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Schedule - Winter 2022

Note that the start of classes has been delayed 1 week

This course follows a Monday/Wednesday Schedule. There is a section for each day, with materials for that day. This schedule is subject to change before a class is held.

Links to readings can be found on the resources page.

Schedule Archives: Winter 2021

Day 00 - 1/10

Introduction to topological data analysis.

Lecture Recording / iPad Notes / Transcribed Notes

Code:

Reading:

Day 01 - 1/12

Preliminaries: Graphs, Clustering, Disjoint Set/Union-find, the Graph Laplacian.

Lecture Recording / iPad Notes / Transcribed Notes

Code:

Reading:

Day 02 - 1/17

MLK Day. No Class

Day 03 - 1/19

Basic Topology (spaces, maps, homotopy). Simplicial Complexes. Simplicial Maps. Constructions.

Lecture Recording / iPad Notes

Code:

Reading:

Day 04 - 1/24

Nerve of a cover, witness complexes, Mapper algorithm. Tries.

Lecture Recording / Zoom dropped the call for the final 20 minutes, which was a discussion of use of Mapper by Li et al. in the readings below, and a brief overview of the trie data structure.

Code: trie.py simplicial_complex.py demo notebook

For an open-source Mapper implementation (in Python), check out Kepler Mapper.

Reading:

Homework 1

Due 10:30am on Feb. 9, 2022. Link

Day 05 - 1/26

(Cellular) chain complexes, (Cellular) homology, reduction algorithm.

Lecture Recording

Code: chain.ipynb

Reading:

Day 06 - 1/31

Reduction algorithm, persistent homology.

Lecture Recording

Code:

Reading:

Day 07 - 2/2

(Persistent) homology wrap-up, basic implementation, clearing & compression optimizations.

Lecture Recording / iPad Notes

Code: filtration.ipynb, reduction.py, chain.py, BATS reduction, Reduction options in BATS

Reading:

Day 08 - 2/7

Pairs, barcodes, diagrams, bottleneck distance, features.

Lecture Recording

Code: notebook on diagrams and distances

Reading:

Day 09 - 2/9

Quiver Representations, Zigzag Homology.

Lecture Recording

Code: Algorithm in BATS

Reading:

Day 10 - 2/14

Interleavings, Interleaving Distance, Isometry Theorem.

Lecture Recording

Reading:

Day 11 - 2/16

Interleavings Part II

Lecture Recording

Homework 2

Due 10:30am on March 2, 2022. Link

Day 12 - 2/21

Klein bottle in Image Patches.

Lecture Recording

Reading:

Day 13 - 2/23

Reach, Weak Feature Size, Sampling.

Lecture Recording

Reading:

Day 14 - 2/28

Cohomology, Applications

Lecture Recording

Code:

Reading:

Day 15 - 3/2

Cohomology II - Hodge laplacians, ranking

Lecture Recording

Code:

Reading:

Day 16 - 3/7

Applications to clustering and regularization.

Lecture Recording

Reading:

Day 17 - 3/9

Homotopy. Discrete Morse theory and simplification.

Reading:

Day ??

Outliers. Metric Measure Spaces, Distance-to-Measure.

Reading:

Day ??

Zigzag zoo, sparse filtrations.

Reading:

Day ??

Multidimensional and Generalized Persistence.

Reading:

Day ??

Project presentations.

Reading Period

Reading Period is 3/12-3/14

Finals Period

Final project report will be due in finals period - 3/18 at midnight.