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)

  • 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
  • Example of a good project report File
  • Example 2 of a good project report File Uploaded 31/05/17, 14:04
  • 
    

    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
  • export triangulation to ply File Uploaded 11/04/18, 13:49
  • Group Project

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

  3 October - 9 October

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

  Textbook: Chapter 1

  • 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
  • Lab work #1 File Uploaded 3/10/22, 09:56
• 

  10 October - 16 October

  Triangulations in the plane, Voronoi diagram, Delaunay triangulation.
  

  Textbook: Chapter 2
  

  • Lab work #2 File Uploaded 9/10/22, 09:10
  • Geogebra URL
  • Cool links (Voronoi diagrams) Page
• 

  17 October - 23 October

  Geometric simplicial complexes, Abstract simplicial complexes, Euler characteristic

  Textbook: Chapter 3
  
• 

  24 October - 30 October

  Triangulated manifolds, orientation. Classification of surfaces.
  
  Textbook: Chapter 4
  
• 

  31 October - 6 November

  Carve a pumpkin
  
• 

  7 November - 13 November

  Simplicial complexes on data sets:
  

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

  Interleaving.

  Textbook: Chapter 5
  

  • Lab work #6 File Uploaded 7/11/22, 08:07
• 

  14 November - 20 November

  Algebraic groups. Intuition and idea of homology.
  

  Textbook: Chapter 6, idea of chapter 7
  

  
  
• 

  21 November - 27 November

  Homology groups

  Textbook: Chapters 7 and 8.1
  

  • Useful links Page
• 

  28 November - 4 December

  Computing homology

  Textbook: Chapters 7 and 8.1
  
• 

  5 December - 11 December

  Persistent homology

  Textbook: Chapter 9

  • Lab work #10 File Uploaded 5/12/22, 16:22
  • Computing homology in Python Page
• 

  12 December - 18 December

  Filtrations, persistence modules, interleavings, Gromov-Hausdorff distance
  

  Textbook: Chapters 9 and 10
  

  • Lab work #11 File Uploaded 19/12/22, 21:36
• 

  19 December - 25 December

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

  Textbook: Chapter 10
  
• 

  26 December - 1 January

  Write to Santa...

  • Persistent homology Page
  • object1 File
  • object2 File
  • object3 File
  • object4 File
• 

  2 January - 8 January
• 

  9 January - 15 January

  Discrete Morse theory: discrete Morse functions, discrete gradient vector fields
  
  Textbook: Chapter 11
  
• 

  16 January - 22 January

  Not available
• 

  23 January - 29 January

  Not available