6/10/2018 CS 598: Computational Topology (Spring 2013) http://jeffe.cs.illinois.edu/teaching/comptop/ 1/3 Codex Seraphinianus, p.166 The 13 basketball posions according to Muthu Alagappan CS 598: Computaonal Topology Spring 2013 Jeff Erickson ( jeff[email protected]) TuTh 2:00–3:15, 214 Ceramics About Schedule References Coursework Projects Announcements Welcome! The schedule and notes from the Fall 2009 iteraon of this course are sll available. About this class Computaonal topology is an emerging field of study at the intersecon of mathemacs and computer science, devoted to the study of efficient algorithms for topological problems, especially those that arise in other areas of compung. Although algorithmic techniques have been ubiquitous in topology since its incepon more than a century ago, the efficiency of topological algorithms and their applicability to other compung domains are relavely recent areas of study. Results in computaonal topology combine classical mathemacal techniques from combinatorial, geometric, and algebraic topology with more recent algorithmic tools from data structure design and computaonal geometry. These results have found applicaons in many different areas of computer science. This course will be a broad introducon to computaonal topology; the precise topics covered will depend on the skills and interests of the course parcipants. Potenal mathemacal topics include the topology of cell complexes, topological graph theory, homotopy, covering spaces, simplicial homology, persistent homology,
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Welcome! The schedule and notes from the Fall 2009 itera�on of thiscourse are s�ll available.
❖ About this class ❖
Computa�onal topology is an emerging field ofstudy at the intersec�on of mathema�cs andcomputer science, devoted to the study ofefficient algorithms for topological problems,especially those that arise in other areas ofcompu�ng. Although algorithmic techniqueshave been ubiquitous in topology since itsincep�on more than a century ago, theefficiency of topological algorithms and theirapplicability to other compu�ng domains arerela�vely recent areas of study. Results incomputa�onal topology combine classical mathema�cal techniques fromcombinatorial, geometric, and algebraic topology with more recent algorithmic toolsfrom data structure design and computa�onal geometry. These results have foundapplica�ons in many different areas of computer science.
This course will be a broad introduc�on to computa�onal topology; the precisetopics covered will depend on the skills and interests of the course par�cipants.Poten�al mathema�cal topics include the topology of cell complexes, topologicalgraph theory, homotopy, covering spaces, simplicial homology, persistent homology,
discrete Morse theory, discrete differen�al geometry, and normal surface theory.Poten�al compu�ng topics include algorithms for compu�ng topological invariants,graphics and geometry processing, mesh genera�on, curve and surfacereconstruc�on, VLSI rou�ng, mo�on planning, manifold learning, clustering, imageprocessing, and combinatorial op�miza�on.
Students in all areas of computer science, mathema�cs, and related disciplines arewelcome. CS 573 and/or Math 525 are recommended as prerequisites, but notrequired; necessary background material will be introduced as needed.
❖ Other computa�onal topology classes ❖
The selec�on of topics in this class is necessarilylimited by the finiteness of a single semester andbiased by my own interests and exper�se. The fulldiversity of techniques, results, applica�ons, andeven defini�ons of computa�onal topology couldeasily fill a dozen courses. Here is a sample of someother classes/seminars in computa�onal topologyand some closely related fields:
O�ried Cheong and Sunghee Choi, KAIST (Fall2006)
Sarah Day, William and Mary (Spring 2008)
Herbert Edelsbrunner, Duke University (Fall2006)
Joachim Giesen and Michael Sagraloff, Max‐Planck‐Ins�tut für Informa�k(Fall 2006)
Rob Ghrist, University of Pennsylvania
Susan Holmes, MSRI (Fall 2006)
Spike Hughes, Brown (Spring 2011)
Bala Krishnamoorthy, Washington State (Spring 2012)
Dmitriy Morozov, Stanford University (Fall 2009)
Abubakr Muhammad, McGill University (Winter 2008)
Chee Yap, NYU (Fall 2006)
Peter Schröder and Keenan Crane, Caltech (Fall 2012)