Conference: Geometric representation theory and moduli spaces

该奖项支持参加为期三天的研讨会，讨论几何表示理论和模空间的最新进展，该研讨会将于2023年10月20日至22日在北卡罗来纳大学教堂山分校举行。研讨会将集中讨论几何表示理论（对称理论）和代数几何中的模空间（多项式方程的零点研究）的最新进展。研讨会将在三天内举行10至12场会谈，以便有足够的时间进行额外的讨论。鼓励研究生和博士后参与。参数化几何对象的空间被称为模空间，是代数几何和表示理论研究的核心。模空间理论最近有了许多发展，也许最重要的是强调一般的堆栈理论结果，而不是传统的基于几何不变理论的模空间理论方法。曲线上束的模堆与共形块理论和几何朗兰兹规划密切相关。最近的发展是一种扭曲的共形块理论。关于几何朗兰兹程序的最新发展，已经有了一系列的文章，它与算术的联系也越来越明显。仿射标志变体（包括仿射格拉斯曼和半无限标志流形）与仿射李代数、量子群和代数群的表示理论有关。研讨会将集中讨论这些主题，并汇集这些领域的专家，重点是年轻数学家的工作。研讨会的网站是https://tarheels.live/grtm/.This，该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 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.