MATH 264: Computational Topology
Instructor: Yuriy Mileyko

The course is an introduction to computational topology, which is an
emerging field devoted to the study of efficient algorithms for
topological problems, especially those arising in science and
engineering. Computational topology builds upon classical results from
algebraic, geometric, and differential topology as well as algorithmic
tools from computational geometry and other areas of computer science.
Specific topics will include elements of point-set topology (topological
and metric spaces, continuity, homeomorphism), manifolds (curves, knots,
surfaces and beyond), fundamental group, homotopy, simplicial complexes
(Alpha, Cech, Rips), simplicial homology and cohomology, duality, Morse
theory, persistent homology, stability of persistence diagrams, and
applications of computational topology with a focus on data analysis.
Exposition of most topics will have both theoretical and algorithmic
parts.