Reading course on Topological Data Analysis

Topological data analysis (TDA) is a way of analyzing large data sets using techniques from topology. The purpose of this reading course is to give students an introduction to TDA.

• [B] Magnus Bakke Botnan, Topological Data Analysis, 2020
• [N] Vidit Nanda, Computational Algebraic Topology, 2021 (Videos)

• [C1] Gunnar Carlsson, Topology and Data, Bull. Amer. Math. Soc. 46, 255-308, 2009
• [C2] Gunnar Carlsson, Persistent Homology and Applied Homotopy Theory. In Handbook of Homotopy Theory, pp. 297–330. CRC Press/Chapman Hall Handb. Math. Ser., Theory, CRC Press, Boca Raton, FL, 2020 (arXiv)
• [CM] Frédéric Chazal and Bertrand Michel, An Introduction to Topological Data Analysis: Fundamental and Practical Aspects for Data Scientists, Front. Artif. Intell., 29 September 2021
• [dSMV-J] Vin de Silva, Dmitriy Morozov and Mikael Vejdemo-Johansson, Persistent Cohomology and Circular Coordinates, Discrete Comput. Geom. 45 (2011), 737–759
• [G1] Robert Ghrist, Barcodes: The Persistent Topology of Data, Bull. Amer. Math. Soc. 45 (2008), 61-75
• [I] Federico Iuricich, Persistent Homology: An Introduction via Interactive Examples, 2019
• [L] Michael Lesnick, Studying the Shape of Data using Topology, IAS Letter, Summer 2013
• [M] Elizabeth Munch, A User's Guide to Topological Data Analysis, Journal of Learning Analytics, 4(2), 47–61, 2017
• [P] Jose Perea, A Brief History of Persistence, arXiv, October 1, 2018
• [S] Dayten Sheffar, Introductory Topological Data Analysis, arXiv, April 7, 2020
• [Wa] Larry Wasserman, Topological Data Analysis, Annu. Rev. Stat. Appl. 5, 501–535, 2018 (arXiv)

• [CV-J] Gunnar Carlsson and Mikael Vejdemo-Johansson, Topological Data Analysis with Applications, Cambridge University Press, Cambridge, in press
• [DW] Tamal Dey and Yusu Wang, Computational Topology for Data Analysis , Cambridge University Press, in press (free electronic copy)
• [EH] Herbert Edelsbrunner and John L. Harer, Computational Topology: An Introduction, AMS, Providence, RI, 2010
• [G2] Robert Ghrist, Elementary Applied Topology, ed. 1.0, Createspace, 2014
• [O] Steve Y. Oudot, Persistence Theory: From Quiver Representations to Data Analysis, Mathematical Surveys and Monographs, vol. 209, AMS, Providence, RI, 2015
• [PRSZ] Leonid Polterovich, Daniel Rosen, Karina Samvelyan and Jun Zhang, Topological Persistence in Geometry and Analysis, University Lecture Series, vol. 74, AMS, Providence, RI, 2020 (arXiv)
• [RB] Raúl Rabadán and Andrew J. Blumberg, Topological data analysis for genomics and evolution. Topology in biology, Cambridge University Press, Cambridge, 2020

• [AATRN] Applied Algebraic Topology Research Network, YouTube channel
• [B1] Ulrich Bauer, Computation of Persistent Homology, Part 1 (1:01:27), IMA, August 13, 2018
  • Notes
• [B2] Ulrich Bauer, Computation of Persistent Homology, Part 2 (1:06:51), IMA, August 14, 2018
  • Slides
• [Wr1] Matthew Wright, Introduction to Persistent Homology (08:46), 2016
• [Wr2] Matthew Wright, Introduction to Persistent Homology (48:56), IMA, August 13, 2018

• We have compiled a list of topics that should be covered for each of the presentations you might be asked to give.
• A preliminary schedule for the exam is listed below. Let us know as soon as possible if you are not taking the exam.