View the Project on GitHub hrzsea/Workshop-on-Algebraic-and-Geometric-Topology
Haibao Duan served as Associate Professor (1991–1995) and Professor (1995–2001) at Peking University, and later as Professor at the Academy of Mathematics and Systems Science, Chinese Academy of Sciences (2001–2021).
Duan established the Multiplication Rules of Schubert Classes and, jointly with Xuzhi Zhao, resolved Schubert’s Problem of Characteristics and Weil’s Problem—central problems of Hilbert’s 15th problem.
Ruizhi Huang, Ping Li, Yang Su
Yi Jiang (Capital Normal University)
Shicheng Wang (Peking University),
Huijun Yang (Henan University),
Xuan Zhao (Beijing Normal University),
Xuezhi Zhao (Capital Normal University)
| Jan. 3, Sat | Jan. 4, Sun | |
|---|---|---|
| 9:30 - 10:15 | Jie Wu | Xuezhi Zhao |
| 10:15 - 10:45 | Tea Break | |
| 10:45 - 11:30 | Zhi Lv | Huijun Yang |
| 11:30-14:30 | Lunch Time | |
| 14:30 - 15:15 | Yi Jiang | |
| 15:15 - 15:45 | Tea Break | |
| 15:45 - 16:30 | Xuan Zhao | |
| 16:30 - 17:00 | Tea Break | |
| 17:00 - 17:45 | Shicheng Wang |
Title: 高连通奇数维流形上的自由圆周群作用
Abstract: 在本报告中，我们关心的主要问题是哪些高连通奇数维流形上存在自由的圆周群作 用。我将介绍关于该问题的一些前期工作, 并着重介绍我和苏阳近期的合作研究进展。
Title: On the calculation of equivariant geometric bordism groups
Abstract: Classifying equivariant smooth closed manifolds up to equivariant bordism is one of fundamental problems in topology. We will mainly focus on the case of equivariant geometric unoriented bordism of 𝐺-actions fixing isolated points where 𝐺 = Z#, which can directly be associated with 𝐺-representation “ theory. In this talk, some new progress, especially for the dimension formulae of equivariant geometric bordism groups, will be introduced by establishing the connections with the universal complexes of DJ theory, GKM theory, matroid theory etc.
Title: 3维流形的伸展指数，躺平映射，机器人堆积
Abstract: 最近有人在计算 3 维流形的伸展指数，用到圆丛上的躺平映射和人形机器人在柄体里的堆积。
Title: Some recent progress in the Chinese school of Topology—in honor of Professor Haibao Duan
Abstract: In this talk, I will present some recent progress of junior Chinese topologists in honor of Professor Haibao Duan, which includes Juxin Yang’s new results on computing homotopy groups, Pengcheng Li’s new progress on cohomotopy theory, and the iterated integral theory on digraphs introduced by Yunpeng Zi and Mengmeng Zhang.
Title: A Bilinear Form for Spin^c Manifolds
Abstract: Let M be a closed oriented spinc manifold of dimension (8n+2) with fundamental class [M], and let ρ2 : H4n(M; Z) → H4n(M; Z/2) denote the mod 2 reduction homomorphism. For any torsion class t ∈ H4n(M; Z), we establish the identity ⟨ρ2(t) · Sq2 ρ2(t), [M]⟩ = ⟨ρ2(t) · Sq2 v4n(M), [M]⟩, where Sq2 is the Steenrod square, v4n(M) is the 4n-th Wu class of M, x · y denotes the cup product of x and y, and ⟨· , ·⟩ denotes the Kronecker product. This result generalizes the work of Landweber and Stong from spin to spinc manifolds. As an application, let β Z/2: H4n+2(M; Z/2) → H4n+3(M; Z) be the Bockstein homomorphism associated to the short exact sequence of coefficients Z×2−−→ Z → Z/2. We deduce that βZ/2(Sq2v4n(M)) = 0, and consequently, Sq3v4n(M) = 0, for any closed oriented spinc manifold M with dim M ≤ 8n+1.
Title: Endomorphisms of the cohomology rings of Lie groups
Abstract: 设𝐺为紧单连通李群，我们有 Boardman 映射𝐵: [𝐺, 𝐺] → 𝐻𝑜𝑚1𝐻∗(𝐺), 𝐻∗(𝐺)4。为了 理解它的像集，我们利用复拓扑 K-理论，及联系 K-理论和奇异同调的Chern特征，给出了 映射𝐵的像的一个逼近。
Title: 自映射不动点与周期点的个数估计
Abstract: 我们介绍，在自映射的不动点与周期点的估计中，基本群与同调群所起的作用。做为一个例子，我们介绍近期的研究结果：基本群为有限循环群的拓扑空间中，周期点估计量的计算。