One-Dimensional Computational Topology

CS 598 JGE, Spring 2023

Instructor
Jeff Erickson (jeffe@illinois.edu)
Lectures
WF 11:00–12:15, 2200 Sidney Lu MEB (floor plans)
Office Hr.
Tuesdays 3-4, open area next to 3237 Siebel

Announcements

Mar 7
As expected, this week's lectures will be held over Zoom.
Mar 2
I am sick with COVID. Class on Friday March 3 is cancelled, and next week's lectures (March 9 and 11) will likely be held over Zoom. Stay tuned for more info.
Feb 22
The Gradescope site for this class is open and accepting submissions for the paper chase assignment. Everyone registered for the class should already be enrolled, but if I missed you, you can self-enroll with the entry code 6ZW4D7.
Feb 2
• The paper chase assignment is due Tuesday, February 28. (I've updated the list of suggested strting points to include only papers published in 2021 or later.) This is the first part of the semester project.
• Starting next week, I will have office hours every Tuesday 3-4. (I'm also usually free immediately after class on Wednesday and Friday.)
Jan 8
Hello and welcome! I'm still setting up the class; please forgive the dust, construction noises, and dead links. First some logistics:
• Formally, registration is currently restricted to graduate students in computer science.
• Graduate students in other fields, especially mathematics, are definitely welcome. Registration should open to non-CS graduate students by the end of the day on January 9, but this is a manual process driven by overworked academic office staff, so please be patient. Please talk to me after class if you are still unable to register by the end of the first week (January 20).
• Undergraduates interested in taking this course should submit a petition to register as soon as possible, but absolutely no later than January 20. Petitions can take several weeks to process (because they must be processed individually by overworked academic office staff).
• We are using Ed Discussion site as an online discussion forum. You can enroll yourself using your university login credentials; no enrollment code is necessary.
• I plan to maintain a list of "homework" exercises. At least for now, these are meant only for your practice and understanding; homework will not be graded. I strongly encourage discussing these exercises (and any similar problems that occur to you) on Ed Discussion.

The selection of topics in this class is necessarily limited by the finiteness of a single semester and by my own interests and expertise. Important topics in computational topology that I will not cover this semester, except perhaps briefly in passing, include automatic groups, knot theory, 3-manifolds, cell complexes (simplicial, cubical, Delta, CW, simplicial sets), algorithms for CAT(0)-complexes, discrete Morse theory, normal surface theory, configuration spaces, dynamical systems, persistent homology and its generalizations, surface reconstruction, manifold learning, topological data analysis, embedding obstructions, higher-order homotopy, discrete differential geometry, applied Hodge theory, fixed-point theorems, PPAD-completeness, algebraic complexity, $\exists\mathbb{R}$-hardness and "Murphy's Law" universality, evasiveness of graph properties, impossibility results in distributed computing, and topological quantum computing. The full diversity of techniques, results, applications, and even definitions of computational topology could easily fill a dozen courses.