45

2. It became apparent through the meeting that even amongst specialists in the field there is limited overlapping knowledge of recent developments in computation, such as TensorFlow, which could be key for future algorithms. This need for training was fed into the recently submitted bid by members of the Institute for Statistical Science for an EPSRC Centre for Doctoral Training in Computational Statistics and Data Science.

The meeting also stimulated a number of on-going collaborations, for instance between Dr. Kari Heine and Dr. Mathieu Gerber on algorithms for streaming data; and between Dr. Lawrence Murray, Prof. Pierre Jacob and Dr. Nick Whiteley on Sequential Monte Carlo methods.

Annual Review | October 2017 – September 2018 Heilbronn Institute for Mathematical Research www.heilbronn.ac.uk Page|46

20-22 June 2018 Bohemian Matrices and Applications Manchester Organisers| Nick Higham (Manchester), Rob Corless, (Western 16 participants Ontario). Participants| Cara Adams (Western Ontario), Pierre Blanchard (Manchester), Eunice Chan, University of Western Ontario), Rob Corless (Western Ontario), Massimiliano Fasi (Manchester), Nick Higham (Manchester), Lalo Gonzalez-Vega (Universidad de Cantabria), Ilse Ipsen (North Carolina State University), Piers Lawrence (EigenPoly Consulting), Matthew Lettington (Cardiff), Theo Mary (Manchester), Vanni Noferini (Essex), Gian Maria Negri Porzio (Manchester), Juana Sendra (Universidad Politécnica de Madrid), Steven Thornton (Western Ontario), Françoise Tisseur (Manchester).

Report The workshop was informal, with plenty of time for participants to work together, as is suited to a nascent field of study where there are many open questions, and it led to the formation of new collaborations.

Annual Review | October 2017 – September 2018 Heilbronn Institute for Mathematical Research www.heilbronn.ac.uk Page|47

The list of 16 = 11 male + 5 female participants included researchers based in England, Canada, Spain, Belgium, USA, and Wales. Half the participants were senior researchers, and the other half included junior faculty, postdocs and students (post graduate and one undergraduate). The areas of expertise ranged among matrix theory, numerical linear algebra, computer algebra, algebraic geometry, and number theory.

Several open problems were solved and numerous new questions were posed. Steven Thornton has created the Characteristic Polynomial Database - http://www.bohemianmatrices.com/cpdb, which contains more than 10^9 polynomials from more than 10^{12} Bohemian matrices and has led to a number of conjectures concerning matches of properties to sequences at the On-Line Encyclopedia of Integer Sequences. Two outputs from the workshop have just appeared on the Arxiv (arXiv:1809.10664 and arXiv:1809.10653) and much other work is ongoing.

Annual Review | October 2017 – September 2018 Heilbronn Institute for Mathematical Research www.heilbronn.ac.uk Page|48

The workshop is described in the blog post https://nickhigham.wordpress.com/2018/10/15/bohemian- matrices-in-manchester/

and will be mentioned in Higham's column in the December 2018 issue of SIAM News.

11-14 July 2018 Cluster Algebras and Algebraic Geometry Nottingham Organisers| Tom Ducat (Bristol) and Andrea Petracci (Nottingham) 27 participants Speakers| Hamid Ahmadinezhad (Loughborough) Gavin Brown (Warwick), Livia Campo (Warwick), Daniel Cavey (Nottingham), Tom Ducat (Bristol), Anna Felikson (Durham), Giulia Gugiatti (Imperial), Liana Heuberger (Warwick), DongSeon Hwang (Ajou University), Anne-Sophie Kaloghiros (Brunel), Alexander Kasprzyk (Nottingham), Edwin Kutas (Warwick), Erik Paemurru (Loughborough), Clelia Pech (Kent), Andrea Petracci (Nottingham), Thomas Prince (Oxford), Imran Qureshi (Tübingen), Peter Spacek (Kent), Rosemary Taylor (Warwick).

