Midwest Workshop on Schubert Calculus

该奖项为参加2018年5月9日至12日在俄亥俄州哥伦布市俄亥俄州立大学举行的舒伯特微积分研讨会的参与者提供旅行和住宿支持。会议的主题起源于19世纪的枚举几何，当时数学家计算满足各种条件的几何图形的数量。这门学科发展成为交叉点理论的试验场，交叉点理论现在是现代数学的基石。本次研讨会将汇集来自不同背景的研究人员和学生，就舒伯特微积分的主题提出不同的观点。舒伯特微积分的很大一部分是关于格拉斯曼子和旗流形的上同环，以及它们的推广。这门学科与组合学、表示理论和代数几何有着深刻的联系，在过去的15年里，舒伯特微积分的技术有了显著的发展。一个指导问题是寻找标志变量中舒伯特类乘法的组合公式；这个问题的几个新案例得到了解决。新的研究将我们对舒伯特微积分的理解扩展到无限维仿射（和Kac-Moody）标志变体，同时加深了与表征理论的联系。本次会议的主要目标包括分享新的成果，并向新一代学生介绍该领域的技术、应用和开放问题。有关研讨会的更多细节可在https://people.math.osu.edu/anderson.2804/schub2018.html.This上获得。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，被认为值得支持。

This award provides travel and lodging support for participants in a Workshop on Schubert Calculus, to take place May 9-12, 2018, at the Ohio State University in Columbus, Ohio. The topic of the conference has its origins in 19th century enumerative geometry, when mathematicians computed numbers of geometric figures satisfying various conditions. The subject grew into a testing ground for Intersection Theory, which is now a cornerstone of modern mathematics. This workshop will bring together researchers and students coming from different backgrounds, to present various points of view on the subject of Schubert Calculus.A large part of Schubert Calculus concerns the cohomology rings of Grassmannians and flag manifolds, as well as their generalizations. The subject has deep connections to combinatorics, representation theory, and algebraic geometry, and the last 15 years have seen remarkable developments in the techniques of Schubert Calculus. A guiding problem is to find combinatorial formulas for the multiplication of Schubert classes in flag varieties; several new cases of this problem were solved. New research has extended our understanding of Schubert calculus to the infinite-dimensional affine (and Kac-Moody) flag varieties, simultaneously deepening the connection with representation theory. Major goals of this conference include sharing new results and introducing a new generation of students to the techniques, applications, and open problems in the field. More details about the workshop are available at https://people.math.osu.edu/anderson.2804/schub2018.html.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.