The MathFIT Town Meeting was held on 11 December 1998 at the The Regency Hotel, Queens Gate, London. Sponsored by the EPSRC and the LMS, the aim was to draw attention to the EPSRC/LMS MathFIT initiative which promotes interdisciplinary research between Mathematics and Computer Science, and to seek input from the community as to how to encourage interdisciplinary work and further develop the initiative. Around 60 mathematicians and computer scientists attended.
After an introduction by Professor Ursula Martin, University of St Andrews, for the LMS, and Mrs Anne Farrow, EPSRC Mathematics Programme, and Dr Dominic Semple, EPSRC IT and Computer Science Programme, three lectures were given by distinguished scientists already engaged in interdisciplinary work which has received support from MathFIT.
Professor Angus Macintyre FRS, University of Edinburgh,
Logic, models and computation
The talk involved a mix of model theory, geometry and probability theory, addressing the question of the theoretical and practical limits of deciding questions in real algebraic geometry, a topic which has application in robotics, neural computation and computational learning.
Professor Frank Kelly FRS, University of Cambridge,
Rate control in communication networks
This talk discussed the stability and fairness of rate control algorithms for communication networks: results in optimisation and dynamical systems are used to provide natural implementations of two proportionally fair pricing algorithms, based on congestion indicators and shadow pricing. As an application of the theory, the talk discussed ways in which the transmission control protocol of the Internet may evolve to support heterogeneous applications.
Professor Iain Stewart, University of Leicester,
Games without frontiers
The talk illustrated how playing games in model theory can provide lower bound results in computational complexity theory. By use of probability theory, we can often dispense with explicit game playing by proving that suitable structures exist on which we might play our games and that if we were to do so then we could be sure that one of our players had a winning strategy. That is, we can play games, and so obtain lower bound results, non-constructively.
After lunch the meeting split into three breakout groups, led by Dr Leslie Goldberg, University of Warwick, Dr Andrew Pitts, University of Cambridge and Dr Pavid Pym, Queen Mary Westfield, to address the following questions.
What are the important areas of interaction for computer science and mathematics?
How can we encourage and support new interdisciplinary work to the benefit of both disciplines?
Lively discussions ensued in all three groups and various aspects of the MathFIT strategy and policy were addressed.
Dr Lincoln Wallen then led the wrap up session: "Where do we go from here?", with informal contributions from Dr Alasdair Rose, Dr Dominic Semple and Mrs Anne Farrow from EPSRC.
The main conclusions of the discussion can be summarised as follows.
The community, both mathematicians and computer scientists, expressed warm support for MathFIT, for the workshops and meetings it had funded and for the new opportunities for interdisciplinary work it had fostered.
Particular stress was placed on the importance of the initiative for encouraging younger scientists to target novel interdisciplinary problems. The apparent dampening effect of the RAE on new initiatives, the perception, even if untrue, that it is easier to attract research funding for "more of the same" or for applied research than for novelor foundational approaches, and the intense pressure on young scientists to perform well against such indicators, were all mentioned as negative drivers for novel interdisciplinary research. MathFIT sends a clear signal to the community of the recognition by EPSRC and LMS of the national importance of such work, and supports this with esteem indicators such as meetings and grants. Since the meeting IMA has approached the LMS with an offer to assist.
There was total agreement that MathFIT should continue.
Examples of MathFIT success include the following.
Dr Pete Jeavons and Professor Iain Stewart hold a MathFIT grant to address novel approaches to scheduling problems. Dr Jeavons' work has recently been used very successfully in British Telecom's "Work Manager" software, which organises the visits of BT's vans to BT's work sites. In 1998, Work Manager saved BT 150 million dollars a year on operational costs.
One of the first MathFIT workshops, organised by Dr Bob Leese of Oxford, was on Radio Channel Assignment, an extremely difficult combinatorial problem which needs to be solved efficiently if mobile phones and other devices are to achieve optimum use of scarce resources. As a result of this workshop, several leading mathematicians became interested in the problem, and the Radiocommunications Agency is keen to co-sponsor another MathFIT meeting.
