Geometry of Moduli Spaces and its Application to Infinite Analysis

模空间几何及其在无限分析中的应用

• 批准号: 19340007
• 负责人: UENO Kenji
• 金额: $ 11.65万
• 依托单位: Tokyo Metropolitan University (2010)Yokkaichi University (2009)Kyoto University (2007-2008)
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B)
• 财政年份: 2007
• 资助国家: 日本
• 起止时间: 2007 至 2010
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-19340007/
• 关键词: 代数科学; 共形場理論; モジュラー函手; 位相的場の理論; タイヒミュラー; GNS構成法; ゲージ対称性; 分岐被覆; 剛幾何学; モジュライ空; 無限可積分系; 代数多様体の退化; 重複ファイバー; トロピカル幾何学; 変形パラメータ; 導来圏; モジュライ空間; 接続; ゲージ理論; 代数曲線; 退化; ユニタリ性; 写像類群; 射影的平坦接続; Hitchin接続; p進剛幾何学; ペンローズ変換

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.

从Tsuchiya， Yamada和Ueno I和Joergen E. Andersen构造的规范对称共形场论出发，构造了模函子，从而得到了三流形的拓扑场理论。当规范对称的李代数为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域与Reshetikhin和Turaev构造的拓扑域同构。作为证明的一个推论，我们还证明了0属的尖黎曼曲面的Teichmueller空间上的共形块束携带与KZ连接相容的酉结构。上野还构造了特征为p的域上的曲线族，其中包含多个纤维pD，其中D是任意约数，表现为2属曲线族的退化，p是任意素数。

项目成果

Hecke algebra at root of unity and quantum invariants of three-manifolds

统一根的赫克代数和三流形的量子不变量

• 发表时间: 2010
• 作者: Andersen;J. E. & Ueno;K.;Hiraku Nakajima;J.E. Andersen & K. Ueno;上野健爾
• 通讯作者: 上野健爾

Loop spaces and conformal field theory

环空间和共形场论

• 发表时间: 2009
• 作者: Andersen;J. E. & Ueno;K.;Hiraku Nakajima;J.E. Andersen & K. Ueno;上野健爾;Yuji Shimizu
• 通讯作者: Yuji Shimizu

Conformal field theory and modular functor, in Advances in Algebraic and Combinatrics

共形场论和模函子，代数与组合学进展

• 发表时间: 2008
• 期刊: World Scientific
• 作者: Ueno;K.
• 通讯作者: K.

From Conformal Field Theory to Topological Field Theory

从共形场论到拓扑场论

• 发表时间: 2007
• 作者: Kato;F.;Fumiharu Kato;Tsuyoshi Kato;K. Ueno
• 通讯作者: K. Ueno

An index theory over Casson handles and complexity of smooth structure on K3 surface

卡森柄指数理论与K3表面光滑结构复杂度

• 发表时间: 2009
• 作者: H.Endo;D.Kotschick;M. Morimoto;加藤毅;遠藤 入顕;T. Kato;M. Morimoto;遠藤久顕;M. Morimoto;Tsuyoshi Kato
• 通讯作者: Tsuyoshi Kato