Quantum Cohomology, Quantum K-theory, Frobenius Manifolds and Integrable Systems

AbstractAward：DMS-0305895主要研究者：李元平本项目的主要重点是研究Gromov-维滕理论及其与其他数学领域的关系和应用，包括枚举几何，可积系统，K-理论和表示理论。重点放在这些领域交叉的一些关键问题上。Gromov-维滕理论是在20世纪90年代初数学和物理的相互作用下诞生的。在数学方面，它始于格罗莫夫发明的一种新方法来产生辛不变量。在物理方面，是维滕对弦理论的研究。虽然历史相对较短，格罗莫夫-维滕理论是一个主要的研究领域。 这不仅是由于它对老问题的强大解决方案，也是由于它的跨学科性质，来自数学和弦理论的几个领域的持续投入。本计画拟从不同的角度探讨格罗莫夫-维滕理论，并探讨其在其他学科领域的应用。

AbstractAward: DMS-0305895Principal Investigator: Yuan-Pin LeeThe main focus of this project is to study Gromov--Witten theoryand its relations and applications to other areas of mathematics,including enumerative geometry, integrable systems, K-theory, andrepresentation theory. The emphasis is placed on some keyproblems where these areas intersect. These problems include thestudy of higher spin curves, quantum K-theory, enumerativegeometry, and Frobenius manifolds.Gromov--Witten theory was born in early 1990's through theinteraction of mathematics and physics. On the mathematical side,it starts with Gromov's invention of a new way to producesymplectic invariants. On the physical side, it was Witten'sstudy of string theory. Although of a relatively short history,Gromov--Witten theory is a major active field of research. Thisis due not only to its powerful solutions to old problems, butalso to its interdisciplinary nature, with continuing inputs fromseveral fields of mathematics and string theory. This projectproposes to investigate Gromov--Witten theory through variousperspectives and to search for its applications in other subjectareas.