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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：应用视角下的代数拓扑
应用视角 代数拓扑 复形三角剖分
2023/4/13
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。
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Unstable homotopy groups of indecomposable A_3^2-complexes
不可分解 A_3^2 配合物 不稳定 同伦群
2023/4/14
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...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Stable commutator length and linear programming
换向器长度 线性规划 曲面 拓扑优化
2023/4/18
Several topological optimization problems involving surfaces can be turned into linear programming problems. In the case of stable commutator length, this was first discovered by Danny Calegari in the...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Topological optimization and the stable commutator length
拓扑优化 稳定换向器 长度
2023/4/19
It is a relatively recent discovery in geometric topology that optimization problems of certain topological complexity are connected to important geometric and topological information. One example is ...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Topology optimization via implicit neural representations
隐式 神经表示 拓扑优化
2023/4/24
Along with the rapid development of artificial intelligence (AI) technology, scientific research enters a new era of AI. Topology optimization (TO) and AI technology are recently showing a growing tre...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Periodic Phenomena in homotopy theory
同伦理论 周期现象
2023/4/25
Chromatic homotopy theory uses the algebraic geometry of smooth 1-parameter formal groups to separate stable homotopy theory into periodic layers. The 1st layer recovers the image of Adams’ J homomorp...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Syntomic cohomology and (φ, Γ)-modules
同调 上同调 （φ，Γ）模块
2023/4/26
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...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Suspension Homotopy of 4-manifolds And the Second 2-local Cohomotopy Sets
4-流形 悬浮同伦 第二个 2-局部 同伦集合
2023/4/28
In this talk we study the homotopy type of the (double) suspension of an orientable, closed, connected 4-manifold M, whose integral homology can have 2-torsion. Moreover, the decomposition results are...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：On the subadditivity of generalized Kodaira dimensions (Part II)
广义 小平维度 次相加性 代数纤维空间
2023/5/4
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...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Bounded Poincaré maps for BGG complexes
BGG复形 有界 Poincaré映射
2023/5/10
Poincaré integral operators give explicit potential and provide an inverse of differential operators in the sense of null-homotopy. These operators play a key role in the mathematical and numerical an...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Computations in equivariant algebraic topology
等变 代数拓扑 计算
2023/5/17
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 ...
Character algebras of decorated SL_2(C)-local systems
Character algebras decorated SL_2(C)-local systems Geometric Topology
2011/9/13
Abstract: Let S be a path-connected, locally-compact CW-complex, and let M be a subcomplex with finitely-many components. A `decorated SL_2(C)-local system' is an SL_2(C)-local system on S, together w...
Normal systems over ANR's, rigid embeddings and nonseparable absorbing sets
absolute neighbourhood retracts nonseparable absorbing sets infinite-dimensional manifolds strong Z-sets
2011/8/29
Abstract: Most of results of Bestvina and Mogilski [\textit{Characterizing certain incomplete infinite-dimensional absolute retracts}, Michigan Math. J. \textbf{33} (1986), 291--313] on strong $Z$-set...
On the self-shrinking systems in arbitrary codimension spaces
self-shrinking systems arbitrary codimension spaces
2011/1/17
In this paper, we discuss the self-shrinking systems in higher codimensional spaces. We mainly obtain several Bernstein type results and a sharp growth estimate.MSC 2010: Primary 53C44.
A modification of the method of characteristics: a new class of multidimensional partially integrable nonlinear systems
modification of the method of characteristics new class of multidimensional partially integrable nonlinear systems
2010/12/28
We represent an algorithm reducing a big class of systems of (M + 1)-dimensional scalar nonlinear partial differential equations (PDEs) to the systems ofM-dimensional first order PDEs. Thus, we integr...