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。
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)
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.
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