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Annual Review | 2016 – 2017

Annual Review | 2016 – 2017

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 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 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 . 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. They have previously tested the Riemann Hypothesis for the Riemann zeta function at what is currently the record for the largest height up the critical line, and have made high profile contributions to the solution of the ternary Goldbach problem. Numerical computations of this kind are highly visible internationally and HIMR is now closely identified with the best work in this area.

Annual Review | October 2016 – September 2017 Heilbronn Institute for Mathematical Research www.heilbronn.ac.uk P a g e | 7

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 2017 continued the tradition of having excellent and distinguished speakers: Noga Alon (Tel Aviv), Paul Bourgade (NYU), Alice Guionnet (ENS Lyon), Radha Kessar (City), Krysta Svore (Microsoft, Seattle), Jack Thorne (Cambride), Péter Varjú (Cambridge), Sir (Oxford) and Ofer Zeitouni (Weizmann). The 2017 annual conference attracted more participants than any previous one and was generally considered to have been most successful. Many of the photographs appearing in this report were taken at the conference.

The Institute also ran a conference in 2017 to mark the 50th anniversary of Christopher Hooley’s seminal paper on the Artin Conjecture: Christopher Hooley and the Artin Conjecture: 50 years on. The speakers were Alina Cojocaru (Illinois), Roger Heath-Brown (Oxford), Christopher Hooley (Bristol), Pieter Moree () and Ram Murty (Queen’s University). We were particular pleased that Christopher Hooley gave an overview of the background to his work in this area. The handwritten notes for his lecture are of considerable historical interest and are available on the Institute’s website.

The Heilbronn Distinguished Lecture Series in 2017 was given by Professor Maciej Zworski (Berkeley). In 2016 the Heilbronn Lecturer was Professor Peter Sarnak (Princeton), and in 2018 it will be Professor Ingrid Daubechies (Duke). These lectures are organised by the University of Bristol in collaboration with HIMR.

Annual Review | October 2016 – September 2017 Heilbronn Institute for Mathematical Research www.heilbronn.ac.uk P a g e | 8

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. This is coming to be viewed as a highly attractive component of our portfolio. We now advertise the scheme in the LMS Newsletter. There is still more work to be done to ensure that our advertising reaches all departments and research areas, but we believe we are making good progress in this direction.

We have started to partner with other major mathematics research institutes, co- sponsoring workshops and other research events. We have for several years provided funding to the LMS for Postgraduate Schools. 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. We ran a workshop, jointly sponsored with the Alan Turing Institute, on large-scale structures in random graphs, and we provided support for two workshops at the ICMS in Edinburgh. We will support another ICMS workshop in the coming year and are in discussion with ATI about a second workshop to be run jointly with them and with Imperial College.

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.

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 and in 2016-17 we supported 35 events. We believe that the quality of the events we are supporting is increasing.

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.

Next year HIMR is taking the lead in organising a major conference on the Riemann Hypothesis – the organising committee includes (AIM/Bristol), Jon Keating (Bristol), Peter Sarnak (Princeton) and Sir Andrew Wiles (Oxford). The conference will take place in Bristol. Participants include Enrico Bombieri (IAS Princeton), Alain Connes (IHES), (Princeton), Henryk Iwaniec (Rutgers), and Kannan Soundararajan (Stanford). This meeting is being organised in

Annual Review | October 2016 – September 2017 Heilbronn Institute for Mathematical Research www.heilbronn.ac.uk P a g e | 9

collaboration with the American Institute of Mathematics, the Clay Mathematics Institute, the EPSRC and the NSF. HIMR is also supporting a major international conference on Probability Analysis and Dynamics, with a number of highly distinguished researchers coming to participate.

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.

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 2016 – September 2017 Heilbronn Institute for Mathematical Research www.heilbronn.ac.uk P a g e | 10

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 last year.

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 last year and we were able to be highly selective. For example, in Bristol there were over 100 applications, we interviewed 18 people, selected from an initial long-list of 50 of the strongest applicants, and appointed four Fellows.

We now 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 2016 – September 2017 Heilbronn Institute for Mathematical Research www.heilbronn.ac.uk P a g e | 11

At present we have Fellows in 8 Universities: Bath, Bristol, Cambridge, Imperial, King’s College London, Leicester, Oxford, and University College London. Most are based in Bristol. Having Fellows hosted 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.

The quality of the Fellows appointed this past year is excellent, especially given that HIMR only appoints from a small subset of mathematicians. Our 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.) The performance of the Fellows and their career trajectories are also comparable with typical Junior Research Fellows. The new website is helping to raise the Fellows’ visibility.

Annual Review | October 2016 – September 2017 Heilbronn Institute for Mathematical Research www.heilbronn.ac.uk P a g e | 12

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 Bristol, 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 Bristol (two Fellows), Exeter and Greenwich.

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.

We have introduced a scheme to support PhD study for women mathematicians who want to work at HIMR. This supported five women last year. HIMR currently supports 9 PhD students, 7 of whom are women.

HIMR funds students involved in two EPSRC Centres for Doctoral Training: the London CDT in and Number Theory (currently three students) and the Bristol CDT in Quantum Engineering (currently two students). These students spend the summer working at the Institute. HIMR is also now supporting the EPSRC-funded Data Innovation Research Institute CDT, led jointly by Cardiff University, the University of Bristol, and Swansea University.

Annual Review | October 2016 – September 2017 Heilbronn Institute for Mathematical Research www.heilbronn.ac.uk P a g e | 13

6. Mentoring Programme

Two 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, led by Dr. Julia Wolf, the Heilbronn Associate Chair in Bristol. 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 two 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 has been 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 2016 – September 2017 Heilbronn Institute for Mathematical Research www.heilbronn.ac.uk P a g e | 14

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 8 universities across the South of England, and funding mathematical activities across the whole country.

In order to provide advice and challenge to the external programme, we established an External Advisory Board to support HIMR’s. The following are 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). In the future we would like to add one or two more people, and hope to expand the geographical representation (currently this is limited by the fact that HIMR activity is centred on Bristol and London).

Annual Review | October 2016 – September 2017 Heilbronn Institute for Mathematical Research www.heilbronn.ac.uk P a g e | 15

The External Advisory Board meets annually, in September.

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, and Abla Hatherell, PA to the Chair.

The Associate Chair, Julia Wolf, has also made an outstanding contribution to further enhancing the relationship with the University of Bristol, which is HIMR’s main academic partner.

A close working relationship between the internal and the external programmes is essential to the success of both, and this continues to be achieved.

Annual Review | October 2016 – September 2017 Heilbronn Institute for Mathematical Research www.heilbronn.ac.uk P a g e | 16

APPENDIX |R1 Highlighted Paper 2016/2017 

. Performance of group testing algorithms with constant tests-per-item. Johnson, Oliver; Aldridge, Matthew; Scarlett, Jonathan. https://arxiv.org/abs/1612.07122

. Isoperimetry in integer lattices. Barber, Ben and Erde, Joshua. https://arxiv.org/abs/1707.04411

. Cyclic contractions of dimer algebras always exist. Beil, Charlie. https://arxiv.org/abs/1703.04450

. Additive energy and the metric Poissonian property. Bloom, Thomas F.; Chow, Sam; Gafni, Ayla; Walker, Aled. https://arxiv.org/abs/1709.02634

. Smooth values of Polynomials. Bober, Jonathan W.; Fretwell, Martin, Greg; Daniel; Wooley, Trevor. https://arxiv.org/abs/1710.01970

. A converse theorem without root numbers. Booker, Andrew R. https://arxiv.org/abs/1703.01834

. Dynamics of modular matings. Bullett, Shaun and Lomonaco, Luna. https://arxiv.org/abs/1707.04764

. Diffusion and superdiffusion in lattice models for colliding particles with stored momentum. Crane, Edward; Ledger, Sean; Tóth, Balint.

. Quadratic Chabauty and Rational Points II. Balakrishnan, Jennifer and Dogra, Netan. https://arxiv.org/abs/1705.00401

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. Visibility of 4-covers of elliptic curves. Bruin, Nils and Fisher, Tom https://arxiv.org/abs/1701.07528

. Generic level p Eisenstein congrunces for GSp4. Fretwell, Dan. https://arxiv.org/abs/1605.03450

. Generalisations of the Symplectic and Orthogonal two-graphs, Gillespie, Neil.

