Workshop on Representation Theory, Combinatorics, and Geometry

表示论、组合学和几何研讨会

• 批准号: 1839534
• 负责人: Leonid Petrov
• 金额: $ 1.5万
• 依托单位: University of Virginia Main Campus
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2018
• 资助国家: 美国
• 起止时间: 2018-09-01 至 2019-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1839534&HistoricalAwards=false
• 关键词: Workshop; Representation; Theory; Combinatorics; Geometry

The award will support participation of primarily early-career researchers in the Workshop on Representation Theory, Combinatorics, and Geometry, and the Distinguished Lecture Series "Virginia Mathematics Lectures" which will take place on October 19-21 and 22-24, 2019, respectively, at the University of Virginia. The workshop will consist of talks by leading experts on connections between quantum groups, quiver varieties, and canonical bases, as well as short talks by early-career participants. Participants will be exposed to exciting new directions in representation theory, geometry, and combinatorics, and will gain fodder for future projects. The diversity of mathematical researchers and areas represented at the workshop will foster new collaborations and new research projects.In more detail, Springer resolutions of nilpotent cones of semisimple Lie algebras provide a fertile ground for geometric representation theory. Maulik and Okounkov introduced a notion of stable envelope in the framework of symplectic resolutions (with Springer resolutions and quiver varieties as most important examples), and used it to provide a first geometric construction of R-matrices and a different construction of Yangians using the equivariant cohomology in a wide context. Their construction is intimately related to quantum cohomology of the symplectic resolutions. These subjects have played an important role in several areas of modern mathematics. Some of the most recent research directions (such as i-quiver varieties) have emerged only in the last year or so, and are currently aligning with Maulik-Okounkov's theory. The events at University of Virginia will provide a timely platform for exchange of emerging new ideas that will facilitate their further development. The website of the workshop is http://math.virginia.edu/ims/workshop-fall-2018/.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.

该奖项将支持主要是职业早期研究人员参加表示理论、组合学和几何研讨会，以及分别于2019年10月19-21日和22-24日在弗吉尼亚大学举行的杰出系列讲座“弗吉尼亚数学讲座”。研讨会将由主要专家就量子群、箭筒变种和正则基之间的联系进行演讲，以及职业生涯早期参与者的简短演讲。参与者将接触到表示理论、几何和组合学方面令人兴奋的新方向，并将为未来的项目提供素材。研讨会上代表的数学研究人员和领域的多样性将促进新的合作和新的研究项目。更详细地说，半单李代数的幂零锥的Springer分解为几何表示理论提供了肥沃的土壤。Maulik和Okounkov在辛分解的框架下引入了稳定包络的概念(其中Springer分解和箭图簇是最重要的例子)，并利用它给出了R-矩阵的第一个几何构造和在更广泛的背景下利用等变上同调的不同的Yangans的构造。它们的构造与辛解的量子上同调密切相关。这些学科在现代数学的几个领域发挥了重要作用。最近的一些研究方向(如i-quiver品种)在过去一年左右才出现，目前与毛利克-奥孔科夫的理论一致。弗吉尼亚大学的活动将为交流新出现的新思想提供一个及时的平台，这将促进它们的进一步发展。研讨会的网站是http://math.virginia.edu/ims/workshop-fall-2018/.This奖，反映了国家科学基金会的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。