北京雁栖湖应用数学研究院 北京雁栖湖应用数学研究院

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关于我们
院长致辞
理事会
协作机构
参观来访
人员
管理层
科研人员
博士后
来访学者
行政团队
学术研究
研究团队
公开课
讨论班
招生招聘
教研人员
博士后
学生
会议
学术会议
工作坊
论坛
学院生活
住宿
交通
配套设施
周边旅游
新闻
新闻动态
通知公告
资料下载
清华大学 "求真书院"
清华大学丘成桐数学科学中心
清华三亚国际数学论坛
上海数学与交叉学科研究院
BIMSA > Dg manifolds and higher structures \(ICBS\)
Dg manifolds and higher structures
ZOOM: 815 762 8413
PASSWORD: BIMSA

DG manifolds are a useful geometric notion that unifies many important structures such as homotopy Lie algebras, foliations, and complex manifolds. In particular, the Todd class of DG manifolds extends both the Todd class of a complex manifold and the Duflo element in Lie theory. DG manifolds also play an important role in the study of the differential geometry of singular spaces. In this series of lectures, we will introduce DG manifolds and discuss various applications in geometry and higher structures. We will describe noncommutative calculi for DG manifolds. In particular, we will prove a Duflo-Kontsevich type theorem for DG manifolds. The classical Duflo theorem in Lie theory and the Kontsevich theorem regarding the Hochschild cohomology of complex manifolds can both be derived as special cases of this Duflo-Kontsevich type theorem for DG manifolds. We will also discuss its application in derived differential geometry, which deals with singularities arising from zero loci or intersections of submanifolds. This is mainly based on joint work with Kai Behrend, Ruggero Bandiera, Zhuo Chen, Hsuan-Yi Liao, Rajan Mehta, Seokbong Seol, Mathieu Stienon, and Maosong Xiang.
Professor Lars Aake Andersson
讲师
徐平
日期
2025年01月22日 至 02月17日
位置
Weekday Time Venue Online ID Password
周一,周三,周五 00:00 - 00:00 - - -
修课要求
Lie algebra, Differential Geometry
参考资料
[1] Mathieu Stiénon, Luca Vitagliano, and Ping Xu, A_∞ algebras from Lie pairs, arXiv:2210.16769.
[2] Kai Behrend, Hsuan-Yi Liao, and Ping Xu, On the structure of étale fibrations of L_∞-bundles, arXiv:2307.08179.
[3] Kai Behrend, Hsuan-Yi Liao, and Ping Xu, Differential graded manifolds of finite positive amplitude, Int. Math. Res. Not. IMRN. 2024, no. 8, 7160–7200. [4] Kai Behrend, Matt Peddie, and Ping Xu, Quantization of (-1)-shifted derived Poisson manifolds, Comm. Math. Phys. 402 (2023), 2301–2338.
[5] Zhuo Chen, Maosong Xiang, and Ping Xu, Hochschild cohomology of dg manifolds associated to integrable distributions, Comm. Math. Phys. 375 (2022), 647–684.
[6] Seokbong Seol, Mathieu Stiénon, and Ping Xu, Dg manifolds, formal exponential maps and homotopy Lie algebras, Comm. Math. Phys. 391 (2022), 33–76. [7] Mathieu Stiénon and Ping Xu, Atiyah classes and Kontsevich-Duflo type theorem for dg manifolds, Banach Center Publications 123 (2021), 63–110.
[8] Ruggero Bandiera, Zhuo Chen, Mathieu Stiénon, and Ping Xu, Shifted Derived Poisson Manifolds Associated with Lie Pairs, Comm. Math. Phys. 375 (2020), 1717–1760.
[9] Hsuan-Yi Liao, Mathieu Stiénon, and Ping Xu. Formality and Kontsevich-Duflo type theorems for Lie pairs. Adv. Math., 352:406–482, 2019.
[10] Zhuo Chen, Maosong Xiang, and Ping Xu, Atiyah and Todd classes arising from integrable distributions, J. Geom. Phys. 136 (2019), 52–67.
[11] Hsuan-Yi Liao, Mathieu Stiénon, and Ping Xu, Formality theorem for differential graded manifolds, C. R. Math. Acad. Sci. Paris 356 (2018), 27–43.
[12] Rajan Amit Mehta, Mathieu Stiénon, and Ping Xu, The Atiyah class of a dg-vector bundle, C. R. Math. Acad. Sci. Paris 353 (2015), no. 4, 357–362.
听众
Graduate , Researcher
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语言
中文 , 英文
北京雁栖湖应用数学研究院
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No. 544, Hefangkou Village Huaibei Town, Huairou District Beijing 101408

北京市怀柔区 河防口村544号
北京雁栖湖应用数学研究院 101408

Tel. 010-60661855
Email. administration@bimsa.cn

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