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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...
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...
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 ...
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...
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...
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 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...
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...
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...
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 ...
Jason Manning,Associate Professor,Department of Mathematics at Cornell University.He is Research Area:Geometric group theory,geometric topology.Selected Publications:Algorithmic detection and descript...
James E. West,Professor,Department of Mathematics at Cornell University.He is Research Area:Geometric topology,infinite-dimensional topology.Selected Publications:Mapping Hilbert cube manifolds to ANR...
The Department of Mathematics at the University of Iowa has 40 faculty members whose research interests include algebra, algebraic topology, analysis, differential geometry, functional analysis, knot ...

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