EMSW21-RTG: Research Training Group in Interactions of Representation Theory, Geometry and Combinatorics

EMSW21-RTG：表示论、几何和组合学相互作用研究培训小组

• 批准号: 0354321
• 负责人: Mark Haiman
• 金额: $ 149.95万
• 依托单位: University of California-Berkeley
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2004
• 资助国家: 美国
• 起止时间: 2004-07-15 至 2011-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0354321&HistoricalAwards=false
• 关键词: EMSW21; RTG; Research; Training; Group

Abstract for RTG award DMS-0354321 of HaimanThe purpose of this project is to bring together U.C. Berkeley'sresearch faculty in the areas of Representation Theory, Geometry andCombinatorics, along with a group of postdoctoral associates andgraduate students, in order to promote collaborative research and thetraining of young people for future work. The three branches ofmathematics addressed by this project are connected in profoundlyimportant ways. In every one of these areas, many of the mostexciting current research advances involve the interconnectionsbetween them, so that serious study of any of them requires strongknowledge of the other two. A central goal of the project is toprovide an environment in which postdocs and graduate students aregiven the time, opportunity and collaborative atmosphere needed tomaster a full range of techniques in all three areas. The projectwill establish two new seminars, to meet throughout the academic year,one concentrating on instruction in specialized topics not usuallyfound in standard courses, and the other a joint seminar on currentresearch. The project will also hold an annual week-long intensivesummer workshop, featuring series of 5--6 lectures on advanced topicsby distinguished outside visitors and U.C. faculty members, intendedfor a graduate student to postdoctoral level audience. We willwelcome and facilitate participation by young researchers from otherinstitutions.Exciting recent mathematical developments lie at the intersection ofrepresentation theory, geometry and combinatorics, with much more tobe done in the future. The faculty members forming the core of theresearch group (Profs. Haiman, Reshetikhin, Borcherds, Frenkel,Givental, Knutson, Serganova and Wolf) have extensive overlappinginterests, each using techniques from all three areas in his or herown work. Specific research interests common to multiple members ofthe group include topics in quantum field theory; representationtheory of infinite-dimensional Lie algebras; quantum groups andcanonical bases; Gromov-Witten invariants and mirror symmetry; andgeometry and combinatorics of Schubert varieties and flag manifolds.The activities of the project are designed to foster researchcollaboration and above all to equip young mathematicians in trainingwith the broad range of intellectual tools needed to reach thefrontiers of research on such topics such as those mentioned.

海曼 RTG 奖 DMS-0354321 摘要该项目的目的是将 U.C.伯克利大学在表示论、几何和组合学领域的研究人员，以及一组博士后和研究生，旨在促进合作研究和对年轻人未来工作的培训。 该项目涉及的数学的三个分支以极其重要的方式相互联系。 在这些领域的每一个领域，当前许多最令人兴奋的研究进展都涉及它们之间的相互联系，因此对其中任何一个领域的认真研究都需要对其他两个领域有深入的了解。 该项目的中心目标是提供一个环境，为博士后和研究生提供掌握所有三个领域的全方位技术所需的时间、机会和协作氛围。 该项目将设立两个新的研讨会，在整个学年举行，一个集中于标准课程中不常见的专业主题的教学，另一个是关于当前研究的联合研讨会。 该项目还将每年举办为期一周的夏季强化研讨会，其中包括由杰出的外部访客和加州大学伯克利分校举办的关于高级主题的 5--6 场系列讲座。教职人员，面向研究生到博士后水平的观众。 我们将欢迎并促进来自其他机构的年轻研究人员的参与。最近令人兴奋的数学发展在于表示论、几何学和组合学的交叉点，未来还有更多工作要做。 构成研究小组核心的教职人员（Haiman、Reshetikhin、Borcherds、Frenkel、Givental、Knutson、Serganova 和 Wolf 教授）有着广泛的重叠兴趣，每个人都在自己的工作中使用了所有三个领域的技术。 该小组多个成员共同的具体研究兴趣包括量子场论主题；无限维李代数的表示论；量子群和规范基； Gromov-Witten 不变量和镜像对称；该项目的活动旨在促进研究合作，最重要的是为接受培训的年轻数学家提供广泛的智力工具，以达到上述主题的研究前沿。