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本报告从应用的视角对代数拓扑研究领域给予概述性介绍,报告将分三个部分。在第一部分,我们从单纯复形三角剖分入手,介绍代数拓扑在数据科学、复杂网络等研究领域应用的动态。在第二部分,我们将根据代数拓扑的基本问题(有限复形的同伦分类)展开讨论,了解代数拓扑的学科内涵,以及同伦群对代数拓扑的重要性。在报告的最后部分,我们将概述同伦群的一些研究成果。
In this talk, I will introduce the methods for calculating the unstable homotopy groups of finite CW-complexes which builds on works of the relative James construction initiated by B. Gray in 1973 and...
The goal of this talk is to compare the local Fontaine–Messing period map and the Lazard type period map [CN17, Thm. 4.16]. Since the notation for the general case is too heavy, you may focus on d = 1...
In these series of talks, we will focus on the study of the Iitaka conjecture, which predicts the subadditivity of Kodaira dimensions for any algebraic fiber space. In the first part, we recall some b...
Modern algebraic topology sees equivariance arising in unexpected context. Equivariant cohomology carries rich structures but is much harder to compute. In 2009, Hill, Hopkins, and Ravenel solved the ...
As one of most important objects in mathematics, ‘manifold’ has provided us more and more insights and benefits. In the past half century, more and more different areas in mathematics have been inters...

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