Development from Poisson Geometry to Noncommutative Differential Geometry via Integrating of Geometry and Physics

通过非交换几何与理论物理的合作研究，我们获得了许多成果，如关于非交换规范理论、p进Iwasawa理论、量子Toda晶格的代数可积性、Bernstein测度、弦论与广义复结构、量子上同调与Frobenius流形、辛拓扑与接触拓扑等方面的建议。研究结果已在国际会议上发表，并在《非交换几何与物理》、《纯数学高级研究》第55期、《数学专著翻译》第237期等刊物上作为专著发表，也有研究者个人发表。

We obtain many results through the cooperation researches between noncommutative geometry and theoretical physics, namely for proposals on noncommutative gauge theory, p-adic Iwasawa theory, algebraic integrability for quantum Toda lattice, Bernstein measure, string theory and generalized complex structure, quantum cohomology and Frobenius manifolds, symplectic topology and contact topology. The results has been presented by the international conferences and published as monographs in 「Noncommutative Geometry and Physics」, 「Advaned Studies in Pure Mathematics 55」, 「Translations of Mathematical Monographs, 237」 and also published by individual researchers.