Report The workshop was a great success. We had three speakers delivering mini-courses of three lectures each and research talks by nine other speakers, including three half-hour talks given by PhD students. There was plenty of discussion amongst participants during coffee and lunch breaks, and the talks stimulated much interest in a fast-growing and exciting area of mathematics. Some interesting new ideas discussed at the workshop include the possibility of generalising cluster algebra mutation to "higher-dimensional quivers" (oriented simplicial complexes) as described in Al Kasprzyk's talk, associating a simplicial complex to a log Calabi-Yau pair that generalises the exchange graph for cluster varieties as described by Anne-Sophie Kaloghiros, and several new developments in mirror symmetry. Moreover, Tom Ducat intends to write up his lectures on Cluster algebras and the 3-dimensional Mori program into a short survey article, as currently this connection between cluster algebras and birational geometry is not very well described in the literature.

Annual Review | October 2017 – September 2018 Heilbronn Institute for Mathematical Research www.heilbronn.ac.uk Page|49

23-27 July 2018 Analytic Number Theory and Quantum Chaos, “L-functions and QMUL Multiplicative Functions” 16 participants Organiser| Steve Lester (QMUL) Participants| Yueke Hu (ETH Zurich), Bingrong Huang (Tel Aviv University), Peter Humphries (UCL), Junehyuk Jung (Texas A&M), Par Kurlberg (KTH), Steve Lester (QMUL, organiser), Jens Marklof (Bristol), Paul Nelson (ETH Zurich), Yiannis Petridis (UCL), Morten Risager (Copenhagen), Lior Rosenzweig (Afeka College), Zeev Rudnick (Tel Aviv University), Abhishek Saha (QMUL), Henrik Ueberschaer (IMJ-PRG ), Igor Wigman (King's College), Nadav Yesha (King's College).

Report The Analytic Number Theory and Quantum Chaos workshop on “L-functions and Multiplicative Functions” took place from July 23-27. During the first two days of the workshop there were nine one hour talks on current developments within the field. On Monday July 23rd there was a workshop dinner during which participants discussed current research and challenging problems to work on over the following week. The last three days of the workshop consisted of focused group research in which participants worked together in groups of 2-4 people on difficult open problems. On the first day of group research there was a 2 hour problem session in which participants described open problems which they would like to discuss over the rest of the

Annual Review | October 2017 – September 2018 Heilbronn Institute for Mathematical Research www.heilbronn.ac.uk Page|50

week. I believe this second stage of the workshop was very effective. For instance, I started working on several new projects as a direct result of the workshop and also received positive feedback from other participants about the format of the workshop. Finally, there were 16 total participants for the workshop (with 9 speakers). Of the total number of participants, 6 are based in London and 2 are postdocs who accompanied their postdoc supervisor to the workshop, these factors contributed to the larger than expected number of total participants.

21-23 August 2018 Challenges in Modern Change-Point Problems Bristol Organisers| Haeran Cho (Bristol) and Yi Yu (Bristol). 12 participants A joint University of Bristol and Heilbronn Focused Research Workshop.

Annual Review | October 2017 – September 2018 Heilbronn Institute for Mathematical Research www.heilbronn.ac.uk Page|51

Report This workshop was on change point detection, which is an area gaining increasing popularity worldwide in the recent years, and on which UK statisticians have a trademark. The purpose of this workshop was 3-fold: a) to have an overview of the current state- of-the-art research on change point detection, b) to address the important but uncharted territory of change point detection, and c) to bring world-leading researchers on change point detection to Bristol such that a wider internal audience will be benefited. Usually a) is relatively easy to achieve, but b) is hard. This workshop, however, has exceeded our expectation in the sense that more than half of the speakers spoke on working projects. Important but challenging directions were identified during the designated discussion slots, and participants were all engaged in the discussion on future directions. Given the highly focused nature of the theme of the workshop, and its timing (end of August), there were quite a few internal people who attended the workshop, and hence c) was partially achieved.