. Choosing Between Methods for Combining p-values. Heard, Nicholas and Rubin- Delanchy, Patrick. https://arxiv.org/abs/1707.06897

. On the ergodic Waring--Goldbach problem. Anderson, Theresa C.; Cook, Brian; Hughes, Kevin; Kumchev, Angel. https://arxiv.org/abs/1703.02713

. The monodromy of F-isocrystals with log-decay. Kramer-Miller, Joe. https://arxiv.org/abs/1612.01164

. Derivatives of representations of Whittaker type and test vectors. Kurinczuk, Robert and Matringe, Nadir. https://arxiv.org/abs/1710.04697

. Euler system for characters over an imaginary biquadratic field. Lamplugh, Jack. https://arxiv.org/abs/1611.05702

. The unicity of types for depth zero supercuspidal representations. Latham, Peter. https://arxiv.org/abs/1606.01691

. Diffusion and superdiffusion in lattice models for colliding particles with stored momentum. Crane, Edward; Ledger, Sean; Tóth, Balint.

. Quantum Key Search with Side Channel Advice. Martin, Daniel P.; Montanaro, Ashley; Oswald, Elisabeth; Shepherd, Dan. SAC, 2017. https://eprint.iacr.org/2017/171

. Code Algebras, Axial algebras and VOAs. Castillo-Ramirez, Alonso; McInroy, Justin; Rehren, Felix. https://arxiv.org/abs/1707.07992

. Upper and lower bounds for rich lines in grids. Murphy, Brendan. https://arxiv.org/abs/1709.10438

. (Some) degree 2 quotients of L-functions have infinitely many poles. Oliver, Thomas and Neuruer, Michalis.

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. The Duffin-Schaeffer theorem in number fields. Palmer, Matthew. https://arxiv.org/pdf/1610.07322

. Separable equivalence, complexity and representation type. Peacock, Simon F. https://arxiv.org/abs/1705.11029

. The generalised random dot product graph. Rubin-Delanchy, Patrick; Priebe, Carey E.; Tang, Minh. https://arxiv.org/abs/1709.05506

. The Exotic Robinson-Schensted Correspondence. Nandakumar, Vinoth; Rosso, Daniele; Saunders, Neil .

. The cycle polynomial of a permutation group. Cameron, Peter J. and Semeraro, Jason. https://arxiv.org/abs/1701.06954

. Inversions in split trees and conditional Galton--Watson trees. Cai, Xing Shi; Holmgren, Cecilia; Janson, Svante; Johansson, Tony; Skerman, Fiona. https://arxiv.org/abs/1709.00216

. Jordan blocks of cuspidal representations of symplectic groups. Blondel, Corinne; Henniart, Guy; Stevens, Shaun. https://arxiv.org/abs/1704.03545

. On the involution fixity of exceptional groups of Lie type. Burness, Tim and Thomas, Adam. https://arxiv.org/abs/1707.03562

. Permutation groups containing an abelian regular subgroup: the tangled history of two mistakes of Burnside. Wildon, Mark. https://arxiv.org/abs/1705.07502

. L-invariants and exceptional zeros of Bianchi modular forms. Williams, Chris and Barrera Salazar, Daniel. https://arxiv.org/abs/1707.04049

Annual Review | October 2016 – September 2017 Heilbronn Institute for Mathematical Research www.heilbronn.ac.uk P a g e | 19

Complete List of Research Papers APPENDIX |R2 2016/2017

. On the optimality of some group testing algorithms. Aldridge, Matthew. https://arxiv.org/abs/1705.02708

. Performance of group testing algorithms with constant tests-per-item. Johnson, Oliver; Aldridge, Matthew; Scarlett, Jonathan. https://arxiv.org/abs/1612.07122

. Isoperimetry in integer lattices. Barber, Ben and Erde, Joshua. https://arxiv.org/abs/1707.04411

. A Finite electrodynamic field theory from Aristotelian time. Beil, Charlie.

. Nonnoetherian coordinate rings with unique maximal depictions. Beil, Charlie. https://arxiv.org/abs/1608.0092

. Cyclic contractions of dimer algebras always exist. Beil, Charlie. https://arxiv.org/abs/1703.04450

. Additive energy and the metric Poissonian property. Bloom, Thomas F.; Chow, Sam; Gafni, Ayla; Walker, Aled. https://arxiv.org/abs/1709.02634

. Smooth values of Polynomials. Bober, Jonathan W.; Fretwell, Martin, Greg; Daniel; Wooley, Trevor. https://arxiv.org/abs/1710.01970

. A conjectural extension of Hecke's converse theorem. Bettin, Sandro; Bober, Jonathan W.; Booker, Andrew R.; Conrey, Brian; Lee, Min; Molteni, Giuseppe; Oliver, Thomas; Platt, David J.; Steiner. Raphael S. https://arxiv.org/abs/1704.02570

. Finite connected components of the aliquot graph. Booker, Andrew R. https://arxiv.org/abs/1610.07471

. A converse theorem without root numbers. Booker, Andrew R. https://arxiv.org/abs/1703.01834

. Rapid computation of L-functions attached to Maass forms. Booker, Andrew R. and Then, Holger. https://arxiv.org/abs/1703.08863

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. A conjectural extension of Hecke's converse theorem. Bettin, Sandro; Bober, Jonathan W.; Booker, Andrew R.; Conrey, Brian; Lee, Min; Molteni, Giuseppe; Oliver, Thomas; Platt, David J.; Steiner. Raphael S. https://arxiv.org/abs/1704.02570

. Subconvexity for modular form L-functions in the t aspect. Booker, Andrew R.; Milinovich, Micah B.; Ng, Nathan. https://arxiv.org/abs/1707.01576

. Turing’s method for the Selberg zeta-function. Booker, Andrew R. and Platt. David J. https://arxiv.org/abs/1710.00603

. Mating quadratic maps with the modular group II. Bullett, Shaun and Lomonaco, Luna. https://arxiv.org/abs/1611.05257

. Dynamics of modular matings. Bullett, Shaun and Lomonaco, Luna. https://arxiv.org/abs/1707.04764

. Diffusion and superdiffusion in lattice models for colliding particles with stored momentum. Crane, Edward; Ledger, Sean; Tóth, Balint.

. Quadratic Chabauty and Rational Points II. Balakrishnan, Jennifer and Dogra, Netan. https://arxiv.org/abs/1705.00401

. Visibility of 4-covers of elliptic curves. Bruin, N. and Fisher, Tom. https://arxiv.org/abs/1701.07528

. Some minimisation algorithms in arithmetic invariant theory. Fisher, Tom. and Radicevic, L. https://arxiv.org/abs/1703.01940

. On some algebras associated to genus one curves. Fisher, Tom. https://arxiv.org/abs/1707.08330

. Generic level p Eisenstein congrunces for GSp4. Fretwell, Dan. https://arxiv.org/abs/1605.03450

. Genus 2 paramodular Eisenstein congruences. Fretwell, Dan. https://arxiv.org/abs/1603.07088

. Generalisations of the Symplectic and Orthogonal two-graphs, Gillespie, Neil.

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. Malware Family Discovery Using Reversible Jump MCMC Sampling of Regimes. Bolton, Alexander; Heard, Nicholas.

. Detecting periodic subsequences in cyber security data. Price-Williams, Matthew; Heard, Nicholas; Turcotte, Melissa. https://arxiv.org/abs/1707.00640

. Choosing Between Methods for Combining p-values. Heard, Nicholas and Rubin- Delanchy, Patrick. https://arxiv.org/abs/1707.06897

. On the ergodic Waring--Goldbach problem. Anderson, Theresa C.; Cook, Brian; Hughes, Kevin; Kumchev, Angel. https://arxiv.org/abs/1703.02713

. Improved ℓp-Boundedness for Integral k-Spherical Maximal Functions. Anderson, Theresa C.; Cook, Brian; Hughes, Kevin; Kumchev, Angel. https://arxiv.org/abs/1707.08667

. The monodromy of F-isocrystals with log-decay. Kramer-Miller, Joe. https://arxiv.org/abs/1612.01164

. p-adic L-functions on Hida Families. Kramer-Miller, Joe. https://arxiv.org/abs/1507.01814

. Derivatives of representations of Whittaker type and test vectors. Kurinczuk, Robert and Matringe, Nadir. https://arxiv.org/abs/1710.04697

. Euler system for characters over an imaginary biquadratic field. Lamplugh, Jack. https://arxiv.org/abs/1611.05702

. On the unicity of types in special linear groups. Latham, Peter. https://arxiv.org/abs/1511.00642

. The unicity of types for depth zero supercuspidal representations. Latham, Peter. https://arxiv.org/abs/1606.01691

. Diffusion and superdiffusion in lattice models for colliding particles with stored momentum. Crane, Edward; Ledger, Sean; Tóth, Balint.

