Hyperplane Arrangements and Singularities

该奖项将为2019年12月2日至6日在东京大学（日本东京）举行的“超平面布置和奇点”国际会议的美国参与者提供部分支持。这次会议将以研究为导向，旨在传播最近的发展，但也将包括研究生可以接受的介绍性讲座。此外，还将举行讨论会议，以便更好地加强各研究小组之间的联系，并为初级研究人员和研究生提供可访问性。会议将集中讨论超平面排列和奇异空间研究的最新进展，以及在代数和几何拓扑、代数几何、群论和组合学中的应用。讨论的主题将包括但不限于以下领域，所有这些领域在过去几年中都有重要的新发展：超平面排列的拓扑和几何，Milnor纤振，上同调跳跃轨迹，光滑子流形的排列，非孤立奇点的几何和拓扑，反常束和混合Hodge模块。这些主题涉及从纯数学到更多应用领域的广泛研究领域，因此会议参与者将反映广泛的数学学科。会议的一个重要目标是促进超平面排列、奇点理论和相关领域之间的信息传播和交流。通过分享各自的技术和观点，与会者有望形成新的合作，并在这些领域的会议点取得进展。有关会议的更多详细信息可在：https://sites.google.com/umich.edu/hyper-jarcs/This该奖项反映了NSF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，被认为值得支持。

This award provides partial support for US-based participants in the international conference "Hyperplane Arrangements and Singularities" to be held at the University of Tokyo (in Tokyo, Japan), during the period December 2-6, 2019. The conference will be research-oriented, intended to disseminate recent developments, but it will also include introductory lectures at a level accessible to graduate students. Additionally, there will be discussion sessions, so as to better strengthen connections among the various research groups represented and to provide accessibility for junior researchers and graduate students. The conference will focus around recent developments in the study of hyperplane arrangements and singular spaces, with applications to algebraic and geometric topology, algebraic geometry, group theory, and combinatorics. The topics to be discussed will include, but will not be limited to, the following areas, all of which have seen important new developments in the past several years: Topology and geometry of hyperplane arrangements, Milnor fibrations, Cohomology jump loci, Arrangements of smooth submanifolds, Geometry and topology of non-isolated singularities, Perverse sheaves, and mixed Hodge modules. These topics intersect a broad range of research endeavors in fields ranging from pure mathematics to more applied areas, and thus conference participants will reflect a broad cross-section of mathematical disciplines. An important objective of the conference is to promote dissemination of information and cross-fertilization between hyperplane arrangements, singularity theory, and related fields. By sharing their respective techniques and perspectives, participants are expected to form new collaborations and make advances at the meeting points of those fields. More details about the conference are available at: https://sites.google.com/umich.edu/hyper-jarcs/This 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.