**Present**

**Chair** Prof H G Dales (Leeds), Chairman of the 52^{nd} Colloquium

**Secretary** Dr H D Macpherson (Leeds) Secretary of the 52^{nd} Colloquium

Prof K A Brown (Glasgow), Secretary of the 53rd Colloquium

Prof A Carbery (Edinburgh), Edinburgh Mathematical Society

Prof R Carter (Warwick), London Mathematical Society

Prof J P C Greenlees (Sheffield), London Mathematical Society

Prof J Howie (Heriot-Watt University), Edinburgh Mathematical Society

Dr I J Leary (Southampton), Secretary of the 51^{st} Colloquium

Prof A G O'Farrell (NUl Maynooth), elected at AGM

Prof A C Newell (Warwick), representative from Warwick for 54^{th} Colloquium

Dr P Rowlinson (Stirling), Edinburgh Mathematical Society

Prof A J Scholl (Durham), London Mathematical Society

Prof C M Series (Warwick), representative from Warwick for 54^{th} Colloquium

Dr R J Steiner (Glasgow), Chairman of the 53^{rd} Colloquium

**Minutes of the 1998 Scientific Committee Meeting at Manchester**

These were approved.**Matters arising**

There were none.**Report on the 51**^{st}BMC at Southampton

Dr Leary reported that the number of participants at the 51^{st}BMC was approximately 165, significantly fewer than the 200 or so at the 50^{th}BMC. These included about 45 postgraduates. He explained that slightly more than expected was spent on room hire, but slightly less than expected on invited speakers, so the budget was as predicted. No travel money was offered for morning speakers, but they were offered free registration and up to 50 per cent reduction on accommodation costs.It was explained that the Edinburgh Mathematical Society holds an emergency fund for the BMC. The London Mathematical Society grant arrived sufficiently early to cover deposits for room hire at Southampton.

Dr Leary commented that there were many refusals among invited plenary speakers, and some from invited morning speakers. Prof Dales recommended that for invitations for plenary speakers, it is good to send out invitations early (about 2 years in advance) and to use any personal contacts available, as this is more likely to lead to acceptance. It was agreed that the local organising committee for a BMC should have some flexibility in adjusting the choice of plenary speakers, in order to retain a balanced programme and react to refusals.

The meeting expressed its appreciation and thanks to the Southampton organisers of the 51

^{st}BMC.**Progress report on the 52**^{nd}BMC at Leeds

Prof Dales circulated a provisional timetable for Leeds, and details on special sessions and suggestions for morning speakers for Leeds.Prof Dales reported that the plenary speakers at Leeds would be Professor S Donaldson FRS (Imperial College), Professor Vaughan Jones (Berkeley), Professor H Friedmann (Ohio State): and Professor J. Jantzen (Aarhus), with Sir Michael Atiyah FRS giving an additional plenary lecture after dinner on the Monday evening. There will be Special Sessions in

*Harmonic maps and minimal surfaces*organised by Prof J C Wood (Leeds) and Dr J Bolton (Durham), and in*Operator Algebras*, organised by Prof E C Lance (Leeds) and Prof A M Sinclair (Edinburgh). Dr Leary reported that at the 51st BMC, the Southampton organisers left the Special Session organisers to operate independently, and issue invitations to speakers directly. It was suggested that in future, organisers of special sessions should have considerable freedom in choice of speakers, though formally invitations should come from the local committee running the BMC.Prof Dales pointed out that some minor timetable changes would be introduced for Leeds: in particular, morning lectures would be 50 minutes, and the slot for Sir Michael Atiyah's lecture was not a regular one.

There was some discussion of satellite conferences, which the meeting considered a good way to boost numbers. Prof Dales reported that there might be a workshop in Operator Algebras at the ICMS in Edinburgh, immediately before the 52

^{nd}BMC, but that funding applications to the EU and to EPSRC had been unsuccessful. Likewise, Prof J C Wood was planning to run a satellite conference on*Harmonic maps and minimal surfaces*in Leeds immediately before the 52^{nd}BMC, but again an EPSRC grant application had been turned down. It is hoped that this meeting will go ahead anyway. Prof Carbery suggested that the LMS might if approached be amenable to funding instructional workshops at the finishing postgraduate/beginning postdoctoral level (distinct from the current LMS/EPSRC short course programme), and that it might be possible to arrange for one of these to coincide with the BMC. Prof Scholl suggested that Prof E Rees (Edinburgh) of the LMS Research Meetings Committee for workshops be approached. Prof Brown suggested that anyone making a grant application for a satellite conference should make explicit the connection with the BMC, and also suggested that for satellites the organisational load should be spread out from the host institution. It was suggested that the LMS be asked to approach EPSRC and urge that satellite conferences should have a high priority for funding.**Host institution in 2003**

Prof Dales circulated a letter of invitation for the 55^{th}BMC in 2003 from Prof J S Wilson (Birmingham). This was approved by the committee. Prof Dales will write to Prof Wilson confirming this, and stating that the invitation should formally be given at the AGM of the 52^{nd}BMC.**Arrangements for the joint meeting with BAMC at Warwick 2002**

Prof Newell reported that feedback from the BAMC so far was positive. There should be a suggested list of plenary speakers and a plan for the meeting within 4-5 months, to be circulated by email.The proposed timetable for the Warwick meeting was circulated, discussed, and provisionally approved. The arrival date would be Sunday 7 April 2002 for the Pure part (lectures starting on the 8

^{th}), and the afternoon of the 9^{th}for the Applied part. The Pure part would end at lunchtime on the 11^{th}, the Applied on the evening of the 12^{th}.(Added 30 April 1999. The committee of the BAMC has now accepted the proposals for a joint meeting in Warwick in 2002.)

