New Class for Fall Quarter 2002

Introduction to Computational Topology
Listed under CS 468: Geometric Algorithms Seminar

Instructor: Afra Zomorodian

Meetings: Wednesdays, 12:30-2 PM, in Gates 392

Description:

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.

Prerequisites:

I assume mathematical sophistication and familiarity with programming. However, the course is designed for a novice in the area. The grade will be based on class participation and a final project, which can be either an implementation or a survey paper.

Class Requirements:

The course will not have any homework or tests. The grade will be based on class participation and a final project, which can be either an implementation or a survey paper. I will provide a list of possible projects early in the quarter.

Literature:

I will be providing notes for the class, as well as survey articles and supplementary readings, when appropriate.

More Information:

First meeting will be on September 25th.
See Course website for more details.