|Computational Topology: Theory and Applications|
|Time：||Tue./Wed. 8:00-9:50 am|
|Instructor：||Yusu Wang [The Ohio State University]|
|Place：||Conference Room 3, Floor 2, Jin Chun Yuan West Building (近春园西楼2层第三会议室)|
Topology aims at studying intrinsic connectivity of a given object or space. Intuitively, it captures properties of an input object that cannot be removed without tearing the object apart. It is a powerful tool for describing essential features of shapes. Recently, there has been a new trend in developing computational topological methods for data analysis. Such methods have been successfully applied in a broad range of fields including computer graphics, visualization, sensor networks, and machine learning.
This course aims at providing an introduction to several topics in point set topology and algebraic topology from computational and algorithmic points of view. It focuses on concepts and topological structures behind recent developments in computational topology, and algorithms to compute them. Topics include: basic concepts of topology, (persistent) homology, critical points and Morse theory, contour trees and Reeb graphs, polygonal schema, homotopy and fundamental groups. We will also discuss applications of these concepts / algorithms.
Students are expected to finish a course project (which can be team projects).
Basic understanding of algorithms, data structures.
Reference for the course:
Book: Computational Topology: An Introduction, by H. Edelsbrunner and J. Harer, AMS Press, 2009. (About half of the course material will follow this book.)
More references / reading lists will be given during the courses.
Lecture notes will be provided for most classes.