Consolidated EPSRC support for Durham Symposia
Lead Research Organisation:
Durham University
Department Name: Mathematical Sciences
Abstract
The LMS-EPSRC Durham Symposia have a long and glorious history and are among the most important regular international mathematical events, reflecting and initiating developments in cutting edge modern mathematics. These 10-day meetings have run since 1974 and have quickly developed their highest international reputation. They are widely associated with the excellence of British mathematics. The programme activity of the Durham Symposia is fully controlled by the London Mathematical Society, and takes place during the summer period, fitting well into the academic diary of mathematicians worldwide.
This proposal seeks support for a continuation of the programme of Symposia for a further four years.
The Symposia bring together the top UK and international researchers, with the aim of finding common ground and discussing exciting recent developments. Nearly all participants reside in the same accommodation block, giving the meetings a closed and informal atmosphere under which the exchange of ideas and cross-fertilization of research expertise can flourish.
Information on each symposium can be found through the actively-managed and easily accessible website (http://www.maths.dur.ac.uk/events/Meetings/LMS/), which contains links to all previous Durham Symposia. The main talks of each symposium are recorded (with permission of the speakers) and made available through this website within days after the end of the meeting. Similarly, lecture notes and presentation slides are also made available.
The outcomes from the symposia impart a large impetus to already dynamic research areas. The UK and international symposium participants are the immediate beneficiaries, but the timely appearance of videos and lecture notes on the Durham Symposium website also informs the research of many other mathematical scientists working in the area. This in turn adds considerably to our understanding of the various research topics studied.
This proposal seeks support for a continuation of the programme of Symposia for a further four years.
The Symposia bring together the top UK and international researchers, with the aim of finding common ground and discussing exciting recent developments. Nearly all participants reside in the same accommodation block, giving the meetings a closed and informal atmosphere under which the exchange of ideas and cross-fertilization of research expertise can flourish.
Information on each symposium can be found through the actively-managed and easily accessible website (http://www.maths.dur.ac.uk/events/Meetings/LMS/), which contains links to all previous Durham Symposia. The main talks of each symposium are recorded (with permission of the speakers) and made available through this website within days after the end of the meeting. Similarly, lecture notes and presentation slides are also made available.
The outcomes from the symposia impart a large impetus to already dynamic research areas. The UK and international symposium participants are the immediate beneficiaries, but the timely appearance of videos and lecture notes on the Durham Symposium website also informs the research of many other mathematical scientists working in the area. This in turn adds considerably to our understanding of the various research topics studied.
Planned Impact
The aim of the current proposal is to continue to provide a framework for the mathematical community of the UK to hold conferences at the highest international standard which can set the research agenda in the field for the next five to ten years. The themes for the Durham Symposia have and will continue to cover almost all areas in the EPSRC portfolio for Mathematical Sciences. As the topics for the coming symposia are not yet decided, it is difficult to predict potential beneficiaries of the impact. Nevertheless, in recent years there have been several symposia with participants from industry and national agencies such as the Met Office, and this is expected to continue in the future.
Communication and enagement - Once a symposium has been been approved by the RMC, it is advertised in the newsletter of the LMS and various websites used for advertising conferences. An important part of the communication is then taking place through the Durham Symposia website. The team has developed a highly interactive webtool, which enables organisers and participants to easily stay up to date. The link to the Durham Symposia website is publicised regularly in the LMS newsletter, and also easily accessible through the webpages of the Department of Mathematical Sciences at Durham University.
Collaboration and exploitation - Each symposium brings together many of the leading experts in the given field, both from the UK and abroad. Organisers are encouraged to leave a lot of time for discussions. Most participants stay at the same resident college, where full internet access is available. Together with the typical length of up to ten days for a symposium this provides a very fertile ground for collaborations among participants.
The Durham Symposia website collects a wealth of information from each symposium. Since 2004 almost all talks have been filmed and the files are made available on the web. Speakers are also asked to make presentations in pdf or ppt files available on our website. The collection of data represents a rich repository that it is widely used throughout the world. As the website is openly accessible, researchers who have not been able to participate in a symposium can still obtain a lot of information that way.
Communication and enagement - Once a symposium has been been approved by the RMC, it is advertised in the newsletter of the LMS and various websites used for advertising conferences. An important part of the communication is then taking place through the Durham Symposia website. The team has developed a highly interactive webtool, which enables organisers and participants to easily stay up to date. The link to the Durham Symposia website is publicised regularly in the LMS newsletter, and also easily accessible through the webpages of the Department of Mathematical Sciences at Durham University.
