AMSI Summer School 2018

I've spent the last four weeks attending the 2018 AMSI Summer School in the Mathematical Sciences at Monash Univeristy. Here's a quick run down. Posted by Thomas Sutton on February 4, 2018

The Australian Mathematical Sciences Institute 2018 Summer School in the Mathematical Sciences at Monash University has just finished. I took the topological data analysis and low-dimensional topology courses.

Topological data analysis

Topological data analysis is a field which uses ideas and techniques from topology to analyse and characterise data sets. This course covered a lot of ground quite quickly:

We can approximate a topological space by simplical complexes (which is closely related to the familiar triangulation used

Using simplical complexes to represent topological spaces and computing their homology.

  • Simplical complexes and computing them from data
  • The homology of simplical complexes
  • Persistent homology, which is the main tool of TDA
  • Comparing persistence diagrams (the space of persistence diagrams)
  • Statistical analysis of persistence diagrams (monte carlo simulation)
  • Some applications

  • Functional summaries of persistence diagrams (rank, landscape, persistence image)
  • Functional principal component analysis (FPCA)
  • Union-Find for connected components
  • Kruskal’s algorithm for MST
  • Smith Normal Form for computing the boundary matrices
  • An incremental algorithm for computing Betti numbers
  • An algorithm to compute persistent homology by pairing simplicies

  • Morse theory for smooth manifolds
  • Discrete Morse theory

Social events

  • A reception
  • A closing dinner.
  • A diversity session and panel discussion.
  • Morning tea every week day.
  • BBQ lunch each Wednesday.
  • A lunchtime lecture each Tuesday.
  • A maths-related movie night on Thursday night.

  • An excursion to the Philip Island and the penguin parade.
  • An excursion to the Yarra valley to visit a winery or two.

  • A tour of the Monash University Wind Tunnel Facility

This post was published on February 4, 2018 and last modified on July 4, 2020. It is tagged with: study, mathematics, university, travel.