. A stochastic partial differential equation model for mortgage backed securities. Ahmad, Ferhana; Hambly, B.M., Ledger, Sean. https://people.maths.ox.ac.uk/hambly/PDF/Papers/mbs.pdf

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. Dynamic Shortest Path and Transitive Closure Algorithms: A Survey, Martin, D.P. https://arxiv.org/abs/1709.00553

. Authenticated Encryption in the Face of Protocol and Side Channel Leakage. Barwell, Guy; Martin, Daniel P.; Oswald, Elisabeth; Stam, Martijn. To appear, Asiacrypt, 2017. https://eprint.iacr.org/2017/068

. Quantum Key Search with Side Channel Advice. Martin, Daniel P.; Montanaro, Ashley; Oswald, Elisabeth; Shepherd, Dan. SAC, 2017. https://eprint.iacr.org/2017/171

. Code Algebras, Axial algebras and VOAs. Castillo-Ramirez, Alonso; McInroy, Justin; Rehren, Felix. https://arxiv.org/abs/1707.07992

. Upper and lower bounds for rich lines in grids. Murphy, Brendan. https://arxiv.org/abs/1709.10438

. Products of Differences over Arbitrary Finite Fields. Murphy, Brendan and Petridis, Giorgis. https://arxiv.org/abs/1705.06581

. Variations on the sum-product problem II. Murphy, Brendan; Roche-Newton, Oliver; Shkredov, Ilya. https://arxiv.org/abs/1703.09549

. New results on sum-product type growth over fields. Murphy, Brendan; Petridis, Giorgis; Roche-Newton, Oliver; Rudnev, Misha; Shkredov, Ilya. https://arxiv.org/abs/1702.01003

. A Second Wave of Expanders over Finite Fields. Murphy, Brendan and Petridis, Giorgis. https://arxiv.org/abs/1701.01635

. (Some) degree 2 quotients of L-functions have infinitely many poles. Oliver, Thomas and Neuruer, Michalis.

. A conjectural extension of Hecke's converse theorem. Bettin, Sandro; Bober, Jonathan W.; Booker, Andrew R.; Conrey, Brian; Lee, Min; Molteni, Giuseppe; Oliver, Thomas; Platt, David J.; Steiner. Raphael S. https://arxiv.org/abs/1704.02570

. The Duffin-Schaeffer theorem in number fields. Palmer, Matthew. https://arxiv.org/pdf/1610.07322

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. Separable equivalence, complexity and representation type. Peacock, Simon F. https://arxiv.org/abs/1705.11029

. The generalised random dot product graph. Rubin-Delanchy, Patrick; Priebe, Carey E.; Tang, Minh. https://arxiv.org/abs/1709.05506

. Consistency of adjacency spectral embedding for the mixed membership stochastic blockmodel. Rubin-Delanchy, Patrick; Priebe, Carey E.; Tang, Minh. https://arxiv.org/abs/1705.04518

. Choosing between methods for combining p-values. Heard, Nicholas A. and Rubin- Delanchy, Patrick. https://arxiv.org/abs/1707.06897

. 3D Bayesian cluster analysis of super-resolution data reveals LAT recruitment to the T cell synapse. Griffié, Juliette; Shlomovich, Leigh; Williamson, David J.; Shannon, Michael; Aaron, Jesse; Khuon, Satya; Burn, Garth L.; Boelen, Lies; Peters, Ruby; Cope, Andrew P.; Cohen, Edward A. K.; Rubin-Delanchy, Patrick; Owen, Dylan M. Scientific Reports, Vol. 7:4077, 2017. https://www.nature.com/articles/s41598-017-04450-w

. Meta-analysis of mid-p-values: some new results based on the convex order. Rubin- Delanchy, Patrick; Heard, Nicholas A.; Lawson, Daniel. https://arxiv.org/abs/1505.05068

. Irreducible Components of Exotic Springer Fibres. Nandakumar, Vinoth; Rosso, Daniele; Saunders, Neil. https://arxiv.org/abs/1611.05844

. The Exotic Robinson-Schensted Correspondence. Nandakumar, Vinoth; Rosso, Daniele; Saunders, Neil.

. Absorption of Direct Factors With Respect to the Minimal Faithful Permutation Degree of a Finite Group. Easdown, David; Hendriksen, Michael; Saunders, Neil. https://arxiv.org/abs/1610.05336

. The cycle polynomial of a permutation group. Cameron, Peter J. and Semeraro, Jason. https://arxiv.org/abs/1701.06954

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. Conway’s groupoid and its relatives. Contemporary Mathematics Volume 694, 2017 in honour of John H. Conway. Gill, Nick; Gillespie, Neil; Praeger, Cheryl; Semeraro, Jason. http://bookstore.ams.org/conm-694/

. Inversions in split trees and conditional Galton--Watson trees. Cai, Xing Shi; Holmgren, Cecilia; Janson, Svante; Johansson, Tony; Skerman, Fiona. https://arxiv.org/abs/1709.00216

. Modularity of regular and treelike graphs. McDiarmid, Colin and Skerman, Fiona. https://arxiv.org/abs/1606.09101

. Jordan blocks of cuspidal representations of symplectic groups. Blondel, Corinne; Henniart, Guy; Stevens, Shaun. https://arxiv.org/abs/1704.03545

. On the involution fixity of exceptional groups of Lie type. Burness, T. and Thomas, Adam. https://arxiv.org/abs/1707.03562

. Generalized Foulkes modules and maximal and minimal constituents of plethysms of Schur functions, Paget, R. and Wildon, Mark. https://arxiv.org/abs/1608.04018

. Permutation groups containing an abelian regular subgroup: the tangled history of two mistakes of Burnside. Wildon, Mark. https://arxiv.org/abs/1705.07502

. L-invariants and exceptional zeros of Bianchi modular forms. Williams, Chris and Barrera Salazar, Daniel. https://arxiv.org/abs/1707.04049

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HIMR-Run Events APPENDIX |E1 The Heilbronn Institute organises a two-day annual conference and a number of workshops, meetings and working groups 

27-29 March 2017 Distinguished Lecture Series 2017 Bristol Speaker: Maciej Zworski, University of California, Berkeley

80 Participants [Organised in cooperation with the School of Mathematics, Conference website University of Bristol]. https://goo.gl/QNK7j8

4 April 2017 Quantum Algorithms Day 2017 Bristol Speakers: Fernando Brandao (CalTech), Elizabeth Crosson 60 Participants (CalTech), Iordanis Kerenidis (Paris), Stephen Piddock (Bristol) Conference website https://goo.gl/emTJ69 This meeting is also supported by EPSRC.

1st September 2017 Christopher Hooley and the Artin Conjecture Workshop Bristol Speakers: Alina Cojocaru (Illinois at Chicago), 50 Participants Roger Heath-Brown (Oxford), Christopher Hooley (Bristol), Workshop website Pieter Moree (Max-Planck Institut) Ram Murtym (Queen’s https://goo.gl/pCghsf University)

Organiser: Jonathan Bober

A celebration of the 50th anniversary of Christopher Hooley’s research on the Artin Conjecture.

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14-15 September 2017 Heilbronn Annual Conference Bristol The Annual Conference is the institute’s flagship event. It 112 Participants brings together members of the Institute, distinguished Conference website visiting speakers, and other members of the UK mathematical https://goo.gl/Z7d6cs community.

The Speakers

Noga Alon (Tel Aviv University) Structure, randomness and universality

Paul Bourgade (New York University) Random matrices, the Riemann zeta function and trees

Alice Guionnet (ENS Lyon) Fluctuations of random tilings and discrete Beta-ensembles

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Radha Kessar (City University London) Local structure and representations of finite groups

Krysta Svore (Microsoft) Quantum computing: revolutionizing computing through quantum mechanics

Jack Thorne (University of Cambridge) Reciprocity and Ramanujan

Péter Varjú (University of Cambridge) Recent progress on Bernoulli convolutions

Andrew Wiles (University of Oxford) A hundred years of elliptic curves

Ofer Zeitouni (Weizmann Institute of Science) Second moment methods and logarithmically correlated fields

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HIMR-Sponsored Events APPENDIX |E2 The Heilbronn Institute supports mathematics in the UK through a programme of conferences, meetings and workshops 

14-15 November 2016 The London-Paris Number Theory (LPNTS) Paris [The theme was Perfectoid spaces/Espaces perfectoïdes]

70 Participants Organisers: Pierre Charollois (Jussieu), Olivier Fouquet (Orsay), Meeting website Michael Harris (Jussieu), Marc Hindry (Jussieu), Benjamin Schraen https://goo.gl/qb4Wpj (École Polytechnique), Jacques Tilouine (Université Paris 13).

