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

University Of California-Berkeley, Berkeley CA

Investigators

Abstract

Abstract for RTG award DMS-0354321 of Haiman The purpose of this project is to bring together U.C. Berkeley's research faculty in the areas of Representation Theory, Geometry and Combinatorics, along with a group of postdoctoral associates and graduate students, in order to promote collaborative research and the training of young people for future work. The three branches of mathematics addressed by this project are connected in profoundly important ways. In every one of these areas, many of the most exciting current research advances involve the interconnections between them, so that serious study of any of them requires strong knowledge of the other two. A central goal of the project is to provide an environment in which postdocs and graduate students are given the time, opportunity and collaborative atmosphere needed to master a full range of techniques in all three areas. The project will establish two new seminars, to meet throughout the academic year, one concentrating on instruction in specialized topics not usually found in standard courses, and the other a joint seminar on current research. The project will also hold an annual week-long intensive summer workshop, featuring series of 5--6 lectures on advanced topics by distinguished outside visitors and U.C. faculty members, intended for a graduate student to postdoctoral level audience. We will welcome and facilitate participation by young researchers from other institutions. Exciting recent mathematical developments lie at the intersection of representation theory, geometry and combinatorics, with much more to be done in the future. The faculty members forming the core of the research group (Profs. Haiman, Reshetikhin, Borcherds, Frenkel, Givental, Knutson, Serganova and Wolf) have extensive overlapping interests, each using techniques from all three areas in his or her own work. Specific research interests common to multiple members of the group include topics in quantum field theory; representation theory of infinite-dimensional Lie algebras; quantum groups and canonical bases; Gromov-Witten invariants and mirror symmetry; and geometry and combinatorics of Schubert varieties and flag manifolds. The activities of the project are designed to foster research collaboration and above all to equip young mathematicians in training with the broad range of intellectual tools needed to reach the frontiers of research on such topics such as those mentioned.