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

这个项目的目的是将加州大学伯克利分校在表示理论、几何和组合学领域的研究人员，以及一批博士后和研究生聚集在一起，以促进合作研究，并为未来的工作培养年轻人。这个项目所涉及的三个数学分支在重要的方面有着深刻的联系。在这些领域中的每一个领域，当前许多最令人兴奋的研究进展都涉及到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。该项目的一个中心目标是为博士后和研究生提供一个环境，让他们有时间、有机会和协作的氛围来掌握这三个领域的全部技术。该项目将建立两个新的研讨会，在整个学年举行，一个集中在标准课程中通常没有的专业主题的教学上，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暑期专题研讨会，由杰出的外部访客和加州大学教职员工就高级主题进行5- 6次系列讲座，面向研究生至博士后水平的听众。我们欢迎并鼓励其他机构的青年研究人员参与。最近令人兴奋的数学发展是在表示理论、几何和组合学的交叉领域，未来还有更多的工作要做。组成研究小组核心的教员（教授）。Haiman, Reshetikhin, Borcherds, Frenkel,Givental, Knutson， Serganova和Wolf)有广泛的重叠兴趣，每个人在他或她自己的工作中都使用了这三个领域的技术。小组成员共同的特定研究兴趣包括量子场论主题；无限维李代数的表示理论；量子群与正则基；Gromov-Witten不变量与镜像对称性舒伯特变体和面形的几何和组合学。该项目的活动旨在促进研究合作，最重要的是为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。

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.