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

海曼的RTG奖DMS-0354321摘要本项目的目的是将U.C.伯克利分校的研究教师在表示理论，几何和组合数学领域，沿着一组博士后助理和研究生，以促进合作研究和年轻人的培训，为未来的工作。 这个项目所涉及的数学的三个分支是以非常重要的方式联系在一起的。 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它们之间的相互联系，因此，要认真研究其中任何一个领域，都需要对其他两个领域有很强的了解。 该项目的一个中心目标是提供一个环境，在这个环境中，博士后和研究生获得掌握所有三个领域的全方位技术所需的时间、机会和合作气氛。 该项目设立了两个新的研讨会，在整个学年中举行，一个集中在标准课程中通常找不到的专业主题的教学，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，由杰出的外部访问者和U.C.就高级主题举办5- 6场系列讲座。教员，拟面向研究生到博士后层次听众。 我们将欢迎并促进来自其他机构的年轻研究人员的参与。令人兴奋的最新数学发展在于表示论，几何学和组合学的交叉，未来还有更多的工作要做。 形成研究小组核心的教师（教授）。Haiman、Reshetikhin、Borcherds、Frenkel、Givental、Knutson、Serganova和Wolf）都有广泛的绘画兴趣，每个人都在自己的作品中使用所有三个领域的技术。 小组多名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理论;量子群和正则基; Gromov-Witten不变量和镜像对称;以及舒伯特簇和旗流形的几何学和组合学。该项目的活动旨在促进研究合作，最重要的是使年轻的数学家在培训中掌握广泛的知识工具需要达到前沿的研究等主题，如那些提到。

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.