New Trends in Localized Patterns in Partial Differential Equations: Mathematical Theory and Applications to Physics, Biology, and the Social Sciences

该奖项支持美国与会者参加将于2020年8月10日至8月13日在不列颠哥伦比亚省大学校园举行的由太平洋数学研究所主办的会议：PDE中本地化模式的新趋势：数学理论与应用于物理、生物学和社会科学。时空模式在生物、物理和社会系统中无处不在：生物系统的行为模式，植物细胞根毛尖端形成的启动，以及社会系统，如城市犯罪的空间分布，仅举几例。近年来，在图案形成的数学理论方面有了许多令人兴奋的新发展。随着旧油田之间的新联系被发现，新的边疆已经打开。该奖项为职业生涯早期的研究人员、属于代表性不足群体的研究人员以及没有其他旅行支持来源的研究人员提供参加和参与的机会。研讨会将邀请高级和初级研究人员在小范围内发表演讲，以鼓励合作并促进新的研究联系。被邀请的演讲者是来自世界各地的知名学者，他们对图案形成和偏微分方程组理论做出了开创性的贡献。该研讨会的目的是概述该领域的现状，并在未来几年在偏微分方程和模式形成的理论、数值和应用方面规划未来的方向。讲习班要探讨的一个共同主题是如何利用时间或空间尺度上的差异来洞察复杂系统的解决方案。通过识别这些尺度上的小参数或大参数区域，奇异摄动理论可以用来系统地将复杂系统归结为一系列更简单的问题。会议的网站是https://www.pims.math.ca/scientific-event/200810-pwntlpipThis奖，它反映了国家科学基金会的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

This award supports travel for US participants to the conference "New Trends in Localized Patterns in PDEs: Mathematical Theory and Applications to Physics, Biology and the Social Sciences" that will be hosted by the Pacific Institute for Mathematical Sciences on the campus of the University of British Columbia from August 10 to August 13, 2020. Spatial-temporal patterns are everywhere in biological, physical, and social systems: the models of behavior of biological systems, the initiation of root-hair tip formation in plant cells, and social systems such as the spatial distribution of urban crime, to name only a few. In recent years, there has been an explosion of many new and exciting developments in the mathematical theory of pattern formation. New frontiers have opened while new connections between old fields have been discovered. This award provides opportunities for early-career researchers, researchers who are members of underrepresented groups, and researchers without other sources of travel support to attend and participate. The workshop will feature invited talks from senior and junior researchers in a small setting to encourage collaboration and foster new research connections. The invited speakers are renowned scholars from around the world who have made seminal contributions to pattern formation and the theory of partial differential equations. An aim of this workshop is to survey the current state of the field and plot out future directions in theoretical, numerical, and applied aspects of partial differential equations and pattern formation over the coming years. A common theme to be explored in the workshop is how disparities in time or spatial scales can be exploited to gain insight into solutions of complex systems. By identification of small or large parameter regimes from such scales, singular perturbation theory can be applied to systematically reduce complex systems to a hierarchy of simpler problems. The website for the conference is https://www.pims.math.ca/scientific-event/200810-pwntlpipThis award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.