Speakers: Benoît Stroh (Institut de mathématiques de Jussieu), Yves André (Institut de mathématiques de Jussieu), Tim Newton (Kings College London), Lorenzo Ramero (Université de Lille I), Alberto Vezzani (Université Paris 13), Caraiani (Universität Bonn/Imperial College London), Matthew Morrow (Institut de mathématiques de Jussieu), Laurent Fargues (Institut de mathématiques de Jussieu).

13 March 2017 STEM for Britain Exhibition of Posters London A Poster Competition at Westminster for early career Event website researchers in Science, Engineering and Mathematics (formerly https://goo.gl/zimErX SET for BRITAIN)

Report from Stephen Metcalfe MP, Chairman, Parliamentary and Scientific Committee & Science and Technology Committee (Commons)

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Report STEM for BRITAIN exists to raise the profile of Britain's early- stage researchers at Westminster by engaging Members of both Houses of Parliament with current science, engineering and mathematics research being undertaken in the UK, especially that by their local constituents and in their local University. Few of them have science or technology degrees, but we usually have around 100 Parliamentarians attending during the day.

The quality of the work displayed by the young scientists, mathematicians and engineers was first class and I know that the judges were extremely impressed, as were my numerous Parliamentary colleagues and other distinguished guests who attended. It was a great pleasure to host STEM for BRITAIN again and after the success of this event I am very much looking forward to 2018!

Without the support of the Heilbronn lnstitute for Mathematical Research the Awards Day would not have been possible and on behalf of the Parliamentary and Scientific Committee, and the learned societies with whom we work to run the competition, I should like to thank you for your generous contribution.

20-24 March 2017 Young Geometric Group Theory VI Oxford Organisers: Aditi Kar (Oxford), John Mackay (Bristol), Anne 170 Participants Thomas (Sydney) Event website https://goo.gl/Unz4QC Mini Course: Goulnara Arzhantseva (), Emmanuel Breuillard (Orsay), Marc Burger (ETH Zurich) and Alan Reid (Texas).

Plenary Speakers: Tullia Dymarz (Wisconsin-Madison), Alireza Golsefidy (California-San Diego), Henry Wilton (Cambridge), Montserrat Casals-Ruiz (Basque Country), Enrico Le Donne, Jyväskylä (Finland), Jon Chaika (Utah, USA), Bruno Duchesne, (Lorraine, France).

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2-8 April 2017 British Isles Graduate Workshop (BIG) UCL/ Isle of Wight Higgs bundles: Algebraic and Differential Geometric Perspectives 40 Participants Workshop website Organised by LSGNT: Andrea Tirelli (Imperial College London) https://goo.gl/fLaJLP Emily Maw (UCL), Pierrick Bousseau (Imperial College London)

3-6 April 2017 British Mathematical Colloquium (BMC) 2017 Durham Organisers: Andrew Lobb and Alexander Stasinski 200 Participants Event website Speakers: Eva Bayer Fluckiger (ÉPFL), Noam Elkies (Harvard), https://goo.gl/kX1bsn Kenji Fukaya (Kyoto University/Simons Center), Isabelle Gallagher (Université Paris-Diderot), Laurent Lafforgue (IHÉS), Jacob Lurie (Hardard), (MIT)

18-21 April 2017 Research Students’ Conference in Probability and Statistics Durham (RSC 2017)

71 Participants Organisers in Durham: Themistoklis Botsas (Durham), Samuel Event website Jackson, Iman Al-hasani, James McRedmond, Ben Lopez, Chak http://rsc2017.org.uk/ Hei Lo, Junbin Chen, Marcelo Costa.

Speakers: Marcelo Costa (Durham), Aoife O’Neill (Limerick), Hana Alqifari (Durham), Kevin Brosnan (Limerick), Cheng Chen (LSE), Hermes Marques Da Silva Junior (Durham), Andrew Garthwaite (Greenwich), Mai Alfahad (Leeds), Nawapon Nakharutai (Durham), Amirah Alharthi (Leeds), Ayon Mukherjee (QMUL), Abdullah Ali H Ahmadini (Durham) Samira Abushilah (Leeds)

Keynote Speakers: Denise Lievesley (Oxford), Nicholas Bingham (Imperial College), Michael Goldstein (Durham), Peter Avery (Newcastle)

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26-28 April 2017 British Colloquium for Theoretical Computer Science (BCTCS) St Andrews LMS Keynote Lecture in Discrete Mathematics: Event website Professor László Babai, University of Chicago https://goo.gl/uRqFjp Speakers: Perdita Stevens (Edinburgh), Conor McBride (Strathclyde), Felix Fischer (Glasgow), Edwin Brady (St Andrews), Mehrnoosh Sadrzadeh (Queen Mary University of London)

22-26 May 2017 Braids in Algebra, Geometry and Topology ICMS, Edinburgh Organisers: Tara Brendle (Glasgow), Jordan Ellenberg 55 Participants (Wisconsin), Andrew Putman (Rice), Andrew Ranicki (Edinburgh) Workshop website https://goo.gl/zddtT8

5-6 June 2017 The London-Paris Number Theory Seminar 2017 UCL Theme: "The Arthur trace formula, automorphic forms, arithmetic manifolds and their homology". 45 Participants Seminar website The London-Paris Number Theory Seminar meets twice per year, https://goo.gl/BjmsAN once in London and once in Paris. Now in its 12th year, it is bringing together mathematicians from both cities and nearby universities (Oxford, Cambridge, Bristol) to learn about recent important progress in diverse areas of Number Theory.

Speakers: Olivier Taïbi (Imperial), Colette Moeglin (Jussieu), Nicolas Bergeron (Jussieu), Philippe Michel (Lausanne), Haluk Şengün (Sheffield)

Organisers: David Burns (KCL), Kevin Buzzard (Imperial) Fred Diamond (KCL), Yiannis Petridis (UCL), Alexei Skorobogatov (Imperial), Andrei Yafaev (UCL), Sarah Zerbes (UCL).

19-23 June 2017 New Trends in Representation Theory: The Impact of Cluster Leicester Theory in Representation Theory [LMS-CMI Summer School]

45 Participants Organisers: Karin Baur (U Graz), Sibylle Schroll (Leicester) and Event website Nick Woodhouse (CMI) https://goo.gl/vRdqBv

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Lecture courses by: Peter Jorgensen (Newcastle), Sophie Morier- Genoud (Paris), Lidia Angeleri-Hügel (Verona),

Guest lectures by: Martin Herschend (Uppsala), Pierre-Guy Plamondon (Orsay), Mike Prest (Manchester)

26-30 June 2017 GAeL XXV, Géométrie Algébrique en Liberté Bath Organisers: Aurelio Carlucci (Oxford), Lorenzo De Biase (Cardiff), 86 Participants James Green (Bath), Leonard Hardiman (Bath), Sara Muhvić Workshop website (Warwick) http://gael-math.org/ Speakers: Arend Bayer (Edinburgh), Alessandra Sarti (University of Poitiers, France), Angela Gibney (University of Georgia, US)

27-30 June 2017 Postgraduate Group Theory Conference (PGTC) Cambridge An Annual conference organised by PhD students for PhD 50 Participants students in group theory and related areas. Conference website https://goo.gl/JhZLYN Organisers: Andreas Bode (Cambridge), Nicolas Dupré (Cambridge), Richard Freeland (Cambridge), Amit Hazi (Cambridge), Stacey Law (Cambridge)

Invited Speakers: Nadia Mazza (Lancaster), Gunter Malle (TU Kaiserslautern

3-5 July 2017 Statistical Data Science Imperial College Organisers: Niall Adams (Imperial), Edward Cohen (Imperial) 65 Participants Yike Guo (Imperial) Conference website https://goo.gl/TYryyZ Invited Speakers: Michael Jordan (California, Berkeley), Emma McCoy (Imperial College London), David Hand (Winton), GCHQ speaker (Government Communications Headquarters), Heather Battey (Imperial College London), David Leslie (Lancaster), Alastair Young (Imperial College London), Mark Briers (Alan Turing Institute), Mark Girolami (Imperial College London).