3-7 September 2018 Equations in one-relator Groups and Semigroups ICMS, Edinburgh Organiser| Laura Ciobanu (Heriot-Watt University). 10 participants Participants| Yago Antolin (UAM Madrid), Andrew Duncan (Newcastle), Murray Elder (UTS Sydney), Albert Garreta (Bilbao), Giles Gardam (Technion, Israel/ HIM Bonn), Robert Gray (East Anglia), Jim Howie (Heriot-Watt), Alan Logan (Glasgow), Alina Vdovina (Newcastle).

Report There were 12 talks, given by all participants, of 50-60 minutes each, some on recent results and some giving the overview of a topic. All speakers gave accessible talks, and the style was informal and very conducive to questions and discussions. There was ample time scheduled for discussions, and 3 groups, each of 3-4 participants, took form. Each group tackled a different set of questions, and set up future directions of research, as well as collaborations. Significant progress was made on the most important classes of one-relator groups, such as cyclically pinched and Baumslag-Solitar, as well as a clear road on how to solve equations in one-relator monoids.

Annual Review | October 2017 – September 2018 Heilbronn Institute for Mathematical Research www.heilbronn.ac.uk Page|52

24-26 Sept. 2018 High-Dimensional Critical Phenomena in Random Environments Bristol Organiser| Tyler Helmuth (Bristol) 19 participants Participants: Sebastien Andres (Cambridge), Márton Balázs (Bristol), Roland Bauerschmidt (Cambridge), Erwin Bolthausen (Zurich), David Brydges (Vancouver), Paul Dario (Paris-Dauphine), A joint University of Ayalvadi Ganesh (Bristol), Takashi Hara (Kyushu), Markus Bristol and Heilbronn Heydenreich (Munich), Francesco Mezzadri (Bristol), Pierre- Focused Research François Rodriguez (UCLA), Akira Sakai (Hokkaido), Gordon Slade Workshop. (Vancouver), Andrew Swan (Cambridge), Lorenzo Taggi (Bath), Christopher Lutsko (Bristol), Bálint Tóth (Bristol/Budapest), Michiel van den Berg (Bristol), Andrew Wade (Durham).

Report The study of critical phenomena is challenging as it concerns problems that have no intrinsic scale. Progress has been made by tools such as rigorous renormalization group analyses, the lace expansion, and by exploiting connections between local times of random walks and the spin systems.

The talks by Heydenreich, Rodriguez, Sakai, Slade, and Swan discussed important recent developments in these areas. We also had excellent talks about random walk in random environments, which is the basis for the study of critical phenomena of more complicated particle systems in random environments. These were given by Andres, Bolthausen, Dario, and Tóth. Outside of the two core areas above we also had two talks by Taggi and Wade, who discussed recent progress on problems concerning self- interacting random walks. Some promising directions for future work have been identified, and fundamental challenges for the application of existing methods to study critical phenomena in random environments have been clarified. The talks by Bolthausen and Sakai have also suggested interesting strategies that warrant further investigation. Discussions and debates between the talks were lively, and participants have already reported productive process on collaborations and ongoing projects.

Annual Review | October 2017 – September 2018 Heilbronn Institute for Mathematical Research www.heilbronn.ac.uk Page|53

APPENDIX |E4 Future Events

22-26 October 2018 Height Functions and Lehmer-Type Programmes Bristol Organiser| Kirsti Biggs (Bristol).

November 2018 The London Paris Number Theory UCL Organisers| Yiannis Petridis (UCL), David Burns (KCL), Kevin Buzzard (Imperial College), Fred Diamond (KCL), Alexei Skorobogatov (Imperial College), Andrei Yafaev (UCL), Sarah Zerbes (UCL).