Collaboration and exploitation - Each symposium brings together many of the leading experts in the given field, both from the UK and abroad. Organisers are encouraged to leave a lot of time for discussions. Most participants stay at the same resident college, where full internet access is available. Together with the typical length of up to ten days for a symposium this provides a very fertile ground for collaborations among participants.
The Durham Symposia website collects a wealth of information from each symposium. Since 2004 almost all talks have been filmed and the files are made available on the web. Speakers are also asked to make presentations in pdf or ppt files available on our website. The collection of data represents a rich repository that it is widely used throughout the world. As the website is openly accessible, researchers who have not been able to participate in a symposium can still obtain a lot of information that way.
Organisations
| Description | The grant enabled us to hold eight EPSRC-LMS Durham Symposia over a period of four years. These extended conferences have brought together world leading experts to discuss and bring forward research in various important areas of Mathematical sciences. Over a period of ten days we host between 60 and 80 participants to engage in presentations and discussions in their respective fields. About half of the participants are from the UK, with the other half consisting of experts from every part of the world. The topics of the symposia were chosen through a stringent evaluation process done by the London Mathematical Society (LMS) that ensured a topic is well represented in the UK, and also that UK practitioners get in contact with international leaders in the field. Thanks to these symposia an important platform for these areas is given to UK researchers, thus ensuring a world leading position of the UK in these areas. Among the participants there were always several postgraduate researchers from the UK, thus giving the new generation of researchers an opportunity to engage and witness the leaders in their field. Most participants stay at a college in Durham, which has lead to continued engagement outside of working hours, resulting in many collaborations among participants. |
| Exploitation Route | These conferences bring together world leading experts, enable them to share knowledge and begin or continue collaborations in their area of research. While most participants are from the academic world, several of the symposia have included so-called Industry Days, with participants ranging from healthcare, government agencies, the met office, engineering industries, among others. These industry days provide important opportunities to foster collaborations between academic and non-academic participants. |
| Sectors | Digital/Communication/Information Technologies (including Software),Financial Services, and Management Consultancy,Healthcare,Government, Democracy and Justice,Other |
| URL | http://www.maths.dur.ac.uk/events/Meetings/LMS/ |
| Description | Organisers and participants of the EPSRC-LMS-Durham symposia have profited in various ways and have been able to combine the findings through outreach activities and other projects which have impact outside academia. While it is difficult to attribute impact directly to a conference, it is clear that participants get the chance to further improve or develop applications that have influence in wider society. Particularly some of the organisers of the symposia are involved in other projects such as improvements to oil drilling technology and data science. |
| First Year Of Impact | 2018 |
| Sector | Digital/Communication/Information Technologies (including Software),Energy |
| Impact Types | Economic |
| Description | Building Bridges: Connections and Challenges in Modern Approaches to Numerical Partial Differential Equations |
| Form Of Engagement Activity | Participation in an activity, workshop or similar |
| Part Of Official Scheme? | Yes |
| Type Of Presentation | workshop facilitator |
| Geographic Reach | International |
| Primary Audience | Professional Practitioners |
| Results and Impact | The Symposium was devoted to recent advances in Numerical Methods for Partial Differential equations (PDEs) using non-polynomial basis functions, mimetic finite difference methods and discontinuous Galerkin (dG) methods.The Durham team provided the organisational and logistical aspects of the symposium. Among the participants of the symposium were several world leading experts in the area of numerical Partial Differential Equations, and it gave the UK community in this area an up-to-date status in the field. |
| Year(s) Of Engagement Activity | Pre-2006,2006,2007,2008,2009,2010,2011,2012,2013,2014 |
| URL | http://www.maths.dur.ac.uk/events/Meetings/LMS/2014/NPDE14/ |
| Description | Geometric and Algebraic Aspects of Integrability |
| Form Of Engagement Activity | Participation in an activity, workshop or similar |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Professional Practitioners |
| Results and Impact | The activity was the 105th EPSRC-LMS Durham Symposium. It focussed on Integrability, which has been an important mathematical concept since the 19th century. The modern theory is grew up around the study of KdV type equations, following the discovery of multi-soliton solutions, infinite number of conservation laws and the Inverse Scattering Transform in the 1960s and 1970s. In the 1980s new ideas came via integrable field theories and connections with harmonic maps and differential geometry were re-established. Links with other areas of mathematics - algebraic geometry, twistor theory, self-duality, representation theory, number theory, enumerative geometry, Gromov-Witten theory and Topological Quantum Field Theories grew in the 1990s and through into the 21st Century. The aim of the Symposium was to bring together leading international researchers in the various sub-fields of integrable systems, concentrating primarily on the mathematical aspects of the theory. Considerable progress in these areas is to be expected from the participants of the symposium. The Durham team provided the organisational and logistical aspects of the symposium. |
