应用拓扑专题讲习班

Applied topology is a new interdisciplinary research field. Based on the theorems and methods in topology, applied topology has demonstrated great power in the field of natural science and engineering. In recent years, applied topology has developed rapidly and has wide and important applications in the fields of AI, information science and biology. In our country, the research and international influence of algebraic topology have developed rapidly, which provided an excellent basis for the development of applied topology. There will be four courses and several related reports in this project including Morse theorem and its applications, Applied Algebraic Topology, TDA-based biomolecular data analysis, Computational topology and geometric algorithm. The purpose of our seminar is to introduce the basic ideas, theories, frontiers and developments of applied topology and build a communicate platform for young scholars and graduate students in related fields. This will make due contributions to cooperation between mathematics and other course and development of applied topology.

应用拓扑学是一个新兴的交叉研究领域，利用拓扑的思想方法结合不同学科背景解决自然科学和工程领域的前沿问题。近年来，应用拓扑研究在国际上发展迅猛，在人工智能、信息科学、生物学等众多领域有着广泛的应用。我国在代数拓扑等学科的理论研究发展迅速，在国际上影响力与日俱增，为应用拓扑的发展奠定了良好基础。本项目将设置4门短课程，包括莫尔斯理论及应用、应用代数拓扑、拓扑数据分析在生物学中的应用、以及计算拓扑与几何算法，并举办多场相关领域的学术报告和科研讲座。项目的实施旨在向相关领域的学者和研究生介绍应用拓扑的理念、基本理论以及当今的学术动态和前沿发展，建立沟通交流的平台，为促进拓扑等数学分支与其它学科交叉合作，推动国内应用拓扑学科领域发展做出应有的贡献。

应用拓扑学是近年来发展迅猛的新兴研究领域，在人工智能、信息科学、生物学等众多领域有着广泛的应用。本项目共举办了4门短课程，分别介绍了拓扑与几何算法、几何相交数的符号计算方法、拓扑数据分析在生物学中的应用以及应用拓扑领域前沿理论。并举办多场相关领域的学术报告，介绍应用拓扑的前沿理论发展以及实际应用的最新研究成果，为大家搭建一个学习、交流的平台，促进应用拓扑研究的发展。