21st November 2018 Heilbronn Colloquium | Homological Stability: What is that for? Bristol By| Nathalie Wahl (Copenhagen) Organiser| Jon Keating (Bristol). Nathalie Wahl is a leading expert in algebraic topology, homotopy theory and geometric topology, and is distinguished for her work on homological stability. She is a professor at the University of Copenhagen and is spending the autumn semester at the Isaac Newton Institute.

11-14 December 2018 Advances in Applied Algebraic Geometry Bristol Organiser| Fatemeh Mohammadi (Bristol). Speakers| Spencer Backman (Frankfurt), Marta Casanellas (Barcelona), Carlos D'Andrea (Barcelona), Emanuele Delucchi (Freiburg), Robin Evans (Oxford), Kaie Kubjas (MIT), Anna Levina (Tübingen), Marta Panizzut (TU Berlin), Johannes Rauh (MPI Leipzig), Cordian Riener (Tromsø), Felipe Rincón (Queen Mary),

Annual Review | October 2017 – September 2018 Heilbronn Institute for Mathematical Research www.heilbronn.ac.uk Page|54

Kayvan Sadeghi (Cambridge), Eduardo Sáenz de Cabezón (Logroño), Anna Seigal (Berkeley), Bernd Sturmfels (MPI Leipzig), Timo de Wolff (TU Berlin), Henry Wynn (LSE), Piotr Zwiernik (Barcelona).

December 2018 Kinetic PDEs with Multiple Equilibria: Beyond Ergodic Theory Heriot-Watt University Organisers| Michela Ottobre (Maxwell Institute, Edinburgh) and Boguslaw Zegarlinski (Imperial College).

17-21 December 2018 Structure and randomness in hypergraphs LSE Organisers| Peter Allen, Julia Böttcher and Jozef Skokan.

January 2019 Algebraic Geometry in Combinatorics Loughborough Organiser| Hamid Ahmadinezhad (Loughborough).

1-5 April 2019 Distinguished Lecture Series 2019 Bristol Speaker | Geordie Williamson (Sydney).

[In cooperation with the School of Mathematics, Bristol].

8-11 April 2019 British Mathematical Colloquium (BMC 2019) Lancaster Organiser| Jan Grabowski (Lancaster).

Annual Review | October 2017 – September 2018 Heilbronn Institute for Mathematical Research www.heilbronn.ac.uk Page|55

8-10 April 2019 Quantum Computing Theory in Practice Bristol Organisers| Steve Brierley (River Lane Research), Noah Linden (Bristol), Ashley Montanaro (Bristol). Keynote Speakers| Iordanis Kerenidis (CNRS, IRIF, Paris Diderot), Hartmut Neven (Google). Invited Speakers| Ryan Babbush (Google), Andrew Childs (University of Maryland), Eleni Diamanti (CNRS, Pierre et Marie Curie), Aram Harrow (MIT), Naomi Nickerson (PsiQuantum), David Poulin (Université de Sherbrooke), Marcus da Silva (Rigetti), Kristan Temme (IBM), Ronald de Wolf (CWI).

15-17 April 2019 British Colloquium for Theoretical Computer Science (BCTCS) Durham Organiser| Matthew Hauge (Durham).

13-17 May 2019 Distinguished Lecture Series 2019 Bristol Speaker | Jordan Ellenberg (UW, Madison).

[Organised in cooperation with the School of Mathematics, University of Bristol].

1 June 2019 Gauge Theory Summer School - British Isles Graduate Workshop UCL Organiser| Benjamin Aslan (UCL).

Annual Review | October 2017 – September 2018 Heilbronn Institute for Mathematical Research www.heilbronn.ac.uk Page|56

17-28 June 2019 CMI-HIMR Summer School | Computational Number Theory Bristol Organisers: Jennifer Balakrishnan (Boston), Tim Dokchitser (Bristol). Speakers| John Cremona (Warwick), Céline Maistret (Boston), Jointly funded by the Adam Morgan (KCL), Jan Steffen Müller (Oldenburg), Rachel Clay Mathematics Newton (Reading), Samir Siksek (Warwick), Andrew Sutherland Institute and the (MIT), John Voight (Dartmouth College). Heilbronn Institute.

