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“pde局部模式的新趋势：数学理论及其在物理学、生物学和社会科学中的应用”会议，该会议将于2020年8月10日至8月13日在不列颠哥伦比亚大学校园由太平洋数学科学研究所主办。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，植物细胞中根尖形成的开始，以及城市犯罪的空间分布等社会系统，仅举几例。近年来，在模式形成的数学理论方面出现了许多令人兴奋的新发展。新的领域开辟了，旧领域之间的新联系也被发现了。该奖项为职业生涯早期的研究人员、代表性不足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一个小型环境中进行演讲，以鼓励合作和促进新的研究联系。邀请的演讲者是来自世界各地的知名学者，他们在模式形成和偏微分方程理论方面做出了开创性的贡献。本次研讨会的目的是调查该领域的现状，并规划未来几年偏微分方程和模式形成在理论、数值和应用方面的未来方向。研讨会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深入了解复杂系统的解决方案。通过从这样的尺度中识别小或大的参数体系，奇异摄动理论可以应用于系统地将复杂系统简化为更简单问题的层次。会议的网站是https://www.pims.math.ca/scientific-event/200810-pwntlpipThis。奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，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.