Exponential asymptotics

Programme theme

Although quantities which are exponentially small are important and arise frequently in applications, until recently the mathematical literature about them has been sparse. One reason could be Poincare's definition of an asymptotic expansion, which although introducing rigour, did so in a way which was not sufficiently refined to deal with small exponentials. Now there is an upsurge in interest in the subject and a central new concept, resurgence, has emerged which describes how small exponentials are responsible for the divergences of asymptotic series. Resurgence enables the divergent tails to be decoded (for example by resummation) to yield these exponentials. New mathematical techniques are being developed as well as new areas of application, for example pattern formation in fluids, chaos in classical and quantum mechanics, and even philosophy. The aim of the programme is to foster a common culture, based on the recognition that (as with chaos in the 1970s) the problems being studied are essentially the same despite differences of language and approach.

Structure of the Programme

In addition to the research activities of the participants there will be a series of seminars and workshops to widen the appeal to outside visitors. The following meetings are planned:

• Hyperasymptotics Wednesday 22nd February

  Topics: Hyperasymptotics for integrals and differential equations, practical implementation of the method.

  Deadlines: Talk applications 25th January, abstracts and participation 1st February.

• Connection Problems and WKB Analysis 14th-16th March

  Topics: Physical applications of exponential asymptotics, WKB/Liouville-Green analysis, connection probems, Stokes multipliers, Painleve equations, singular perturbation theory, exact quantum mechanics, perturbation field theory.

  Deadlines: Talk applications 14th February, abstracts and participation 28th February.

• Asymptotic Analysis 4th-6th April

  Topics: Applications of exponential asymptotics, Stokes phenomena, high order expansions, singular perturbation theory, ODEs (linear and nonlinear), integrals, eigenvalues.

  Deadlines: Talk applications 7th March, abstracts and participation 21st March.

• Resurgence and Non-Standard Asymptotic Analysis 19th-20th April

  Topics: Resurgence theory, non-standard asymptotic analysis.

  Deadlines: Talk applications 21st March, abstracts and participation 4th April.

• Spitalfields Day 25 April 1995

• Spectral Theory 11th May

  Topics: Semiclassical spectra, eigenvalue asymptotics, chaotic systems.

  Deadline: Talk applications 13th April, abstracts and participation 27th April.

• Summary Meeting week of 19th June

  Topics: To be announced

  More detailed lists of speakers at these meetings will be confirmed on separate posters. We invite both current and potential participants to submit papers to the organisers via Dr. Chris Howls at the address given below. In addition to a weekly seminar programme, we hope to advertise further lectures in due course.

• Stokes Commemoration Meeting

  There will be a Stokes Commemoration Meeting on 9-10th June 1995 in Sligo, Ireland. People wishing to attend this event should contact directly Professor A. Wood, Stokes Conference, School of Mathematical Sciences, Dublin City University, Dublin 9, Ireland, phone +353 1 7045293, fax +353 1 7045786.

Participation

The following people have been invited to participate during the weeks shown. Financial support is now quite limited. However enquiries are always welcomed, especially from postdoctoral workers and self-supporting participants.

Aoki, T (27 Feb-24 Mar) Joshi, N (9 Jan-30 Jun) Baesens, C (16 Jan-27 Jan) Joye, A (15 Jan-28 Jan) Bender, C (5 Jun-30 Jun) Kawai, T (27 Feb-1 Apr) Bogomolny, E (1 May-2 Jun) Keating, J (22 May-9 Jun) Boyd, W (20 Feb-14 Apr) Kruskal, M (1 Jan-30 Jun) Braaksma, B (15 Jan-27 Jan) Lochak, P (17 Apr-12 May) Braaksma, BLJ(27 Feb-17 Mar) Lutz, D (8 Jan-30 Jan) Costin, O (25 Mar-14 Apr) Majima, H (27 Feb-24 Mar) Delabaere, E (20 Feb-17 Mar) McLeod, J (1 Apr-14 Apr) Diener, F (10 Apr-6 May) Mulholland, A (16 Jan-27 Jan) Diener, M (24 Apr-20 May) Nikishov, A (3 Apr-26 May) Dunster, T (2 Jan-30 Jun) Odlyzko, A (20 Mar-31 Mar) Fröman, N (6 Feb-31 Mar) Ohyama, Y (27 Feb-24 Mar) Fröman, P (6 Feb-31 Mar) Olde Daalhuis, A(9Jan-30Jun) Giller, S (5 Jun-30 Jun) Olver, F (11 Jan-30 Jun) Goldhaber, A (15 Mar-30 Jun) O'Malley, R (2 Jan-30 Jun ) Guttman, A (1 May-19 May) Paris, R (20 Mar-14 Apr) Hakim, V (17 Apr-5 May) Pham, F (17 Apr-30 Apr) Howls, C (2 Jan-30 Jun) Ritus, V (3 Apr-26 May) Hu, J (5 Jun-30 Jun) Sacchetti, A (16 Jan-27 Jan) Jaksic, V (6 Feb-3 Mar) Salvy, B (2 Jan-31 Jan) Jones, D (20 Mar-14 Apr) Schafke, R (17 Apr-12 May) Shatalov, V (17 Apr-31 May) Silverstone, H (6 Mar-13 Apr) Slavyanov, S (15 Jan-15 May) Solov'ev, E (1 May-30 Jun) Spigler, R (3 Apr-21 Apr) Sternin, B (17 Apr-31 May) Tajima, S (27 Feb-24 Mar) Takasaki, K (20 Mar-9th Apr) Takei, Y (27 Feb-24 Mar) Tanveer, S (23 Apr-7 Jun) Temme, N (2 Jan-31 Jan) Tovbis, A (8 May-30 Jun) Ursell, F (5 Jun-30 Jun) van den Berg, I (17 Apr-9 Jun) Voros, A (27 Mar-22 Apr) Wei, J (16 Jan-27 Jan) Weniger, E (15 Jan-27 Jan) Wickham, G (5 Jun-30 Jun) Wong, R (11 Jun-24 Jun) Wood, A (17 Apr-30 Apr) Yngve, S (1 Jun-30 Jun) Zinn-Justin, J(13 Mar-31 Mar)