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3-7 July 2017 Workshop on BSDES, SPDES and their Applications Edinburgh Organisers: Samuel Cohen (Oxford), Dan Crisan (Imperial College 210 Participants London), Michela Ottobre (Heriot-Watt), Gonçalo dos Reis Workshop website (Edinburgh), Lukasz Szpruch (Edinburgh), David Siska https://goo.gl/NERnYE (Edinburgh), Anke Wiese (Heriot-Watt)

Invited Speakers: Rainer Buckdahn, Peter Imkeller, Monique Jeanblanc, Juan Li, Jin Ma, Anis Matoussi, Annie Millet, Etienne Pardoux, Shige Peng, Michael Röckner, Saïd Hamadene, Panagiotis Souganidis, Nizar Touzi, Thaleia Zariphopoulou.

[This meeting included the 8th symposium on BSDEs.]

17-21 July 2017 Harmonic Analysis and its Interactions: in honour of Tony ICMS, Edinburgh Carbery

117 Participants Organisers: Juan Antonio Barcelo (Madrid), Jonathan Bennett Conference website (Birmingham), Philip Gressman (Pennsylvania), Jim Wright https://goo.gl/fSv1my (Edinburgh)

Speakers: Keith Ball (Warwick), Bill Beckner (Texas), Neal Bez (Saitama), Michael Christ (California, Berkeley), Michael Cowling (New South Wales), Ciprian Demeter (Indiana), Phil Gressman (Pennsylvania), Larry Guth (MIT), Jonathan Hickman (Chicago), Tuomas Hytonen (Helsinki), Marina Iliopoulou (California, Berkeley), Nets Katz (Caltech), Sanghyuk Lee (Seoul), Victor Lie (Purdue), Marius Mirek (Princeton), Detlef Muller (Christian- Albrechts-Universität zu ), Tuomas Orponen (Helsinki), Maria Reguera (Birmingham), Fulvio Ricci, Scuola Normale Superiore (Pisa), Keith Rogers (ICMAT), Betsy Stovall (Wisconsin-Madison), Andreas Seeger (Wisconsin-Madison), Eli Stein (Princeton), Terry Tao (California, Los Angeles), Christoph Thiele (Universität Bonn), Hong Wang, (MIT), Josh Zahl (University of British Columbia), Ruixiang Zhang (Princeton)

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2 July – 12 August 2017 PROMYS Europe: Programme in Mathematics for Young Oxford Scientists

PROMYS website A challenging six-week summer program designed to www.promys.org encourage ambitious high school students to explore the creative world of mathematics.

Two participants were sponsored by the Heilbronn Institute.

1-4 August 2017 Young Researchers in Mathematics Kent Organisers: Nitin Serwa, Jocelyne Ishak, Ellen Dowie, Ana Rojo- 67 Participants Echeburúa, Will Grummitt, Alex Rogers and Floris Claassens. Conference website https://goo.gl/r4nwHj Speakers: Martina Balagovic (Newcastle), Keith Ball (Warwick), Elizabeth Mansfield (University of Kent), Alex Bartel (Warwick), Shabnam Beheshti ((QMUL), Martin Crossley (University of Swansea), Claire Gilson (Glasgow), Steffen Krusch (Kent), Hendrik W. Lenstra (Leiden), David J.B. Lloyd (Surrey).

7-8 September 2017 LMS Prospects in Mathematics Reading The LMS Prospects in Mathematics Workshop 2017 is an 50 Participants event for all finalists Maths Undergraduates who are Workshop website considering applying for a Maths PhD in 2018. https://goo.gl/JyUeEZ Organisers: Rachel Newton (Reading), Danica Vukadinovic Greetham (Reading), Michael Levitin (Reading), Tristan Pryer (Reading)

Speakers: Ginestra Bianconi (QMUL), Thomas Forster (Cambridge), Ben Green (Oxford), Jon Keating (Bristol), Valerio Lucarini (Reading), Marco Marletta (Cardiff), Beatrice Pelloni (Heriot-Watt), Sarah Rees (Newcastle), Jennifer Ryan (UEA), Samir Siksek (Warwick), Richard Thomas (Imperial), Amanda Turner (Lancaster)

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11-15 September 2017 Diophantine problems (DIOP) Manchester Organisers: Gareth Jones (Manchester), Daniel Loughran 69 Participants (Manchester) Conference website https://goo.gl/1RP4uL Speakers: Tim Browning (Bristol), Laura Capuano (Oxford), Sara Checcoli (Institut Fourier Grenoble), Jean-Louis Colliot- Thélène (Orsay), Phillipp Habegger (Universität ), Roger Heath-Brown (Oxford), Rachel Newton (Reading), David Masser (Universität Basel), Jennifer Park (Michigan), Jonathan Pila (Oxford), Damaris Schindler (Universiteit Utrecht), Samir Siksek (Warwick), Alexei Skorobogatov (Imperial College London), Michael Stoll (Universität ), Margaret Thomas (Universität ), Ila Varma (Columbia), Trevor Wooley (Bristol)

11-12 September 2017 K-Theory, Representation Theory and Automorphic Forms Sheffield Organisers: Paul Mitchener (Sheffield), Roger Plymen 30 Participants (Manchester), Haluk Sengun (Sheffield) Workshop website https://goo.gl/5CRZvA

Report by We welcomed participants from 6 universities (from 4 Haluk Sengun different countries). Experts from automorphic forms, representation theory and noncommutative geometry were present. There were 5 talks over two half-days with ample amounts of discussion times and one event dinner. While the number of official participants was 12, with the attendance of locals, the first day talks (which were of more expository/inquisitive nature) attracted a crowd of 30 people.

The meeting was a success. This opinion was clearly shared by all participants. The gathering of experts from different areas around adventurous open questions that lie in the intersection of their areas was exciting for everyone and led to very interesting discussions. One of highlights of the meeting was the philosophical conversation about the nature of KK- theory which was very helpful in shaping the conjectural role of KK-theory in the theory of automorphic forms. Another topic of heated discussions was on the interaction between the Baum-Connes conjecture for p-adic Lie groups and local

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Langlands correspondence. While the former discussion hinted at involving cyclic cohomology in the automorphic picture, the latter discussion suggested that an adelic picture involving local spherical Hecke algebras might be possible.

The small scale of the meeting was felt to be an advantage by everyone. It allowed substantial interactions, both mathematically and personally. It was decided that a follow up meeting would be organised in the near future.

11-15 September 2017 Algebraic Topology of Manifolds [LMS-CMI Research Schools] Oxford Organiser: Ulrike Tillmann (Oxford) 34 Participants Event website Lecturers: Greg Arone, Dan Freed, Oscar Randal-Williams and https://goo.gl/RioWDp Nathalie Wahl

The Research School is organised by a partnership of the London and Mathematical Society (LMS) and the Clay Mathematics Institute (CMI). Additional funding is provided by the Heilbronn Institute for Mathematical Research (HIMR).

25-27 September 2017 Data Science and Cyber-Security Imperial College London Organisers: 110 Participants Niall Adams (Imperial College London), Nick Heard (Imperial Conference website College London), Melissa Turcotte (Los Alamos National https://goo.gl/sbMjip Laboratory), Alex Kent (Los Alamos National Laboratory), Patrick Rubin-Delanchy (Oxford/ Bristol)

Speakers: Ian Levy (National Centre for Cyber Security), Mike Fisk (Los Alamos National Laboratory), Mark Briers (Alan Turing Institute), David Marchette (Naval Surface Warfare Center, Dahlgren Division) George Cybenko (Dartmouth College), Siraj Shaikh (Coventry University), Niall Adams (Imperial College London), Christoforos Anagnostopoulos (Mentat), Melissa Turcotte (Los Alamos National Laboratory), Blake Anderson (Cisco)

The conference was a great success, attracting more than 110 applicants. Support from HIMR, and other sponsors, was primarily used to subsidize attendance for PhD students (and GCHQ attendance), and support the expenses of invited speakers.

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Report The programme consisted of talks by (10) invited speakers, (17) contributed speakers, and 10 posters. A prize, sponsored by World Scientific (a publishing house) was awarded for the best poster. The conference had many business delegates, from diverse organizations including GCHQ, DSTL, BT, Cisco, EY, BT and GSK. Compared to previous years, the level of international attendance was much increased.

Informal feedback suggested the conference was interesting and enjoyable. Many delegates enjoyed the tours of the “Global Data Observatory” at Imperial.

We plan, with permission from speakers, to post speakers slides and video of presentations. The exact mechanism is to be determined. An edited volume consisting of papers from invited and contributed speakers (whose papers underwent a review process) is forthcoming. This will feature the HIMR logo, as have previous such volumes.