The work of Professor Abbas Edalat, of Imperial College, uses domain theory to define a new approach to real number computation, now being explored in high-precision applications as an alternative to floating point by Escardo and Potts. MathFIT sponsored a workshop on this material in Birmingham in 1997, which brought several bright young analysts in contact with the field for the first time. A further workshop exploring connections with semi-algebraic sets, which turn up in a variety of applications such as learning theory and neural nets, will be held in 1999.
New markov chain methods use techniques which were traditionally the domain of proability theorists to understand simulation algorithms and model problems such as contention resolution in networks. The work of Dr Leslie Goldberg of Warwick and Professor Frank Kelly of Cambridge shows that this has immediate practical application in devising network routing, protocols and pricing technqiues for the internet. MathFIT sponsored a summer school on this material in Warwick in 1998.
A part-time coordinator (who would be an experienced scientist with a vision for interdisciplinary research, the technical understanding to assess the opportunities available, and the interpersonal skills to draw together and mentor disparate groups) should be appointed so as to allow EPSRC and the LMS to be proactive in contacting researchers and pump-priming new opportunities, as well as supporting existing activity.
PhD students who attend MathFIT meetings are generally enthusiastic, motivated and appreciate the opportunity for informal interaction with world leaders in new research areas. However there is a problem in persuading research students to attend: perhaps because of the intense time pressure in the UK PhD system. One suggestion was to open up participation to students at an earlier stage, such as Masters students: another to ensure a higher profile for MathFIT through an internet presence, email discussion groups, expository articles and so on.
Flexible funding to encourage collaboration between complementary research groups. MathFIT already offers funding for visiting fellowships, which allow established researchers to spend six months in a complementary department: anecdotal feedback suggests that the slightly disappointing take-up has been partly due to the reluctance of more senior figures or those with family responsibilities to live away from home. More flexible schemes and encouragement to apply for small grants might target younger, more mobile, researchers, encourage short visits to several sites to ensure greater interaction, or provide pump-priming funds to establish networks of collaborating researchers.
There should be a regular high-quality MathFIT conference with plenary presentations by leading international researchers backed up by other talks and discussion groups. A key aim would be to showcase successful interdisciplinary work and present new interdisciplinary challenges. Attendance by key opinion formers in the mathematical and computer science community, both academic and industrial, and by younger scientists, would be encouraged and heavily subsidised. (In this regard we note also that LMS, in collaboration with the IMA, is becoming actively involved in shadowing Foresight.)
MathFIT should organise interdiscplinary study groups, following the model of the European Study Groups with Industry (http://www.maths.soton.ac.uk/esgi98/what_is_esgi_frame.html) which are very successful in encouraging novel interdisciplinary work in Applied mathematics. Such groups would encourage early interaction on live challenges, provide a forum for exploiting the expertise of leading mathematicians to find solutions to problems arising in computer science, would aid in clarifying and clearly formulating problems, bring new perspectives and fresh ideas and encourage brainstorming on mechanisms and methodologies.
MathFIT should be widened to include "IT for Mathematics". There is increasing recognition that the diverse applications of computation in mathematical research throw up a wide variety of challenging problems in computer science. The distinction between "maths applied to IT" and "IT applied to maths" can become increasingly prescriptive and unnecessary in the development of novel science. Examples of IT for mathematics include:
exact arithmetic as an alternative foundation for numerical computation;
high performance computational environments for large symbolic problems (for example, the GAP system used in the classification of finite simple groups and later developments such as those leading to the recent Fields Medal for Richard Borcherds); and
resolving the problems of soundness and performance in the use of computer algebra systems in applications as diverse as quantum mechanics and homological algebra.
Ursula Martin, 13 April 1999
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