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，将于2023年10月20日至22日在查佩尔山的北卡罗来纳州大学举行。讲习班将侧重于几何表示理论（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。研讨会将在三天内举行10至12次会谈，以便有足够的时间进行额外的讨论。研究生和博士后的参与将受到鼓励。 参数化几何对象的空间被称为模空间，并且是代数几何和表示论研究的中心。模空间理论最近有了许多发展，也许最重要的是强调一般堆栈理论的结果，而不是传统的基于几何不变理论的方法来模空间理论。曲线上丛的模叠加与共形块理论和几何Langlands程序密切相关。最近的发展是共形块体的扭曲理论。几何朗兰兹纲领的最新发展已经有了一系列的论述，它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）与仿射李代数、量子群和代数群的表示论有关。讲习班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。研讨会网站是https://tarheels.live/grtm/.This奖反映了NSF的法定使命，并已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的支持。

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.