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HIMR Focused Research Events APPENDIX |E3 Heilbronn Focused Research Workshops, formed with the aim of facilitating research groups to work on adventurous and challenging mathematical problems 

24 October – Kac-Moody Groups and L-functions 2 November 2016 Nottingham Organisers: Sergey Oblezin (Nottingham), Tom Oliver (Bristol)

Speakers: Robert Kurinczuk (Imperial College), Thomas Oliver 12 Participants (Bristol), Sergey Oblezin (Nottingham), Oliver Braunling Workshop website (Freiburg), Jens Eberhardt (Freiburg), Katerina Hristova https://goo.gl/hjPSDX (Warwick), Dmitriy Rumynin (Warwick), Kyu-Hwan Lee (UConn, USA), Michael Groechenig (Imperial College), Matthew Waller (Nottingham)

Report by Tom Oliver The workshop was focused on automorphic representations of Kac-Moody groups. For example such representations may arise from Eisenstein series, which played a prominent role. In attendance were 12 participants, including 10 speakers delivering lecture series of up to 3 hours each. Speakers were

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from German, UK and US institutions, covering topics such as classical, affine and double affine Hecke algebras, Whittaker patterns, and Beilinson-Bernstein localisation. The programme also allowed plenty of time for collaboration, resulting in several projects still under development. Of particular interest was the problem of extending the results of Braverman- Kazhdan (2012), and a conjecture of Gaitsgory-Kazhdan (2003). In the longer term, we are interested in applications to classical automorphic L-functions.

18-27 November 2016 Good Birational Models Through Moduli Theory Edinburgh Organiser: Igor Krylov (Edinburgh)

12-16 December 2016 Large Scale Structures in Random Graphs Alan Turing Institute, London Organisers: Peter Allen, Julia Böttcher, Jozef Skokan (all LSE)

27 Participants Speakers: Rob Morris (IMPA), Stefanie Gerke (RHUL), Workshop website https://goo.gl/QDihvV A joint ATI-HIMR Focused Research Workshop.

Report The aim of this workshop primarily was to work on open problems which should lead to a better understanding of the general area of large-scale structures in random graphs. The workshop featured 11 invited participants, who presented recent research in the mornings. The afternoons were dedicated to research projects in small groups. In total there were 27 participants.

Good progress was made during the workshop concerning several of the suggested problems. Some of the results were fit to be written up directly after the workshop, already leading to submitted papers. For other groups the workshop initiated longer term research projects. Afterwards, the participants sent us very positive feedback, indicating that they were very happy with the quality and the format of the workshop.

A more detailed report can be found on: https://goo.gl/qKFnVm

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11-13 January 2017 New Results and Challenges with Random Walks in Dynamic Bristol Random Environment

20 Participant Organisers: Luca Avena (Leiden), Márton Balázs (Bristol), Frank Workshop website den Hollander (Leiden), Frank Redig (Delft) https://goo.gl/NrU86D Speakers: Luca Avena (Leiden), Christian Maes (), Stein Andreas Bethuelsen (), Frank Redig (Delft), Oriane Blondel (Lyon), Alexandre Stauffer (Bath), Jiří Černý (Vienna), Augusto Teixeira (Rio de Janeiro), Dmitry Dolgopyat (Maryland) Stanislav Volkov (Lund), Frank den Hollander (Leiden), Florian Völlering (Bath), François Huveneers (Paris)

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

Report by The workshop "New results and challenges with random walks Márton Balázs in dynamic random environment" was held in Bristol, UK, between 11-13 January 2017. We had 13 talks by colleagues in the frontline of this area, representing a significant part of the research that is happening in the field.

Random walk in (static) random environment (RWRE) is a well established and famously difficult part of probability theory. This meeting was about a further step from here, where the background environment is changing in time instead of staying static once and for all. This on one hand eases the problem by introducing an extra level of stochastic mixing. On the other hand, especially when this mixing is slow, significant challenges remain in place while most classical tools of RWRE are not applicable anymore. In certain regimes fundamental questions like the law of large numbers or central limit theorem are far from being answered. The workshop provided us with an overview of the latest results, and lots of communication between participants, including University of Bristol members of staff. Besides the core subject, we also took a look at connections with other parts of probability: random graphs (den Hollander), none-quilibrium statistical physics (Maes), interacting particles (Redig, Blondel), percolation (Stauffer), population models (Černý). In the last talk, Luca Avena gave a beautiful overview of recent developments and open problems of the field to work on.

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16-20 January 2017 The Sarnak Rigidity Conjecture Bristol Organisers: Andrew Booker (Bristol), Min Lee (Bristol) 9 Participants Participants: Sandro Bettin (University of Genova), Brian Conrey (AIM & University of Bristol), Giuseppe Molteni (University of Milan), Thomas Oliver (University of Bristol), Raphael Steiner (University of Bristol)

Report by We are pleased to report that the HIMR workshop on the Andrew Booker Sarnak Rigidity Conjecture was a success. Although our results fall short of proving the full conjecture, we have made some partial progress that we expect to submit for publication in the near future.

The week began with an overview talk by Booker introducing the Sarnak Rigidity Conjecture and posing several related open problems to work on, followed by a lecture by Lee on the functional equation satisfied by twists of modular form L- functions by Ramanujan sums. During the week we also had talks by Tom Oliver on extending Weil's converse theorem to Maass forms and Raphael Steiner on the minimum number of twists needed without assuming an Euler product.

One of the main outcomes was the identification of Ramanujan sum twists as a linear replacement for the information supplied by the Euler product in the context of converse theorems for modular forms. We formulated a precise conjectural extension of Hecke's converse theorem that assumes the analytic properties of Ramanujan sum twists but does not require an Euler product or twists by Dirichlet characters. We then proved the conjecture in various particular cases or under stronger hypotheses. In addition to the paper described above, we identified some potential directions for future research that we intend to pursue.

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13-17 February 2017 Homotopy Theory and Arithmetic: Around Galois Groups Imperial College London Organisers: A. Pal (Imperial College) C. Lazda (Padova), and 30 Participants Tomer Schlank (Hebrew University of ) Workshop website https://goo.gl/aW1asd Speakers: Michel Gros (Rennes), Fréderic Déglise (Lyon), Moshe Jarden (Tel Aviv), Alex Betts (Oxford), Charles Vial (Cambridge), Chris Lazda (Padova), Ido Efrat (De’er Sheva), Kirsten Wickelgren (Atlanta), Olivier Wittenbert (Paris), Ambrus Pál (London), Jonathan Pridham (Edinburgh), Netan Dogra (London)

Report by Ambrus Pal The workshop was a great success. In spite of its relatively short length it had 12 talks and covered a broad range of subjects, including the arithmetic of fields, p-adic cohomology and p-adic Simpsons correspondence, and application of motivic homotopy to problems with arithmetic flavour. It introduced to the London maths community some of the biggest names in arithmetic of fields, namely Moshe Yarden and Ido Efrat. Efrat’s talk was an excellent introduction to the embedding problem and Galois theory and the current intensive work on the vanishing of Massey products in Galois cohomology, and generated an enthusiastic response from the attending PhD students. One of the most exciting talks, which generated a lot of interest, especially among the members of the geometry group at Imperial, was by Kirsten Wickelgren, who talked about her recent joint work with Kass on an arithmetic refinement of the classical counting of lines on a smooth projective hypersurface of degree 3. The new count takes values in the Grothendieck-Witt ring of quadratic forms, and takes into account the arithmetic of the individual lines. It is very likely that this work will generate a lot of research in the Gromov- community, an area which is a major strength of British Mathematics. We also believe that this event helped in securing funding for a CMI-LMS grant for organising a summer school at ICL during July 2018 aimed at PhD students and young posdocs where one of the lecturers will be Kirsten.

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30 May – 2 June 2017 Maximal Subgroups of E8(2) Manchester Organiser: Peter Rowley (Manchester) 6 Participants Participants: John Ballantyne, Alex McGaw, Ali Aubad, Peter Neuhaus, David Ward and Peter Rowley

Report Dr John Ballantyne's visit to Manchester earlier this year was supported by the Heilbronn Institute. During this period we worked intensively on the maximal subgroups of E_8(2). Highlights from this period were showing that there is only one E_8(2) conjugacy class of subgroups isomorphic to L_2(31):2, and that they are maximal subgroups, and being able to successfully implement (in ) a strategy for finding subgroups isomorphic to L_2(128). A number of other subcases were resolved.

At the time of writing, there are five or six outstanding cases to be dealt with to complete this project and it is hoped to organize further meetings of this type to help in achieving a complete classification of the maximal subgroups.