| Year(s) Of Engagement Activity | 2016 |
| URL | http://www.maths.dur.ac.uk/events/Meetings/LMS/105/index.html |
| Description | Markov Processes, Mixing Times and Cutoff |
| Form Of Engagement Activity | Participation in an activity, workshop or similar |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Professional Practitioners |
| Results and Impact | The activity was the 108. EPSRC-LMS Durham Symposium. Probability is a rapidly growing sub-discipline within mathematical science, connected not only with many other areas of mathematics and statistics but also with a vast range of applications. This symposium focussed on recent developments in the area of Markov chains, particularly related to questions of convergence. "Mixing" refers to the question of, how fast does the Markov chain move around the state space once in statistical equilibrium. "Cutoff" refers to an intriguing and wide-spread phenomenon, namely that the distance to equilibrium (when measured in an appropriate metric) can stay large for a substantial period of time and then move almost instantaneously very close to equilibrium. Both topics, together with related issues, are currently the subject of much international research activity. The Symposium aimed to provide an opportunity for mathematical scientists to consider these research areas and their applications. There was also an Industrial Engagement afternoon, co-organized with the RSS Applied Probability Section, in which 4 speakers presented problem opportunities from various areas of industry and government. The following themes arise from several groups of presentations: 1. The big data challenge, and the use of multi-core implementations of algorithms, is forcing us to construct practical links between statistical issues (how to make a good draw from an MCMC algorithm) and highly sophisticated considerations such as exact simulation from diffusion processes and quasi-stationary distributions; 2. More generally, MCMC is now engaging with new theoretical machinery involving for example Dirichlet form theory and McKean-Vlasov mean-field diffusion theory so as to produce useful results with an increasingly wide range of validity; 3. Work on random processes in random environments is now developing striking results by making essential intrinsic use of mathematical concepts such as Gromov-Hausdorff vague topology. The Durham team provided organisational and logistical aspects of the symposium. |
| Year(s) Of Engagement Activity | 2017 |
| URL | http://www.maths.dur.ac.uk/events/Meetings/LMS/108/index.html |
| Description | Mathematical and Computational Aspects of Maxwell's Equations |
| Form Of Engagement Activity | Participation in an activity, workshop or similar |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Professional Practitioners |
| Results and Impact | The activity was the 104th EPSRC-LMS Durham Symposium. This symposium explored the mathematical problems associated with Maxwell's equations in several modern application areas. These main areas are 1) Photonics and Resonances: This looks at the propagation of electromagnetic waves in periodic structures. Mathematical questions include the study of affects on the spectrum of the underlying operator resulting from the geometry or strength of perturbations to the periodic structure. 2) Metamaterials and Cloaking: Metamaterials are usually constructed by using repeated microscopic structures to achieve properties not observed in natural materials. These properties are usually achieved in some abnormal regimes, which can only be approximated in actual production processes. This provides difficult mathematical problems, such as analysing the rate of convergence of various approximations and defining the optimal way to approximate. Mathematical techniques include homogenization theory. 3) Inverse Problems in Electromagnetism: Many (medical) imaging techniques make use of electromagnetic waves. Recently, there has been much interest in so called mixed mode or hybrid imaging. Mathematical questions include: unique reconstruction of the image, development of reconstruction algorithms and reconstruction in the presence of incomplete data. One tool used successfully in this area has been harmonic analysis. Considerable progress in these areas is to be expected from the participants of the symposium. The Durham team provided the organisational and logistical aspects of the symposium. |
| Year(s) Of Engagement Activity | 2016 |
| URL | http://www.maths.dur.ac.uk/events/Meetings/LMS/104/index.html |
| Description | Model Order Reduction |
| Form Of Engagement Activity | Participation in an activity, workshop or similar |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Professional Practitioners |
