报告题目： Topological methods for decision making
报告时间：2025年3月30日 （周日）15:00-16:00
报告地点：综合楼644会议室
报告人：M. El Safty (埃尔. 萨夫提)
报告人简介：
M. El Safty received the Ph.D. degree in Science (Pure Mathematics-C Topology) Tanta University, in 2012. He is currently working as an A. Professor of Applied Mathematics with the Department of Mathematics and Statistics, Faculty of Science, Taif University, Taif, Saudi Arabia. He has authored and co-authored more than 50 peer-reviewed papers and has served as a reviewer in many prestigious peer-reviewed international journals and conferences. His research interests include pure mathematics especially Topology and Decision-Making.
报告摘要：
This report introduces Topology, which is a branch of mathematics, studies properties of space that are preserved under continuous deformations. It provides a powerful lens to analyze the shape, connectivity, and structure of data. By applying topological tools, such as persistent homology, simplicial complexes, and Morse theory, we can uncover hidden patterns, relationships, and hierarchies that are not immediately apparent through traditional methods. These insights are particularly valuable in decision-making contexts, where understanding the global structure of data can lead to more robust and informed choices.
In this talk, we will explore how topological methods are revolutionizing decision making across various domains, from machine learning and robotics to economics and network analysis. We will discuss how topological data analysis (TDA) can identify critical features in high-dimensional datasets, how Morse theory can help navigate complex decision landscapes, and how persistent homology can reveal stable structures in dynamic systems. Through real-world examples, we will demonstrate how these methods enhance our ability to make decisions in uncertain, noisy, and high-dimensional environments.
Ultimately, this talk aims to highlight the transformative potential of topology in decision making, offering a fresh perspective that bridges mathematics, data science, and practical applications.