18-22 June 2019 Research Students’ Conference (RSC) in Probability and Statistics Exeter Organiser| Victoria Volodina (Exeter)

8-12 July 2019 Measurability, Ergodic Theory and Combinatorics Warwick Organisers| Miklós Abért (MTA Alfréd Rényi Institute of Mathematics), Tim Austin (UCLA), András Máthé (Warwick) and Oleg Pikhurko (Warwick). Speakers| Ágnes Backhausz (Eötvös Loránd), Vitaly Bergelson (Ohio), Lewis Bowen (Texas at Austin), Clinton Conley (Carnegie Mellon), Endre Csóka (Alfréd Rényi Institute), Gábor Elek (Lancaster), Damien Gaboriau (ENS Lyon), Łukasz Grabowski (Lancaster), Ben Green (Oxford), Kate Juschenko (Northwestern), Gábor Kun (Alfréd Rényi Institute), Hanfeng Li (SUNY at Buffalo), Andrew Marks (UCLA), Joel Moreira (Northwestern), Nikolay Nikolov (Oxford), Tom Sanders (Oxford), Brandon Seward (Courant Institute), Andreas Thom (TU Dresden), Anush Tserunyan (Illinois at Urbana-Champaign), Robin Tucker-Drob (Texas A&M), Tamar Ziegler (Hebrew).

Annual Review | October 2017 – September 2018 Heilbronn Institute for Mathematical Research www.heilbronn.ac.uk Page|57

22-26 July 2019 21st Postgraduate Group Theory Conference (PGTC) Birmingham Organisers at Birmingham| Mark Butler, Ollie Jones, Andrea Pachera, Jack Saunders and Martin van Beek.

An annual conference organised by PhD students for PhD students in group theory and related areas.

29 July – 2 August 2019 2019 British Combinatorial Conference Birmingham Organiser| Richard Mycroft (Birmingham).

12-13 September 2019 Heilbronn Annual Conference Bristol Speakers | Julia Wolf (Cambridge), Bianca Viray (Washington), Emmanuel Kowalski (ETH Zurich), Hugo Duminil-Copin (IHES, Paris-Saclay), Holly Krieger (Cambridge), Melody Chan (Brown), Kannan Soundararajan (Stanford).

23-28 September 2019 Geometry and Analysis: celebrating the mathematics of Pierre Oxford Pansu Organisers| Emmanuel Breuillard (Cambridge), Cornelia Drutu (Oxford), Enrico Le Donne (Jyvaskyla).

Annual Review | October 2017 – September 2018 Heilbronn Institute for Mathematical Research www.heilbronn.ac.uk Page|58

APPENDIX |P1 Fellows Joining in 2017|2018

Ducat, Thomas Ph.D., 2017 (Warwick) | 1st October 2017 Bristol Research Interest | Algebraic Geometry and I am primarily interested in the explicit birational geometry of 3-folds.

Jones, Nick Ph.D., 2017 (Bristol) | 1st October 2017 Bristol Research Interest | Integrable models, Discrete complex analysis, Fractional quantum Hall effect and anyons, Random Matrix Theory.

Kopp, Gene Ph.D., 2017 (Michigan) | 1st October 2017 Bristol Research Interest | Number Theory, Modular Forms, Special Functions, Random Matrix Theory, Secure Multiparty Computation.

Malcolm, Alex Ph.D., 2017 (Imperial College London) | 1st October 2017 Bristol Research Interest | Algebra.

Annual Review | October 2017 – September 2018 Heilbronn Institute for Mathematical Research www.heilbronn.ac.uk Page|59

APPENDIX |P2 Fellows Leaving since September 2017

Aldridge, Matthew End date at Bath | 31 August 2018 Current Position | Lecturer in Statistics, School of Mathematics, University of Leeds.