| Results and Impact | The activity was the 107. EPSRC-LMS Durham Symposium. The behaviour of processes in mechanics, engineering, geophysics, tomography, seismic modelling, climate/weather prediction and many other application and research areas is usually modelled by dynamical systems. Such models often involve systems of nonlinear partial differential equations. Their linearisation, and discretisation by means of finite difference and finite element methods, leads to high-dimensional systems of linear ordinary differential equations or difference equations. The number of equations is typically very large and can easily reach a few million. It is therefore at best very time-consuming, and sometimes infeasible, to simulate such systems. The aim of model order reduction (MOR) is to find reduced order models that approximate and reflect the dynamics of the underlying large-scale system accurately, in ways that enable the reduction process to be implemented efficiently. The symposium focused on the themes listed below. These were chosen to mix topics where substantial theoretical advances had been made with newly emerging fields. This resulted in advanced presentations with relatively mature results and many open questions, which encouraged lively discussions. The key stated aims of the meeting were • To enhance the status of the UK's research in MOR and help engineers to solve demanding problems of increasing complexity. • To provide a stimulating discussion and research atmosphere and to facilitate new collaborations between several areas of theoretical and applied mathematics as well as engineering. • To increase the links between UK mathematicians and engineers and the EU-MORNET network and bring the EU-MORNET initiative to the UK. • To discuss different methodologies and algorithms. • To encourage discussions and transfer of ideas between experts in different areas, in particular experts from model order reduction and other areas of numerical analysis/applied mathematics. • To encourage the interaction of young UK mathematicians (PhD students and PostDocs) and allow them to discuss their research with national and international experts. The Durham team provided organisational and logistical aspects of the symposium. |
| Year(s) Of Engagement Activity | 2017 |
| URL | http://www.maths.dur.ac.uk/events/Meetings/LMS/107/index.html |
| Description | New Moonshine, Mock Modular Forms and String Theory |
| Form Of Engagement Activity | Participation in an activity, workshop or similar |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Professional Practitioners |
| Results and Impact | The activity was the 103. EPSRC-LMS Durham Symposium. The three main mathematics areas represented were Number Theory, Algebraic Geometry and Group Theory, and mathematicians from these areas interacted productively with a number of string theorists and conformal field theorists who are at the origin of the renewed activities on Moonshine phenomena. The Durham team provided the organisational and logistical aspects of the symposium. |
| Year(s) Of Engagement Activity | Pre-2006,2006,2007,2008,2009,2010,2011,2012,2013,2014,2015 |
| URL | http://www.maths.dur.ac.uk/events/Meetings/LMS/103/index.html |
| Description | Permutation Groups and Transformation Semigroups |
| Form Of Engagement Activity | Participation in an activity, workshop or similar |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Professional Practitioners |
| Results and Impact | The activity was the 102. EPSRC-LMS Durham Symposium. This Symposium explored the connections between several topics of high recent activity: homogeneous structures in model theory and their automorphism groups, and connections to topological dynamics, structural Ramsey theory, and constraint satisfaction; homomorphisms of relational structures, transformation semigroups, and synchronization; different approaches to random graph theory, through graphons and through exchangeable measures; and recent advances in computational algebra, with possible applications for transformation semigroups. The symposium combined a series of short courses, stand-alone lectures, and time for discussion. The Durham team provided the organisational and logistical aspects of the symposium. |
| Year(s) Of Engagement Activity | Pre-2006,2006,2007,2008,2009,2010,2011,2012,2013,2014,2015 |
| URL | http://www.maths.dur.ac.uk/events/Meetings/LMS/102/index.html |
| Description | Stochastic Analysis |
| Form Of Engagement Activity | Participation in an activity, workshop or similar |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Professional Practitioners |
| Results and Impact | The activity was the 106. EPSRC-LMS Durham Symposium. Stochastic Analysis is the branch of probability theory that deals with the behaviour of stochastic dynamical systems. It emerged as a core area of mathematics in the late 20th century, and important developments have continued in the 21st century. The array of applications of Stochastic Analysis is vast and encompasses weather prediction, the risk management of pension funds to the modelling of earthquakes. The mathematical study of stochastic dynamical systems involves a wealth of tools such as martingales, analysis of path spaces, Itô calculus, Malliavin calculus, stochastic integrals, large deviations, log-Sobolev inequalities, measure valued branching processes and stochastic partial differential equations. The subject occupies a somewhat unique position in modern mathematics; it draws heavily on techniques and ideas from several major areas of pure mathematics, such as measure and probability theory, real and functional analysis, Lie groups and differential geometry; but it also has important interactions with a wide range of applied areas such as finance, optimisation, control theory, quantum theory, meteorology and ecology. The symposium was planned around four key areas: stochastic partial differential equations (SPDEs), rough paths theory, numerics, algorithms and statistics, and mean field games. Over the ten days of the symposium there were over ninety participants with over sixty talks. In addition tjhere was a poster session for young participants and two debates organised on the topics of "stochastic analysis and data science" and "the future of stochastic analysis", respectively. The Durham team provided organisational and logistical aspects of the symposium. |
| Year(s) Of Engagement Activity | 2017 |
| URL | http://www.maths.dur.ac.uk/events/Meetings/LMS/106/index.html |