**The possibility of future joint meetings with BAMC**

Prof Scholl proposed that the current BMC scientific meeting should hold a further meeting in Warwick in the autumn, to discuss the Warwick colloquium and possible future joint colloquia. The objective would be to hold a further joint meeting in 2005 or 2006. Prof O'Farrell urged that in the meantime, the BMC and BAMC should avoid clashes of dates.**Future host institutions of the BMC**

Prof Dales circulated letters from the Queen's University of Belfast, with a bid from Dr M Mathieu (Department of Pure Mathematics) to hold the 56th BMC in Belfast in 2004, with support from Prof K L Bell (School of Mathematics), and from the Vice-Chancellor. It was reported that Liverpool might also be interested in holding it. A decision on the host for 2004 would be made at the AGM in 2001. It was commented that Belfast might be a rather small department to act as host, and that the total travel costs might be high, but generally the meeting strongly supported the Belfast application. Prof Dales will write to Belfast, indicating the committee's very positive view of the application.**Special sessions and plenary speakers for Glasgow 2001**

A sheet was circulated with proposals for Special Sessions in*Modular Forms, Representations of Algebras, Differential Geometry, and Computational and Algorithmic aspects of Group Theory*. There was strong support for a Special Session in Modular Forms. Representations of Algebras was strongly supported as an area for a Special Session, but it was suggested that it be deferred for a year or two, to ensure a wide spread at Glasgow. The Glasgow organisers were asked to put together a second Special Session, possibly in the area of Partial Differential Equations, and Prof S B Kuksin (Heriot- Watt) was named as a possible organiser. This might not be too far from the present Glasgow proposal of a Special Session in Differential Geometry.For plenary speakers, there was time only for provisional discussion. Glasgow should send out some invitations now, and the situation will be reviewed at the September/October meeting. Suggestions were: one of B Mazur (Harvard), K Ribet (Berkeley), J Coates (Cambridge), H Lenstra (Berkeley). In PDEs, names suggested were C Kenig (Chicago), V Maz'ya (Linkoping, Sweden), P Lax (NYU Courant), J Moser (ETH), with S B Kuksin to be asked for further names. Other names mentioned were V Kac (MIT), D Knuth (Stanford), Y Manin (Bonn), B Kahn (Paris VII), E Witten (Princeton), M Hopkins (MIT), R E Borcherds (Cambridge), M Broué (Paris VII).

**Establishment of a BMC archive**

Professor Dales reported that there is material on past BMCs in the UCL manuscript library, and Dr Leary pointed out that there is a BMC minute book going back some 15 years. Prof O'Farrell urged that the Scientific Committee Secretary should keep all documents relating to the BMC and send them to UCL. There was discussion of finding a BMC archivist, but this was postponed to the October meeting.**Possible UK-based morning speakers for Leeds 2000**

Invitations should go out in the next few weeks. It was agreed to exclude from the list of speakers (i) people in Leeds. (ii) people who have spoken in recent years, and (iii) people who would fit into special session areas. There will be 14 morning speakers, and suggested names were the following.

*Logic*

(1) B Zil'ber (Kemerovo, going to Oxford) or A J Wilkie (Oxford) - not both, (2) M Dzemonja (UEA). Reserve: M Hyland (Cambridge).

*History of Mathematics*

(1) D van Dalen (Utrecht). Reserve: D Fowler (Warwick).

*Analysis, Differential equations, Dynamical Systems*

(1) J Brodzki (Exeter), (2) N Young (Newcastle), (3) J Sherratt (Heriot-Watt), (4) Kozlowski (Warwick). Reserves: B E Johnson (Newcastle) - for Young: C Batty (Oxford), K Ball (UCL), I McGillivray (Bath), V Liskevich (Bath).

*Number Theory*

(1) J Nekovar (Cambridge), (2) R Heath-Brown (Oxford). Reserves: M Spiess (Oxford); A Skorobogatov (Imperial).

*Discrete Mathematics*

(1) K Edwards (Dundee). Reserves: A Hilton (Reading); A Stacey (Cambridge): P Fitzpatrick (Cork).

*Topology, Geometry*

(1) U TilImann (Oxford), (2) B Totaro (Cambridge), (3) S Merkulov (Glasgow). Reserves: A Corti (Cambridge) - for Totaro; A Reznikov (Durham); D Joyce (Oxford) - for Merkulov; R Levi (Aberdeen) - for Tillmann.

*Algebra*

(1) I Grojnowski (Cambridge), (2) G Robinson (Birmingham), (3) M Nazarov (York). Reserves: J S Wilson (Birmingham) - for Robinson; K Erdmann (Oxford); R Sharp (Sheffield).