Workshop on Symmetric Spaces, Their Generalizations, and Special Functions

该奖项将支持美国数学家，特别是研究生和其他早期职业研究人员参加即将于2020年5月14日至5月17日在渥太华大学举行的关于对称空间，其推广和特殊函数的国际研讨会和会议。研讨会的目标是促进与表示理论和代数组合有关的几个领域的研究人员的国际合作，包括李超代数、量化包络代数和代数组合。这项活动的基本原理是，最近的进展表明上述领域之间存在新的联系，其目标是调查由这些进展产生的开放性问题，并研究解决这些问题的新策略。讲习班还将以三门小型课程的形式包含大量的教学内容，这些课程将涵盖其重点领域的背景和最近令人兴奋的进展。这些迷你课程将对非专家开放，包括研究生和初级研究人员。最近的研究结果暗示了量子化对称空间和插值多项式之间的一种新的、有前途的联系。在上述领域的交叉点上，一个自然而重要的问题是以统一的方式定义和研究Capelli算子的q-变形的性质。此外，对于与bc型根相关的李超代数的（非量子化）对称空间，不变微分算子与插值多项式之间的类似关系尚未建立。我们希望这次会议能为专家们就这些跨学科问题交换意见提供一个环境。研讨会的网站是http://www.fields.utoronto.ca/activities/19-20/symmetric-spaces.This，该奖项反映了NSF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 will support participation by U.S.-based mathematicians, especially graduate students and other early-career researchers, in the upcoming international workshop and conference on Symmetric Spaces, Their Generalizations, and Special Functions, which will be held at the University of Ottawa from May 14 until May 17, 2020. The goal of the workshop is to foster the international collaboration of researchers in several areas connected to representation theory and algebraic combinatorics, including Lie superalgebras, quantized enveloping algebras, and algebraic combinatorics. The rationale for this activity is recent advancements that indicate new links between the aforementioned areas, and its goal is to investigate open problems that are spawned by these advancements and examine new strategies for solving them. The workshop will also have a substantial pedagogical component in the form of three mini-courses that will cover background and recent exciting progress in its focus areas. These mini-courses will be accessible for non-experts, including graduate students and junior researchers.Recent results hint at a new and promising connection between quantized symmetric spaces and interpolation polynomials. A natural and important problem that lies at the intersection of the aforementioned areas is to define and investigate the properties of q-deformations of Capelli operators in a uniform way. In addition, for (non-quantized) symmetric spaces of Lie superalgebras that are associated to BC-type root systems, an analogous relation between invariant differential operators and interpolation polynomials is yet to be established. We hope that the conference will provide an environment for experts to exchange their ideas for these interdisciplinary problems. The website for the workshop is http://www.fields.utoronto.ca/activities/19-20/symmetric-spaces.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.