Asymptopia September 2004 | Alumni and Friends

skip to content

Asymptopia - Centre for Mathematical Sciences Newsletter

Contents

News from the CMS

CMS Colloquia

Towards a New Generation Climate Model

The UK Mathematics Trust Team Maths Challenge

Cambridge-MIT Exchange Program: Another View

News from the CMS
The last six months have seen several prestigious awards to members of the CMS, and congratulations are due to them all. In July, Professor Sir John Kingman, Director of the Isaac Newton Institute for Mathematical Sciences (INI), received the honorary degree of Doctor of Science for his outstanding service to mathematics. The first director of INI, Sir Michael Atiyah, was awarded the Abel Prize for 2004 jointly with Professor Isadore M. Singer, in recognition of their "discovery and proof of the index theorem, bringing together topology, geometry and analysis, and their outstanding role in building new bridges between mathematics and theoretical physics". INI's Deputy Director, Dr Robert Hunt, was formally appointed in January as a Special Adviser to the Treasury Select Committee of the House of Commons. Dr Ian Grojnowski has become the first recipient of the LMS Fröhlich Prize, in recognition of his originality and influence across a wide range of problems in representation theory and algebraic geometry, and Professor Frank Kelly received the IEEE Koji Kobayashi Award for his contributions to the development of fundamental theories for the understanding, performance evaluation and enhancement of telecommunications networks. Professor Peter Landshoff retires at the end of September, and the CMS owes him particular gratitude for his great contribution to the Centre's genesis and development. Professor Anne Davis succeeds him as Deputy Head of the Department of Applied Mathematics and Theoretical Physics, with particular responsibility for CMS affairs.
Professor Peter Landshoff (right) with Mr John Woods (Estate Management and Buildings Service) and the British Construction Industry's award for Major Project of the Year 2004.
In July, H.R.H. Prince Turki Al-Faisal, the Ambassador of the Kingdom of Saudi Arabia, visited the Isaac Newton Institute as part of a wider tour of the University. The CMS has hosted a wide range of other visits and activities, including the Maths Team Challenge described below.
Back to top

CMS Colloquia

Nicholas Manton

The move to CMS has created a new opportunity for a regular series of Colloquia covering all areas of mathematics. While still located in central Cambridge, collaboration between the two maths departments was mainly limited to undergraduate teaching and examining, and there were relatively few links at the research level.

CMS has now joined forces with the Isaac Newton Institute to have a joint programme of CMS Colloquia and INI Seminars. Held fortnightly during term time, they are followed by a social gathering with nibbles and a glass of wine. Here one can really appreciate the central space of CMS as somewhere for mathematicians from across the spectrum to meet and talk, a facility we lacked before coming here.

The Colloquium provides an opportunity for the speaker to review their research area and its recent achievements, and to outline their hopes for the future. The series started in January and so far there have been seven Colloquia, with topics ranging from the relation of game theory to computer programs, to the mathematical modelling of complex, non-Newtonian fluids. Speakers from both departments have communicated the excitement of their area to others in CMS with quite different interests, and the first series attracted a wide audience from all the sub-areas of mathematics.

We plan in future to have occasional visiting speakers, but there are still plenty of CMS members whom it would be interesting to hear at future Colloquia.

