Midwest Workshop on Schubert Calculus

该奖项为舒伯特微积分研讨会的参与者提供旅行和住宿支持，将于2018年5月9日至12日在俄亥俄州哥伦布市的俄亥俄州州立大学举行。 会议的主题起源于世纪的枚举几何，当时数学家计算满足各种条件的几何图形的数量。 这门学科后来发展成为交叉理论的试验场，而交叉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，提出关于舒伯特微积分的各种观点。舒伯特微积分的很大一部分涉及格拉斯曼流形和旗流形的上同调环，以及它们的推广。该主题与组合数学，表示论和代数几何有着深刻的联系，并且在过去的15年中，舒伯特微积分的技术取得了显着的发展。 一个指导性的问题是找到组合公式的乘法舒伯特类的旗帜品种;几个新的情况下，这个问题得到了解决。 新的研究将我们对舒伯特演算的理解扩展到了无限维仿射（和卡茨-穆迪）旗的种类，同时加深了与表示论的联系。 本次会议的主要目标包括分享新成果，并向新一代学生介绍该领域的技术，应用和开放问题。关于研讨会的更多细节可在www.example.com上获得https://people.math.osu.edu/anderson.2804/schub2018.html.This奖项反映了NSF的法定使命，并被认为值得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来支持。

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.