Geometry of Moduli Spaces and its Application to Infinite Analysis

从Tsuhiya，Yamada和Ueno I和Joergen E.Andersen构造的规范对称的共形场论出发，构造了模函子，从而得到了三种流形的拓扑场论。当规范对称的李代数是sl(n，C)时，我们利用Hecke代数表示的GNS构造证明了我们的拓扑场与Reshetikhin和Turaev构造的拓扑场同构。作为证明的推论，我们还证明了亏格为0的点Riemann曲面的Teichmueller空间上的共形块丛具有与KZ联络相容的酉结构.Ueno还构造了特征域p上的一族曲线族，其中D是出现退化的亏格2曲线族的任意因子，p是任意素数.

From conformal field theory with gauge symmetry constructed by Tsuchiya, Yamada and Ueno I and Joergen E. Andersen constructed modular functors so that we had topological filed theory for three manifolds. When the Lie algebra for gauge symmetry is sl(n, C) we proved that our topological field is isomorphic to the one constructed by Reshetikhin and Turaev by using GNS construction of representations of Hecke algebra. As a corollary to our proof we could also prove that conformal block bundles on the Teichmueller space of pointed Riemann surfaces of genus 0 carry unitary structure compatible with KZ connections.Ueno also constructed a family of curves over a field of characteristic p, which contain multiple fiber pD where D is any divisor appearing a degeneration of a family of curves of genus 2 and p is any prime number.