Topological data analysis

Weekly outline

• 

  General course info

  Lecturer: 
  

  • Žiga Virk (ziga.virk@fri.uni-lj.si)

  Assistants: 
  

  • Aleksandra Franc (aleksandra.franc@fri.uni-lj.si)
    
  • Gregor Jerše (gregor.jerse@fri.uni-lj.si)

  • Oral exams TDA Zoom meeting
  • News Forum
  • Questions, answers and discussions Forum
  • Course description - Opis predmeta Page
  • Student requirements - Obveznosti študentov Page
  • Lab work - Delo na vajah Page
  • Literature and other sources Page
  • 
    

    A topologist is a person, who doesn't know a donut from a coffee cup

    
    

    
    

  • Homework 1

  • HW1 Dropbox Assignment
  • Homework 2

  • HW2 Dropbox Assignment
  • Homework 3

  • HW3 Dropbox Assignment
  • Group Project

  • Group Project Dropbox Assignment
  • Project documentation Page
  • Presentation schedule Page
• 

  4 October - 10 October

  Introduction. Basic definitions and concepts: metrics, continuous maps, homeomorphisms, homotopy type. 

  • There is no difference between a donut and a coffee cup ... URL
  • Topology and topological data analysis (from AYASDI) URL
  • The intuition behind topology Page
  • Book chapter 1 File Uploaded 5/10/21, 12:10
  • Lab work #1 File Uploaded 6/10/21, 22:47
• 

  11 October - 17 October

  Triangulations in the plane, Voronoi diagram, Delaunay triangulation.
  

  • Book chapter 2 File Uploaded 12/10/21, 10:40
  • Lab work #2 File Uploaded 11/10/21, 10:23
  • Geogebra URL
  • Cool links (Voronoi diagrams) Page
• 

  18 October - 24 October

  Geometric simplicial complexes, Abstract simplicial complexes, Euler characteristic

  • Book chapter 3 File Uploaded 13/10/21, 10:41
• 

  25 October - 31 October

  Triangulated manifolds, orientation. Classification of surfaces.

  • Book chapter 4 File Uploaded 20/10/21, 14:01
• 

  1 November - 7 November

  Simplicial complexes on data sets:
  

  • Vietoris Rips complex
  • Cech complex
  • The nerve construction
  • Mapper

  Interleaving.

  • Book chapter 5 File Uploaded 20/10/21, 14:02
• 

  8 November - 14 November

  Algebraic groups. Intuition and idea of homology.
  

  
  

  • Book chapter 6 File Uploaded 20/10/21, 14:03
  • Lab work #6 File Uploaded 8/11/21, 10:37
  • Whiteboard (1st group) File Uploaded 9/11/21, 19:29
  • Whiteboard (2nd group) File Modified 9/11/21, 19:37
• 

  15 November - 21 November

  Homology groups

  • Book chapter 7 File Uploaded 8/11/21, 14:11
  • Useful links Page
• 

  22 November - 28 November

  Computing homology

  • Book chapter 8 File Uploaded 9/11/21, 10:38
  • Lab work #8 File Uploaded 22/11/21, 20:11
• 

  29 November - 5 December

  Persistent homology

  • Lab work #9 File Uploaded 22/11/21, 20:12
  • Computing homology in Python Page
  • Book chapter 9 File Uploaded 26/11/21, 11:23
• 

  6 December - 12 December

  Filtrations, persistence modules, interleavings, Gromov-Hausdorff distance
  

  • Book chapter 10 File Uploaded 2/12/21, 14:02
• 

  13 December - 19 December

  Stability theorem for persistent homology, Wasserstein distance, further developments of persistence, examples of applications

  • Notes File Uploaded 17/12/20, 10:36
  • Lectures, Part 1 URL

    Persistence: stability

  • Lectures, Part 2 URL

    Discrete Morse theory: discrete Morse functions, discrete vector fields

  • Lectures, Part 3 URL

    Discrete Morse theory: sublevel complexes

  • Lab work #11 File Uploaded 15/12/20, 16:27
• 

  20 December - 26 December

  Discrete Morse theory: discrete Morse functions, discrete gradient vector fields
  

  • Book chapter 11 File Uploaded 16/12/21, 18:24
• 

  27 December - 2 January

  Not available
• 

  3 January - 9 January

  Discrete Morse theory: Morse chain complex and Morse homology

  • shape1 File Uploaded 4/01/22, 09:14
  • shape2 File Uploaded 4/01/22, 09:14
• 

  10 January - 16 January

  Project presentations
• 

  17 January - 23 January

  Not available