CS 598: Computational Topology

Jeff Erickson
TuTh 11:00-12:15, 1302 Siebel Center
CCN: 54314

Computational topology is an emerging field of study at the
intersection of mathematics and computer science, devoted to the study
of efficient algorithms for topological problems, especially those
that arise in other areas of computing. Although algorithmic
techniques have been ubiquitous in topology since its inception over a
century ago, the efficiency of topological algorithms and their
applicability to other computing domains are relatively recent areas
of study. Results in computational topology combine classical
mathematical techniques from combinatorial, geometric, and algebraic
topology with more recent algorithmic tools from data structure design
and computational geometry. These results have found applications in
many different areas of computer science.

This course will be a broad introduction to computational topology;
the precise topics covered will depend on the skills and interests of
the course participants. Potential mathematical topics include the
topology of cell complexes, topological graph theory, homotopy,
covering spaces, simplicial homology, persistent homology, discrete
Morse theory, discrete differential geometry, and normal surface
theory. Potential computing topics include algorithms for computing
topological invariants, graphics and geometry processing, mesh
generation, curve and surface reconstruction, VLSI routing, motion
planning, manifold learning, clustering, image processing, and
combinatorial optimization.

Students in all areas of computer science, mathematics, and related
disciplines are welcome. CS 573 and/or Math 525 are recommended as
prerequisites, but not required; necessary background material will be
introduced as needed.

For more details, see http://www.cs.uiuc.edu/~jeffe/teaching/comptop/
or contact Jeff.