Isaac Newton Institute for Mathematical Sciences

Exponential Asymptotics

January - June 1995

Organisers: MV Berry (Bristol), CJ Howls (Manchester), MD Kruskal (Rutgers), FWJ Olver (Maryland)

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:

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)

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