The local conference committee comprised

Prof Peter Giblin (Chair)

Prof Hugh Morton (Secretary)

Prof Alexander Movchan

Dr Ke Chen (Treasurer)

Mathematics 2005 combined the 2005 meetings of the British Applied Mathematics Colloquium (BAMC) and the British Mathematical Colloquium (BMC). The format was different from the previous combination which took place in Warwick in 2002, in which there was a single common day and the whole meeting spread over five days. Here in Liverpool the meetings were truly simultaneous, from Monday lunchtime to Thursday lunchtime.

Final registration was about 530 which included 180 research students and 99 females. Registration fees were waived for local members, exhibitors (commercial and academic), morning speakers and principal speakers. Altogether 107 participants had their registration fees waived.

There were 11 principal lectures, the lecturers being John Ball, Michael Berry, Noam Elkies, Barbara Fantechi, Avner Friedman, Askold Khovanskii, Vladimir Maz'va, Dusa McDuff, Graeme Milton, John Toland, Wendelin Werner. All these speakers made a genuine effort to address a broad mathematical audience. In addition there were 12 Morning Speakers in the BMC style, whose talks were in pairs, taking place at the same time as BAMC parallel sessions.

Five of the principal lectures took place at times when no other activity was scheduled, and for these a video link was provided from the largest lecture theatre to the second largest. The only university lecture theatre which holds more than 500 people is several minutes walk away from the main conference venues, and this was regarded as too far bearing in mind the tight scheduling needed for such a large number of talks (about 260 in all).

The scale of the meeting implied that publishers and other exhibitors were more interested in having substantial exhibits than might be the case for a smaller meeting. In fact the income from exhibitors (including advertisements in the programme book) was much more than anticipated and completely offset the fairly substantial charges for the hire of a large hall in the Guild of Students where all the exhibitions were mounted. The meeting as a whole had a small surplus of income over expenditure; this was used to partially reimburse the Department for the purchase and installation of two fixed data projectors in early 2005, in preparation for the conference.

The 'BMC' had Special Sessions on Arithmetic and Algebraic Geometry (organisers E V Flynn and P E Newstead), and on Dynamical Systems (S van Strien and S M Rees); the 'BAMC' had Minisymposia on a variety of topics. The latter Special Session featured talks by young people including postgraduates whereas the former concentrated on two major speakers (Alessandro Verra and Nils Bruin).

There were also Splinter Groups, that is contributed talks, in many areas of Pure and Applied mathematics. Chairs of the various sessions were appointed well in advance (about November 2004). Submission of abstracts was on-line; the work involved in forwarding abstracts to Chairs and compiling the accepted abstracts into a programme book was very considerable, and was mostly carried out by postgraduates. Because of the large number of parallel sessions, it was necessary to use lecture rooms in three adjacent buildings of the University. Altogether the topics covered in sessions of one kind or another were

- Algebra and representation theory

- Algebraic and Arithmetic Geometry

- Analysis

- Biological Fluid Dynamics

- Differential Equations

- Dynamical Systems

- Fluids

- Group Theory

- Geometry and Topology

- History of Mathematics

- Industrial Mathematics

- Integrable Systems

- Mathematical Biology

- Mathematical Modelling

- Mechanics of Fluids

- Number Theory

- Numerical Mathematics

- Population dynamics, epidemiology and evolution

- Random Matrix Theory

- Solid Mechanics

- Stability of Autowave Vortices

- Statistics

- Statistics, Random Processes and Optimisation

- Trapped vibration modes and models of photonics and phononics

- Waves

Registration was almost entirely on-line, using software developed in Liverpool and based on that used at the 2004 BAMC in UEA. A dozen or so participants used the alternative of paper registration which was provided on the website. The handling of payments, contact with participants, liaison with university catering, local transport and the manning of the office during the conference were handled by the University's Conference Office, at a very modest charge of £10 per delegate. This is regarded by the organisers as a

The Halls of Residence which are available during vacations are all situated about 4 miles from the main precinct, and buses were hired from the local bus company Arriva to transport participants between the Halls and the main conference venue. A member of the conference committee (Ke Chen) was present to assist in ensuring that the buses left on time. The bus company was very flexible about providing additional journeys as needed. Ke Chen, Peter Giblin and Hugh Morton all stayed in Hall during the conference (but PG and HM left before breakfast each day to attend to arrangements for lectures). There were some complaints about the ensuite accommodation which, though newly furnished, was still somewhat shabby; also the private bathrooms lacked showers. The Halls provided a venue for the Tuesday evening Education Session, at which Prof Celia Hoyles, Chief Adviser on Mathematics to the DfES, gave an address which was followed by short presentations by several people involved in promoting mathematics to young people.

All the refreshments during the conference were served in the Mountford Hall, which is also where the exhibitions were sited and where pre-paid packed lunches were available. The existence of a large hall was a major attraction for the exhibitors. Representatives of Springer and CUP visited in February 2005 and were impressed with the exhibition space, and were very pleased that refreshments would be delivered in the same space.

The **registration fee** of £60, with reductions to £30 for students and retired people, was based on an attendance of 400 and was intended to cover the following: Conference Office (£10), transport from Halls (£7), production of programme book (£4), subsidy on conference dinner (£10), hire of rooms (£7), tea and coffee (£10), technical help and student helpers (£3). These add to £51, so the fee was set at £60 to allow for unexpected expenses, small items like stationery, and the expected large number of participants whose registration fees are waived. Our advance estimates of costs were reasonably accurate, except that the final cost of transport was less than expected. The remaining cost of transport from halls was included in the **accommodation charges**. Lunches were paid for by participants at cost, with the exception of invited speakers.

The **expenses of invited speakers** were covered by various grants, notably the £10,000 from the London Mathematical Society, £3,000 from EPSRC and special grants for named lectures from the IMA and the Stewartson Memorial Fund (UCL). Some of the distinguished invited speakers were from the UK which helped to reduce the total expenses bill.

SIAM provided four **prizes** of £50, for the best three student talks and the best student poster, and three of these four were presented by Sir Michael Berry after the final lecture of the conference.

AUGUST 2005