14-18 August 2017 Quantum Computational Supremacy Bristol Organisers: Noah Linden (Bristol), Ashley Montanaro (Bristol) 23 Participants Participants: Scott Aaronson (UT Austin); Sergio Boixo (Google); Michael Bremner (University of Technology Sydney); Harry Buhrman (CWI / QuSoft); Edward Farhi (MIT); Aram Harrow (MIT); Richard Jozsa (Cambridge); Noah Linden (Bristol); Ashley Montanaro (Bristol); Dan Shepherd (CESG); John Smolin (IBM); Barbara Terhal ().

Report The Heilbronn Focused Research Group on Quantum Computational Supremacy was held in Bristol during the week of 14-18 August. Participants included 11 external senior invitees and around 12 members of Bristol's quantum information theory group, many of whom were junior researchers. The schedule included only carefully selected talks, with 2-3 scheduled for each of the first three days, to allow extensive time for discussion. This proved fortunate, as the intensity of questions from the audience and discussion during the talks was

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such that they all overran substantially, some by more than a factor of 2.

The scientific discussions during the meeting were exceptionally fruitful. Two particular highlights were: talks presenting ongoing, unpublished work on verification and simulation of certain quantum supremacy experiments, which led to a new appreciation of the issues involved (particularly the subtle theoretical challenges in being able unambiguously to demonstrate that the experiments do indeed go beyond classical simulations); and discussions by participants which identified - and resolved - an unexpected limitation in a significant recent work on verification of quantum computations. Productive interactions with industry participants (Google and IBM) seem likely to lead to new collaborations.

Finally, we would like to thank the Heilbronn Institute for funding this very stimulating event, and the Heilbronn administrators for their hard work, which resulted in a very well- organised workshop with many compliments from participants.

21-24 August 2017 Toric Degenerations of Grassmannians and Flag Varieties Bristol Organisers: Fatemeh Mohammadi (Bristol) 25 Participants Participants: Robert Marsh (Leeds), Jürgen Herzog (- ), Volkmar Welker (), Diane Maclagen (Warwick), Milena Hering (Edinburgh), Chris Manon (George Mason), Laura Escobar (Illinois), Kalina Mincheva (Yale), Nelly Villamizar (Swansea), Sara Lamboglia (Warwick), Lara Bossinger (Koeln), Martina Lanini (Edinburgh), Kristin Shaw (), Alex Fink (QMUL), Takuya Murata (Pittsburgh), Ollie Clark (Warwick), Elisa Postinghel (Loughborough), Lars Halvard (Copenhagen), Xing Fang (Koeln), Emilie Dufresne (Nottingham), Henry Wynn (LSE), Bernt Ivar Utstøl Nødland (Oslo)

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

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4-9 September 2017 Stochastic Control, Ambiguity and Games Leeds Organiser: Tiziano De Angelis (Leeds) and Jan Palczewski (Leeds) 40 Participants Conference website Speakers: Anna Aksamit (Oxford, UK), Natalie Attard https://goo.gl/dA1SKa (Manchester, UK), Alexander Cox (Bath, UK), Erik Ekström (Uppsala, Sweden), Saïd Hamadene (Le Mans, France), David Hobson (Warwick, UK), Goran Peskir (Manchester, UK) Catherine Rainer (Brest, France), Frank Riedel (, ), Mete Soner (ETH Zurich, Switzerland), Yavor Stoev (Michigan)

Report The conference provided a broad overview of stochastic control methods for problems involving strategic interaction and uncertainty. Starting from the afternoon of 5 September a smaller group of 15 researchers (including 2 self-funded, 2 organisers and 1 local PhD student) started discussing specific topics related to the theme of the research week. The activities were organised in focussed sessions (each day we had 2 sessions). Each session was chaired by one of our senior participants who would give a subjective overview of their research area, its relation to ambiguity and games, and explain research challenges and questions that they find fascinating. We allowed the chair to structure the session as they preferred and their introduction would normally last between 30 minutes to 1 hour. After that, all participants would engage in discussions in groups and use 6 large whiteboards in the seminar room to go through mathematical details of the proposed problems. Participants engaged in discussions on the following topics: robust finance and Skorokhod embedding, nonzero-sum optimal stopping games, games with asymmetric information, games and BSDEs, time inconsistency arising in prospect theory and mean-variance optimisation. These topics/mathematical tools relate to different definitions of “ambiguity”. As a result of the discussions we formulated and started to address questions concerning: (i) construction of (non trivial) non-Markovian Nash equilibria for nonzero-sum stopping games (mostly theoretical), (ii) stopping games in which the player is not fully informed about the competition (a simple practical example is the situation of someone who is unsure whether to buy online a flight ticket at the current price or wait for a better deal), (iii) methods for explicit solution of zero-sum stopping games with asymmetric information. We are aware of the fact that some

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participants have already started research collaborations as consequence of these discussions (e.g., Caruana, De Angelis, Ekstrom, Palczewski, Rainer). As a concluding remark, we would like to mention that our participants enjoyed the format and content of the event to the point that we have been invited (with funding to be confirmed) to organise a follow-up workshop in 2019.

4-8 September 2017 Substructure in Pseudo-reductive Groups Newcastle Organiser: David Stewart (Newcastle) 18 Participants Speakers: Gopal Prasad (Michigan), Michael Bate (York), George McNinch (Tufts), Karsten Naert (Ghent), Sasha Premet Website (Manchester), David Stewart (Newcastle), Alastair Litterick https://goo.gl/DELWHb (Bochum), Seidon Alsaody (Lyon), Ben Martin (Aberdeen)

Report The meeting on Pseudo-reductive groups went off as planned. We managed the coup of getting Gopal Prasad to come to the event, who is one of the key people involved in the recent major developments in the area. He gave four hours of overview lectures on the topic, which set the scene for the rest of the event. We also invited participants from the UK, US, Sweden, France, , the and Germany. In terms of research dissemination, we were particularly pleased to hear from some younger post-graduate researchers working on pseudo-reductive groups from France, but also from more senior people such as Sasha Premet, Alex Stasinski and George McNinch.

A lot of time was allotted for discussion and research. Significant progress was made on studying some of the representation theory of pseudo-reductive groups by myself, together with Michael Bate and Ben Martin—this had been previously thought intractable—and together with Gerhard Roehrle, understanding some of the subgroup structure and orders of elements that can occur. Two groups of younger people struck up new research collaborations: Benoit Loisel and Raphael Achet; Adam Thomas (Heilbronn fellow), Alastair Litterick and Tomohiro Uchiyama. Particularly it was extremely helpful to have Gopal Prasad’s comments on our ongoing work and he was able to steer us in the right direction on a number of different occasions.

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APPENDIX |E4 HIMR Future Events

2-6 October 2017 Non-Signalling Correlations, Games and Graph Parameters Belfast Organiser: Ivan Todorov (Belfast) Focused Research

27-28 November 2017 The London-Paris Number Theory Paris Organisers: Pierre Charollois (Jussieu), Olivier Fouquet Sponsored Event (Orsay), Michael Harris (Jussieu), Marc Hindry (Jussieu), Website Benjamin Schraen (École Polytechnique), Jacques Tilouine https://goo.gl/q7nVob (Université Paris 13).

4-5 January 2018 Lagrangian Mean Curvature Flow: Progress and Problems UCL Organisers: Jason Lotay and Felix Schulze Focused Research Website Participants : Chris Evans (UCL), Kim Moore (UCL), Tommaso https://goo.gl/yVYguj Pacini (Torino), Felix Schulze (UCL), Matthias Wink (Oxford)

19-23 February 2018 Automorphic Forms, Equiangular Lines and Kac - Moody Oxford Groups

Focused Research Organiser: Tom Oliver (Oxford), Neil Gillespie (Bristol)

10-12 January 2018 Dispersive Equations with Random Initial Data Bristol A joint University of Bristol and Heilbronn Focused Research Workshop. Focused Research Website Organisers: Tamara Grava (Bristol), Sean Ledger (Bristol) https://goo.gl/5LSQij

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Participants: Herbert Spohn (Munich), Christian B. Mendl (Stanford), Anne Sophie de Suzzoni (Paris), Nikolay Tzvetkov (Cergy-Pontoise), Benedek Valk ́ (Wisconsin Madison), Sergey Nazarenko, (Warwick), Miguel Onorato, (Turin), Pierre Suret, (Lille), Kennet McLaughlin, (Colorado), Gennadi El, (Loughborough), Tadahiro Oh (Edinburgh), Oana Pocovnicu (Heriot-Watt)

January 2018 LANL Data Set Bristol Organiser: Dan Martin (Bristol) Focused Research

19 February 2018 Galois distinction in algebraic families and the Langlands Imperial College London correspondence

Sponsored Event Organiser: Robert Kurinczuk (Imperial College)

22 February 2018 LMS Women in Mathematics Bristol Organisers: Tim Browning (Bristol) and Lynne Walling (Bristol) Sponsored Event

16-20 March 2018 New Trends in Renormalisation Group Theory and Regularity Warwick Structures

Sponsored Event Organiser: Stefan Adams (Warwick)

TBC Bourgain-Chang solution to the weak sum-product Bristol conjecture over the integers

Focused Research Organiser: Brendan Murphy (Bristol)

March 2018 Theory of Fusion within Algebraic Groups Bristol Organiser: Adam Thomas(Bristol) Sponsored Event

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26-28 March 2018 British Colloquium for Theoretical Computer Science (BCTCS) Royal Holloway The British Colloquium for Theoretical Computer Science Sponsored Event (BCTCS) is an annual event for UK-based researchers in Website theoretical computer science. A central aspect of BCTCS is the https://goo.gl/vZPqFC 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.

