Workshops in Spectral Methods in Algebra, Geometry, and Topology

美国国家科学基金会（NSF）的这一奖项为美国早期职业数学家提供支持，让他们参加于2022年9月至12月在德国波恩豪斯多夫数学研究所（HIM）举办的暑期学校和两个研讨会。暑期学校被称为“代数、几何和拓扑中的光谱方法”（2022年9月19日至23日），两个研讨会是“等变数学中的光谱方法”（2022年10月24日至28日）和“光谱、三角形和更高结构”（2022年12月5日至9日）。这些事件与“代数、几何和拓扑学中的谱方法”三个月课程有关，该课程建立在对代数拓扑学、代数几何、表示理论和代数等数学领域的各个领域的观察基础之上，这些领域在历史上被认为是分开的和不同的，现在实际上是通过重叠的问题、共同的目标、相关的基础问题和类似的技术而结合在一起的。该基金将为学生、博士后研究人员和早期职业教师提供培训和职业发展。该计划将涵盖从代数，几何和代数拓扑主题的多样化混合物，围绕研究和应用谱技术和张量三角结构的主题为中心。这包括传统的主题，如代数中的分类问题或色同伦理论中的计算，但也包括动机同伦理论中的新兴主题以及无穷范畴与表示理论之间的相互作用。关于研讨会和项目的更多信息可以在https://www.him.uni-bonn.de/programs/future-programs/future-trimester-programs/spectral-methods/description/This上找到，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 NSF award provides support for early career U.S. based mathematicians to attend a summer school and two workshops to be held in the period from September to December 2022 at the Hausdorff Research Institute for Mathematics (HIM), Bonn, Germany. The summer school is called “Spectral Methods in Algebra, Geometry, and Topology” (September 19-23, 2022), and the two workshops are “Spectral Methods in Equivariant Mathematics” (October 24-28, 2022) and “Spectra, Triangles, and Higher Structures” (December 5-9, 2022). These events are associated with the trimester program "Spectral Methods in Algebra, Geometry, and Topology", founded on the observation that various areas of the mathematical fields of algebraic topology, algebraic geometry, representation theory, and algebra that have been historically regarded as separate and distinct are now in fact united by overlapping problems, common goals, related foundational questions, and similar techniques. The grant would provide training and career development for students, postdoctoral researchers, and early career faculty. The program will cover a diverse mixture of topics from algebra, geometry, and algebraic topology, centered around the theme of studying and applying spectral techniques and tensor-triangular structure. This includes traditional topics, such as classification problems in algebra or computations in chromatic homotopy theory, but also emerging topics in motivic homotopy theory and the interplay between infinity categories and representation theory. Further information about workshops and the program in general can be found at https://www.him.uni-bonn.de/programs/future-programs/future-trimester-programs/spectral-methods/description/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.