The main goal of this paper is to provide a brief survey of recent results which connect together results from different areas of research. It is well known that numerical integration of functions with mixed smoothness is closely related to the discrepancy theory. We discuss this connection in detail and provide a general view of this connection. It was established recently that the new concept of {\it fixed volume discrepancy} is very useful in proving the upper bounds for the dispersion. Also, it was understood recently that point sets with small dispersion are very good for the universal discretization of the uniform norm of trigonometric polynomials.
Dispersion Analysis of Finite Difference and Discontinuous Galerkin Schemes for Maxwell's Equations in Linear Lorentz Media
University of Science and Technology of China（中国科学技术大学）；King Mongkut’s Institute of Technology Ladkrabang（拉加邦国王科技大学）；Oregon State University（俄勒冈州立大学）；Michigan State University（密歇根州立大学）；Rensselaer Polytechnic Institute（伦斯勒理工学院）
Asymptotic dispersion correction for the isotropic elastic Helmholtz equation discretized with a MAC scheme
Université de Pau et des Pays de l’Adour（波城及阿杜尔地区大学）；Normandie University, INSA de Rouen Normandie（诺曼底大学，鲁昂诺曼底国立应用科学学院）；Ben-Gurion University of the Negev（内盖夫本-古里安大学）
Analysis and Computation of a Discrete KdV-Burgers Type Equation with Fast Dispersion and Slow Diffusion
The Weizmann Institute of Science（魏茨曼科学研究所）；Princeton University（普林斯顿大学）；University of Wisconsin–Madison（威斯康星大学麦迪逊分校）；Weizmann Institute of Science（魏茨曼科学研究所）；University of California Irvine（加州大学尔湾分校）
Numerical Exploration of Nonlinear Dispersion Effects via a Strongly Coupled Two-scale System
Linnaeus University（林奈大学）；University of Bonn（波恩大学）；University of Regensburg（雷根斯堡大学）；University of Colorado Boulder（科罗拉多大学博尔德分校）；Karlstad University（卡尔斯特德大学）
