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DG manifolds in Geometry and Physics

几何与物理中的微分分次流形

会议编号:  M240110

时间:  2024-01-22 ~ 2024-01-26

浏览次数:  1512

组织者:   Zhuo Chen, Honglei Lang, Nicolai Reshetikhin, Maosong Xiang, Ping Xu

会议介绍

      会议主题(Theme)

      Dg 流形是具有同调向量场 Q 的分次光滑流形,即函数代数上的 1阶导数。它们也在数学物理文献中被称为 Q 流形,重要的工作例如Schwartz关于Batalin–Vilkovisky量子化几何的开创性贡献, 以及Alexandrov – Kontsevich – Schwarz - Zaboronsky关于主方程和拓扑量子场论几何的工作(称为 AKSZ)。从局部来看,dg 流形可以看作是一个分次的有限维向量空间,其上的形式多项式函数代数是一个微分分次代数(DGA)。众所周知,分次向量空间上的 dg 流形等价于一个带曲率的 L_∞-代数。Dg 流形的应用深入研究发生于代数拓扑学、弦理论、Hamilton力学、Poisson几何和derived几何等多个数学和理论物理领域。

      拟举办的研讨会旨在促进数学家和物理学家以及从事相关领域工作的团体之间的互动。它将致力于交流研究dg流形的不同方法,并确定新的工作方向。随着这些领域的发展,这一点变得越来越迫切。该计划将汇集这些学科的顶尖专家和年轻研究人员,以促进互动,鼓励不同领域之间的交叉融合,并推动当前研究最新成果的传播。

      DG manifolds are graded smooth manifolds equipped with a homological vector field Q, i.e., a degree 1 derivation on the algebra of functions. They are sometimes referred to as Q-manifolds in the mathematical physics literature, for instance, in Schwartz's pioneering work on geometry of Batalin–Vilkovisky quantization, and that of Alexandrov-Kontsevich-Schwarz-Zaboronsky on the geometry of the master equation and topological quantum field theory (known as AKSZ). Locally, a dg manifold can be thought of a graded finite dimensional vector space on which the algebra of formal polynomial functions is a DGA. It is well known that a dg manifold on a graded vector space is equivalent to a curved L_∞-algebras. Dg manifolds emerged from a number of areas of mathematics and theoretical physics such as algebraic topology, string theory, Hamiltonian mechanics, Poisson geometry, and derived geometry.

      The proposed workshop aims to promote interaction between mathematicians and physicists, and groups working in related areas. It will be devoted to gathering together

      these different approaches to DG manifolds as well as identifying new emerging directions. This is becoming more and more urgent as these fields progress. The program will bring together leading experts and young researchers in these subjects to foster interaction, encourage cross-fertilization between different fields, and to promote the dissemination of the most recent results of current research.

      举办意义(Description of the aim)

      我们希望这次研讨会将汇聚从事这些快速发展学科研究的知名数学家、物理学家和年轻研究人员。我们预计将邀请许多博士后和研究生级别的研究人员参加研讨会。我们还期待来自中国、欧洲和美国的大量与会者。此次研讨会将为中国科学家提供一个与国外同行交流思想、开展合作的绝佳机会。我们将通过推动会议的两个组成部分来推进学术研讨的目标:第一项内容是合作研究,特别是高级研究人员与初级研究人员(博士后)之间的合作。第二项内容是国内研究生与其他国内外大学的研究人员进行工作汇报与交流。事实证明,这些面对面的交流对于促进有研究生参与的合作研究非常有意义。

      We expect that the workshop will bring together established mathematicians, physicists and younger researchers working on these rapidly developing subjects. We anticipate inviting many researchers at the postdoctoral and graduate-student levels to the workshop. We also expect a significant number of participants from China, Europe,  and the United States. The workshop will provide an excellent opportunity for Chinese scientists to exchange ideas with their colleagues abroad and to jump-start collaboration.

      We will further strengthen the program by continuing to develop two components that have proved to be extremely fruitful in the past and will, in our opinion, remain as important in the future. The first component is collaborative research, especially collaborations between senior and beginning researchers (postdocs or graduate students). The second component is graduate student consultations with researchers from other universities. These consultations have proved to be extremely useful in facilitating collaborative research involving graduate students.

组织者

Zhuo Chen, Tsinghua University
Honglei Lang, China Agricultural University
Nicolai Reshetikhin, Tsinghua University
Maosong Xiang, Huazhong University of Science and Technology
Ping Xu, Penns State University

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