Towards a New Generation Climate Model Nikos Nikiforakis
Extreme weather phenomena feature with increasing frequency in the news, raising concerns about climate change. Scientists use computational models to predict the weather (short-term fluctuations of the atmosphere) and climate (average weather conditions over the longer term). These models take into account key processes of the climate system (atmosphere, ocean and land-surface), which are represented in mathematical terms, usually as complex systems of partial differential equations (PDEs). The atmosphere and oceans are divided into 'boxes' or computational cells (a process known as 'space discretisation'), and the PDEs are evaluated at the centres (or edges) of these cells. As the cell density (resolution) increases, so does the accuracy of our weather and climate predictions.
The resolution of global atmospheric models has increased significantly thanks to the latest generation of supercomputers. The model used by the European Centre for Medium-Range Weather Forecasts, which runs on two IBM Cluster 1600 supercomputer systems, has a horizontal resolution of about 40 km around the globe and 60 levels (computational cells) along the vertical dimension. This amounts to 20,911,680 computational cells to discretise the earth's atmosphere. However, this resolution is still not adequate to resolve many important atmospheric phenomena which have an impact on short- to medium-term numerical weather prediction, such as orographic effects and their interaction with weather phenomena (e.g. rain bands), and extreme events such as tropical cyclones. The obvious solution is a uniform increase of the model resolution, but this is not a viable option due to prohibitive computational costs, particularly for the multi-decadal integrations required for climate change. Higher resolution computations can be performed by other means (e.g. limited area or nested models), but there are limitations to their accuracy and validity.
In any case, discretisation along the third (vertical) dimension remains an issue. Most of the current models attempt to capture the vertical structure of the atmosphere from the ground to its uppermost limit (including regions with significant gradients like the boundary layer and the tropopause) using 30 to 60 computational cells (levels). However, this is not adequate, even with the use of subgrid-scale models. If the processes along the vertical are to be studied by capturing them explicitly, then a new, radical approach to modelling is needed. To this end, researchers in the Laboratory of Computational Dynamics at DAMTP have developed a prototype global atmospheric model, which can dynamically alter the resolution of the computational domain along all three dimensions in response to evolving atmospheric flows. The technique is known as AMR (Adaptive Mesh Refinement) and, although it has widespread use in other disciplines, this is its first application to global atmospheric modelling.
As a result, it has been possible to perform very high effective-resolution simulations using desktop workstations rather than supercomputers, and to capture in detail the three-dimensional structure of the atmosphere. The two figures show how these techniques captured a number of essentially 3D features (filaments and tubes) in the tropopause region during a stratosphere-troposphere atmospheric exchange event over the North Atlantic in June 1996. These integrations use a chemistry and transport model combined with meteorological analyses. Current development is concentrating on introducing more complex dynamics, thermodynamics and physics into this model, as well as full orography.
The model development is taking place within the framework of an international collaboration between the United Kingdom (UK-HiGEM: A National Programme in 'Grand Challenge' High Resolution Modelling of the Global Environment involving the Hadley Centre and NERC institutions) and Japan (The Earth Simulator Center, whose computer is currently ranked first in the top 500 supercomputers worldwide). The collaboration is funded by NCAS (NERC Centres for Atmospheric Science), the Hadley Centre (DEFRA) and the Foreign and Commonwealth Office.
Back to top

The UK Mathematics Trust Team Maths Challenge Terry Heard, Claire Metcalfe, Susanna Bridge and Chloe Martindale
In March, the CMS common room was considerably enlivened by the presence of around eighty school students competing in two Regional Finals of the Team Maths Challenge (TMC), organised by the UK Mathematics Trust (UKMT). The mathematical challenges culminated in an energetic relay race, using the full length of the central core. The competition is described below by Terry Heard, Chairman of the Team Maths Challenge organisers, and by members of the Perse School for Girls, winners of one of the days hosted by the CMS.
The Team Maths Challenge The UK Mathematics Trust is a registered charity set up in 1996 "to advance the education of children and young people in mathematics". This year over 540,000 UK secondary school pupils took part in UKMT competitions. The Team Maths Challenge (TMC) is an inter-school competition open to all schools in the UK with students in Years 8 and 9. This year 1,016 schools entered, each selecting its team of four using materials supplied by UKMT. Thirty four Regional Finals were held in venues generously provided by schools and universities, including two at Cambridge's splendid Centre for Mathematical Studies. Each Regional Final is a varied day of mathematical activities, designed to be challenging and fun. This year sixty winners and high-scoring runners-up went on to compete at the National Final in the City of London Guildhall. The TMC, like all UKMT activities, depends on the work of volunteers. For more information please contact Angela Gould, Executive Director: email angela.gould@kcl.ac.uk, tel. 020 7848 1406.
Terry Heard, Chairman, TMC subtrust
The Regional Final In 2003, Perse School for Girls entered the UKMT Team Maths Challenge for the first time, and were delighted to qualify for the national final. So it was with great excitement that we entered the 2004 competition. The team arrived at the competition excited and eager, and started with a very strong performance in the first two rounds. Undaunted by a slightly disappointing performance in the head-to-head competition, the team delivered a dazzling (and exhausting) performance in the relay race. After a nail-biting wait whilst scores were collated, we were delighted to learn that they had won! They had enjoyed the opportunity to discuss mathematical problems with each other and all worked well as a team. The team had another enjoyable and memorable day at the National Final, and finished a very respectable 13th out of the 60 teams qualifying.
Claire Metcalfe, Acting Head of Mathematics, Perse School for Girls
The Two Finals - Regional and National In March 2004, our team was one of over 20 taking part in the UKMT TMC Regional Final held at the Centre for Mathematical Sciences on Wilberforce Road - a very prestigious venue. The event consisted of four very different activities. Firstly, we had to solve ten very difficult mathematical problems between us. Secondly, we completed a Cross Number in which one pair had the across clues, and the other the down clues. Then, after lunch we took part in the 'head to head', which involved competing with another team to finish a sequence of numbers. The final challenge was a relay race, in which one pair answered a question, and then ran to the teacher with the answer, and then to the other pair with the next question! This was our biggest strength, since we all enjoyed the quick thinking involved, and were enthusiastic about running. We were understandably exhausted as we waited for the results, only to discover that we had won the competition, and would proceed to the National Final! We thoroughly enjoyed the competition, which gave us the opportunity to think hard about mathematical problems while having a great time.
Susanna Bridge (year 9)
The team from Perse School for Girls: Genna Bowes, Susanna Bridge, Chloe Martindale, Rowena Paren.
On Monday 5th July, we set off for the National Final at London Guildhall, where we were one of 59 teams competing. There were five different parts to the competition - the poster competition, the circus, the cross number, the head to head and the relay race. In the poster competition, we had to make a poster and answer three questions on cyclic quadrilaterals. The circus involved doing ten activities at ten different stations - some of which we did straight away and some of which we couldn't do at all! The cross number was harder than the one in the Regional Final, and we did less well in the head to head. However, the last event was the relay race - which is our strong point. We work well together on the questions - but we all wanted to run! We didn't win, but it was really fun - I hope we get to the national final next year and would like to participate again.
Chloe Martindale (year 8)
Back to top

