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

高振荡问题，在应用中普遍存在，通常被认为是非常困难的理论和计算要求。然而，最近的发展为治疗快速振荡问题提供了非常有效的手段。艾萨克·牛顿研究所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，均质化，辛积分，黎曼-希尔伯特技术，高振荡正交和指数积分器，以及理论家和广泛应用的工人。通过多学科合作，我们寻求解决的典型重大挑战是薛定谔、亥姆霍兹和麦克斯韦方程的解决方案，以及源自分子动力学的方程的长期集成。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，计算机断层扫描，等离子体输运，天体力学，医学成像，信号处理. . . .它已经被广泛的数学技术，从渐近理论，调和分析，动力系统理论，可积系统理论和微分几何解决。高振荡问题的计算产生了大量不同的数值方法和算法。该计划的目的是从统一的角度促进对高振荡的不同方面的研究，包括理论，计算和应用，并促进跨学科活动中的协同作用。

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.