Bloom, Thomas End date at Bristol | 31 August 2018 Current Position | Research Fellow, Department of Pure Mathematics and Mathematical Statistics, University of Cambridge.

Brierley, Steve End date at Cambridge | 28 February 2018 Current Position | CEO of River Lane Research in Quantum Computing, Cambridge

Dogra, Netan End date at Imperial College | 30 September 2018 Current Position | Junior Research Fellow in Mathematics, Jesus College, University of Oxford.

Kramer-Miller, Joseph End date at UCL | 31 August 2018 Current Position | Visiting Assistant Professor, Department of Mathematics, University of California, Irvine.

Ledger, Sean End date at Bristol | 15 July 2018 Current Position | Position in a financial organisation in London

Annual Review | October 2017 – September 2018 Heilbronn Institute for Mathematical Research www.heilbronn.ac.uk Page|60

Murphy, Brendan End date at Bristol | 31 August 2018 Current Position | Research Associate, Department of Mathematics, University of Bristol.

Thomas, Adam End date at Bristol | 31 August 2018 Current Position | Research Fellow in Representation Theory, School of Mathematics, University of Birmingham.

Annual Review | October 2017 – September 2018 Heilbronn Institute for Mathematical Research www.heilbronn.ac.uk Page|61

APPENDIX |P3 Fellows Moving with 3 Year Extensions

Lamplugh, Jack London > London 1st October 2017 to September 2020.

Annual Review | October 2017 – September 2018 Heilbronn Institute for Mathematical Research www.heilbronn.ac.uk Page|62

APPENDIX |P4 Future Fellows

Allen, Demi Ph.D., University of York, UK 1st January 2019 Research Interest| Pure Mathematics.

Barrett, Benjamin Ph.D., Cambridge, UK 1st October 2018 Research Interest| Geometric group theory.

Beckwith, Olivia Ph.D., Emory University, Atlanta, USA 1st October 2018 Research Interest| Analytic number theory.

Doris, Christopher Ph.D., University of Bristol, UK 1st December 2018 Research Interest| Computational p-adics. | Galois theory and ramification theory | Factorization and root-finding of systems of equations.

Dougall, Rhiannon Ph.D., Warwick, UK 1st October 2018 Research Interest| Dynamics and ergodic theory.

Grace, Kevin Ph.D., Louisiana State University, LA, USA 1st October 2018 Research Interest| Matroids theory and graph theory.

Hsu, Catherine Ph.D., University of Oregon, USA 1st October 2018 Research Interest| Algebraic number theory.

Page, Janet Ph.D., University of Illinois, Chicago, USA 1st October 2018 Research Interest| Commutative algebra and algebraic geometry.

Annual Review | October 2017 – September 2018 Heilbronn Institute for Mathematical Research www.heilbronn.ac.uk Page|63

APPENDIX |M1 Mentoring Programme

Led by | Julia Wolf, Associate Chair [2014 – 2018] Career Development Heilbronn Institute for Mathematical Research

19 October 2017 Talent, Leadership, Effectiveness 23 participants By| Martin Sadler, Special Advisor to the VC (Bristol).

16 November 2017 Telling the World about your Work 20 participants By| Julian Wolf (Bristol).

8 March 2018 Teaching 13 participants By| Thomas Jordan (Bristol).

26 April 2018 Long Term Research Agenda 25 participants By| Corinna Ulcigrai (Bristol), Simon Wood (Bristol) and Philip Welch (Bristol).

24 May 2018 The REF – observations and thoughts from a HIMR perspective 26 participants By| Jon Keating (Bristol)

Annual Review | October 2017 – September 2018 Heilbronn Institute for Mathematical Research www.heilbronn.ac.uk Page|64

Heilbronn Institute for Mathematical Research School of Mathematics | University of Bristol Howard House | Queens Avenue Bristol | BS8 1SD www.heilbronn.ac.uk