Cambridge-MIT Exchange Program: Another View Aaron Marcus
The Cambridge-MIT Exchange Program is run by the Camridge-MIT Institute (CMI), a joint initiative run by the University of Cambridge and the Massachusetts Institute of Technology. Following Dan Abramson's description of his year at MIT in the last issue of Asymptopia, Aaron Marcus describes his experience in Cambridge.
When I first decided to take part in the Cambridge-MIT exchange, I didn't know what to expect. While I had heard many people say many things about how the experience would be, I had done very little independent research into Cambridge. All I really knew before the plane touched down was that I would have regretted not going and that I had no idea what I was getting myself into. Now that the year has passed, I can say with some certainty that spending the year at Cambridge was a good decision.
Students from MIT spend their third year (out of four) in Cambridge, and study classes which allow them to receive credits towards their MIT degree. Those studying mathematics normally follow the second year of the Tripos syllabus. Cambridge and MIT are different in many respects. While concepts like supervisions, non-compulsory example sheets, and classes without textbooks struck me as foreign, the most striking difference for me was social and cultural. My friends in Cambridge have much more free time than my friends at MIT and use it differently. At MIT, if I just stopped by someone's room, we would talk and hang out while doing work. Doing anything larger than hanging out or eating dinner generally required sufficient notice to get all the work due the next day out of the way. My work was a large part of my life, and crept into almost all aspects of it. However, at Cambridge, stopping by someone's room seemed to lead to an offer of tea and biscuits, hours of conversation, and formulation of the evening's plans. These plans often included hanging out in the bar and playing pool, but sometimes involved watching movies, going clubbing, going out to pubs, and many other things. This was a very drastic change from what I was used to. Of course, there are many at MIT who have more free time than I did and use it more productively, but it was nice to experience such a lifestyle myself. While the social aspect of the exchange was brilliant, the reason I got into the exchange was for academics, and it would be dishonest to describe my experience without touching upon some mathematics. First, working in the CMS is a joy. Between the library, the cafeteria, the classrooms, and everything else I experienced this year, I have to declare it the best maths-related building I have ever been in. However, I came to Cambridge to study maths and not architecture, so the CMS was just an ancillary benefit. It was a pleasure having the chance to take maths classes only, and that alone is enough to justify the experience for me. It is hard to compare the classes directly as, even when there was overlap in material between what I took here and what I took at MIT, the context was completely different. Overall, I would say that Cambridge classes are denser and very on topic. However, as a 16 hour lecture class has less than half the 'in class' time of a 12 unit class at MIT, there isn't the time to cover the depth, breadth, or explanation that MIT classes include. Coming to Cambridge made me appreciate how much each individual class at MIT covers. This is necessary, as MIT 'mathmos' don't take as many maths classes as their Cambridge counterparts, so I can't really say that one system is better than another. Supervisions lend another interesting aspect to the education here. Cambridge gives its students much more freedom to do what they please within individual classes, and supervisions give a way both to monitor the students and to clarify anything which they have had difficulty in understanding. While I am not convinced that this is better than continual assessment combined with tutorials and recitations at the lower levels and office hours from graders and lecturers at higher levels, I don't think that MIT's system is necessarily better either. They are both good systems, and I think declaring one superior to the other would be missing the point entirely. I just feel fortunate that I have had the chance to experience them both and form my own opinions. Overall, I would say that the year was great. I learned a lot, both as a mathematician and as a person. I only hope that many more will do what I did and discover the differences between MIT and Cambridge for themselves.
Back to top
To discuss any aspect of making a donation in support of mathematics at Cambridge, please contact Professor Anne Davis (A.C.Davis@damtp.cam.ac.uk) or Mr Christopher Hesketh (ch10002@cam.ac.uk).