Spring 2005

MATH 491/591

Senior Seminar/Masters Essay

Applications of Algebraic Topology in Sciences and Engineering

How many tunnels does this protein (left) have? How many voids? What about that piece of an alloy (right)? How do you teach a computer to distinguish between letters C and O, O and P, P and B? These and related questions are more and more often addressed via computations of Betti numbers and homology groups of these objects. As a result we have on one hand something classical (algebraic topology) and on the other something much more recent (applications). Topics of possible research projects are: Image processing and recognition; Structure of proteins; Topology of data structures; Topology of networks; Computational topology. If you have questions, please contact the instructor.

• Time and Place: MW 5:00-6:15, SH 509. 
• Instructor: Peter Saveliev (http:\\saveliev.net).
• E-mail: saveliev@marshall.edu.
• Text: Computational Homology by Tomasz Kaczynski, et al.
• Prerequisites. Good knowledge of linear algebra as well as some fundamentals of group theory (Math 450), in particular, quotient groups, properties of Abelian groups, and examples.