Introduction to Computational Topology
Listed under CS 468: Geometric Algorithms Seminar
Instructor: Afra Zomorodian
Meetings: Wednesdays, 12:30-2 PM, in Gates 392
The emerging field of computational topology utilizes theory from topology and the power of computing to solving problems in diverse fields. Recent applications include computer graphics, computer-aided design (CAD), and structural biology. In each case, we are interested in understanding the intrinsic shape of some real or abstract space.
The primary goal of the course is to present basic concepts from topology and Morse theory to enable a non-specialist to grasp and participate in current research in computational topology. As such, this course will not be a readings course in computational topology. I will present material from a computer scientist's point of view, focusing on computational challenges, and presenting algorithms and data-structures when appropriate. Near the end of the course, we will examine recent advances in the area.
The course combines concepts from point set topology, algebraic topology, group theory, differential manifolds, Morse theory, and normal surface theory.