Conference on Highly Ocillatory Problems: Computation, Theory and Applications.

在应用中普遍存在的高度振荡问题通常被认为是非常困难的理论和计算要求。然而，最近的发展提供了非常有效的手段来处理快速振荡的问题。艾萨克·牛顿研究所的项目汇集了关注高振荡现象的专业人士，重点是多尺度建模、齐次化、辛积分、Riemann-Hilbert技术、高振荡求积和指数积分器，以及广泛应用的理论家和工作人员。我们寻求通过这种多学科合作来解决的典型重大挑战是薛定谔方程、亥姆霍兹方程和麦克斯韦方程的解，以及源于分子动力学的方程的长期积分。高振荡遍及非常广泛的应用：电磁学、流体动力学、分子建模、量子化学、计算机化层析成像、等离子体传输、天体力学、医学成像、信号处理。。。。从渐近理论、调和分析、动力系统理论、可积系统理论到微分几何，它已经被广泛的数学方法研究过。高振荡问题的计算催生了大量不同的数值方法和算法。该计划的目的是促进对高振荡的不同方面的研究，包括理论、计算和应用，从统一的角度出发，促进跨学科活动中隐含的协同效应。

Highly oscillatory problems, ubiquitous in applications, are typically consider to be very difficult theoretically and demanding computationally. However, recent developments provide highly effective means to treat problems with rapid oscillation. The Isaac Newton Institute program brings together professionals concerned in highly oscillatory phenomena, with an emphasis on multiscale modeling, homogenization, symplectic integration, Riemann-Hilbert techniques, highly oscillatory quadrature and exponential integrators, together with theoreticians and with workers in a wide range of applications. Typical grand challenges that we seek to address by this multidisciplinary collaboration are the solution of Schroedinger, Helmholtz and Maxwell equations, as well as long-term integration of equations originating in molecular dynamics.High oscillation pervades a very wide range of applications:electromagnetics, fluid dynamics, molecular modelling, quantum chemistry, computerized tomography, plasma transport, celestial mechanics, medical imaging, signal processing. . . . It has been addressed by a wide range of mathematical techniques, ranging from asymptotic theory, harmonic analysis, theory of dynamical systems, theory of integrable systems and differential geometry. The computation of highly oscillatory problems has spawned a large number of different numerical approaches and algorithms. The purpose of this program is to foster research into different aspects of high oscillation, including the theoretical, the computational and the applied, from a united standpoint and to promote the synergy implicit in an interdisciplinary activity.