4-6 April 2018 Probability, Analysis and Dynamics 2018 Bristol Organisers in Bristol: Marton Balazs, Edward Crane, Thomas Jordan, John Mackay, Balint Toth HIMR-Run Event Website Speakers: Viviane Baladi (Paris VI), Krzysztof Burdzy (Seattle) https://goo.gl/NGNXb4 Sourav Chatterjee (Stanford), Laura DeMarco (Northwestern) Dmitry Dolgopyat (Maryland), Tatjana Eisner () Alison Etheridge (Oxford), (Cambridge) (Warwick), Mike Hochman (Jerusalem) Konstantin Khanin (Toronto), Antti Kupiainen (Helsinki) Jens Marklof (Bristol), Vladimir Markovic (Caltech), Felix Otto (Max Planck Institut), Steffen Rohde (Seattle)

9-13 April 2018 Easter Probability Meeting 2018 ‘Random Structures and Sheffield Other Recent Developments’ Focused Research Organisers: Nic Freeman Website https://goo.gl/vyzths Speakers: Christina Goldschmidt (Oxford), Pierre Tarrès (NYU Shanghai), Robin Pemantle (Pennsylvania)

11-13 April 2018 Distinguished Lecture Series 2018 Bristol HIMR Run Speaker: Prof. Ingrid Daubechies (Duke University)

Website [Organised in cooperation with the School of Mathematics, https://goo.gl/29UM3Q University of Bristol].

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4-7 June 2018 Perspectives on the Reimann Hypothesis Symposium Bristol Organisers: Brian Conrey (AIM/Bristol), Peter Sarnak (IAS, HIMR-Run Princeton), Andrew Wiles (Oxford) and Jon Keating (Bristol)

A meeting on the Riemann Hypothesis and on the theory of Website the zeta-function and other L-functions. Sponsored by: https://goo.gl/CtzVi7 American Institute of Mathematics, University of Bristol, EPSRC, Heilbronn Institute for Mathematical Research and the National Science Foundation

Speakers: Enrico Bombieri (IAS Princeton), Andrew Booker (Bristol), Alain Connes (IHES), Alexandra Florea (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)

9-13 July 2018 LMS-CMI Research School | Homotopy Theory and Imperial College London Arithmetic: Motivic and Diophantine Aspects Sponsored Event Organisers: Frank Neumann (Leicester), Ambrus Pal (Imperial Website College London) https://goo.gl/J7EkLz

24-27 July 2018 Research Students Conference in Probability and Statistics Sheffield Sponsored Event Organiser: Mark Yarrow (Sheffield) Website www.rsc2018.co.uk

9-14 July 2018 Building Bridges: 4th EU/US Summer School Budapest The workshop is organised in partnership with the Clay Sponsored Event Mathematics Institute, with additional funding from the Website Heilbronn Institute for Mathematical Research and the afw-eu.org/ National Science Foundation.

13-17 August 2018 LMS-CMI Research School | New Trends in Analytic Number Exeter Theory

Sponsored Event

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29-31 August 2018 Simple Groups: New Perspectives and Applications Bristol Organiser: Adam Thomas (Bristol)

HIMR-Run Speakers: Inna Capdeboscq, Pierre-Emmanuel Caprace, David Website Craven, Steve Donkin, Robert Guralnick, Kay Magaard, Gunter https://goo.gl/Q2MyRX Malle, Ben Martin, Tom De Medts, Martin Liebeck, Colva Roney-Dougal, David Stewart, Donna Testerman, Pham Tiep,

3-7 September 2018 Groups, Geometry and Representations Oxford Organisers: Martin Liebeck (Imperial), Martin Bridson (Oxford), Inna Capdeboscq (Warwick), Benjamin Klopsch Sponsored Event (Düsseldorf) , Alex Lubotzky (Hebrew University), Nikolay Website Nikolov (Oxford), Efim Zelmanov (UC San Diego) https://goo.gl/poepWT

6-7 September 2018 Heilbronn Annual Conference Bristol Speakers: Mark Gross (Cambridge), Jacob Fox (Stanford) , HIMR Run Yuval Peres (Microsoft Research), Tamar Ziegler (The Hebrew University of Jerusalem), Martin Hairer (Imperial College London), Francis Brown (Oxford), and others TBC

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APPENDIX |P1 Fellows joining in 2016/2017

Dogra, Netan PhD Oxford | Joined Imperial on the 1st October 2016 from a post-doc in Radboud University. Research Interest: Arithmetic Geometry

Kramer-Miller, Joseph PhD CUNY Graduate Centre, NY | Joined UCL on 1st October 2016 Research Interest: and Arithmetic Geometry.

Latham, Peter PhD East Anglia | Joined King’s College London on the 1st October 2016, Research Interest: Representation theory of reductive p-adic groups.

Martin, Dan PhD Bristol | Joined 1st October 2016 Research Interest: Statistics & Combinatorics

Murphy, Brendan PhD Rochester | Joined 1st October 2016 Research Interest: Combinatorics and harmonic analysis

Palmer, Matthew PhD Bristol | Joined 1st October 2016 Research Interest: Diagonal diophantine approximation

Peacock, Simon PhD Bristol | Joined 1st October 2016 Research Interest: Modular representation theory of finite dimensional algebras

Williams, Christopher PhD Warwick | Joined Imperial on the 1st October 2016 Research Interest: Automorphic Forms and .

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APPENDIX |P2 Fellows Leaving since Sept 2016

Beil, Charlie End date at Bristol 31st August 2017 Current Position: Research Fellow, University of Graz, Austria

Blake, Chris End date at King’s College London 15 September 2017 Current Position: Industry position at a financial institution

Rubin-Delanchy, End date at Oxford University 31 June 2017 Patrick Current Position: Lecturer in Statistical Science, University of Bristol

Saunders, Neil End date at City University 3rd September 2017 Current Position: Permanent Lectureship at Greenwich University

Skerman, Fiona End date at Bristol University 31st August 2017 Current Position: Postdoctoral fellow, Uppsala University

Stankewicz, Jim End date at Bristol 30 December 2016 Current Position: US Government Agency

Tseng, Jimmy End date at Bristol 31st August 2017 Current Position: Senior Lectureship, University of Exeter

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Fellows Moving with 3 Year Extensions APPENDIX |P3

Oliver, Thomas Bristol > Oxford End date at Bristol 30 September 2017

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APPENDIX |P4 Future Fellows

New Starters October 2017

Kopp, Gene PhD 2017 (Michigan)

Research Interest: Number Theory, Modular Forms, Special Functions, Random Matrix Theory, Secure Multiparty Computation

Jones, Nick PhD 2017 (Bristol)

Research Interest: Integrable models, Discrete complex analysis , Fractional quantum Hall effect and anyons, Random matrix theory

Malcolm, Alex PhD 2017 (Imperial College London)

Research Interest: Algebra

Ducat, Thomas PhD 2015 (Warwick)

Research Interest: Algebraic Geometry and I am primarily interested in the explicit birational geometry of 3-folds.

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APPENDIX |M1 Mentoring Programme

Led by: Julia Wolf, Associate Chair Heilbronn Institute for Mathematical Research

5 October 2016 Career Development 18 Participants Exhausted Mathematician or Valiant Hero? Motivating Yourself on your Research Journey

16 November 2016 Career Development 25 Participants Research Assessment and Open Access

7 December 2016 Career Development 4 Participants Mock Interviews (for those with upcoming interviews)

15 February 2017 Career Development 25 Participants How to get the most out of mentoring

4 April 2017 Career Development 15 Participants Teaching: the good, the bad and the ugly

24 May 2017 Career Development 23 Participants Funding opportunities for early-career mathematicians

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