Conference: Geometric representation theory and moduli spaces

会议：几何表示理论和模空间

• 批准号: 2328483
• 负责人: Jiuzu Hong
• 金额: $ 2.99万
• 依托单位: University of North Carolina at Chapel Hill
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2023
• 资助国家: 美国
• 起止时间: 2023-09-01 至 2024-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2328483&HistoricalAwards=false
• 关键词: Conference; Geometric; representation; theory; moduli

This award supports participation in a three-day workshop on recent advances in geometric representation theory and moduli spaces to be held October 20-22, 2023 at the University of North Carolina, Chapel Hill. The workshop will focus on recent advances in geometric representation theory (the theory of symmetries) and moduli spaces in algebraic geometry (the study of zeroes of polynomial equations). The workshop will consist of ten to twelve talks spread over three days, allowing plenty of time for additional discussions. Participation of graduate students and postdocs will be encouraged. Spaces that parameterize geometric objects are known as moduli spaces, and are central to the study of algebraic geometry and representation theory. There have been many recent developments on moduli space theory, perhaps the most significant is the emphasis of general stack theoretic results over traditional Geometric Invariant Theory based approaches to moduli space theory. Moduli stacks of bundles over curves are closely related to the theory of conformal blocks and the geometric Langlands program. A recent development has been a twisted theory of conformal blocks. There have been a series on recent developments in the geometric Langlands program, and connections with arithmetic are getting more apparent. Affine flag varieties (including affine Grassmannians and semi-infinite flag manifolds) are known to be related to representation theory of affine Lie algebras, quantum groups, and algebraic groups. The workshop will focus on these topics, and bring together experts in these areas, with an emphasis on the work of younger mathematicians. The workshop website is https://tarheels.live/grtm/.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.

该奖项支持参加将于 2023 年 10 月 20 日至 22 日在北卡罗来纳大学教堂山分校举行的为期三天的研讨会，主题是几何表示理论和模空间的最新进展。研讨会将重点关注几何表示理论（对称理论）和代数几何中的模空间（多项式方程零点的研究）的最新进展。该研讨会将包括为期三天的十到十二场演讲，以便有充足的时间进行其他讨论。将鼓励研究生和博士后的参与。 参数化几何对象的空间称为模空间，是代数几何和表示论研究的核心。模空间理论最近有许多发展，也许最重要的是一般堆栈理论结果相对于传统的基于几何不变量理论的模空间理论方法的强调。曲线上束的模堆叠与共角块理论和几何朗兰兹纲领密切相关。最近的发展是共形块的扭曲理论。几何朗兰兹纲领的最新发展已经出现了一系列，并且与算术的联系也越来越明显。仿射旗簇（包括仿射格拉斯曼流形和半无限旗流形）已知与仿射李代数、量子群和代数群的表示论有关。该研讨会将重点讨论这些主题，并汇集这些领域的专家，重点关注年轻数学家的工作。研讨会网站是 https://tarheels.live/grtm/。该奖项反映了 NSF 的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。