2024 CMS Summer Meeting Mini-Courses: Applied Topology: Persistent Homology
Topic
Applied Topology: Persistent Homology
Details
Persistent Homology is an application of algebraic topology (filtered chain complexes) to statistics. Roughly speaking, one naturally associates filtered chain complexes to data in a variety of ways. Persistent homology is the structure of how the homology changes as the filtration evolves. Homology classes that exist for `long' or `big' regions in the filtration are deemed more significant than ones that exist for shorter or smaller periods. Research in persistent homology centres around issues such as 1) efficient computation for various filtration types, parallelization, etc, 2) theoretical significance of computations: stability or lack of it, and the ability to infer structure in the underlying data from computations, noise vs. signal.
The mini-course on Persistent Homology will be structured as follows:
- Discussion of motivating examples and basic ideas from algebraic topology: homology, manifolds, Steenrod realization.
- A sampling of a few different filtered chain complex types. Computation of persistent homology. Computer examples.
- Basics of the theory: computational complexity, stability, signal vs. noise theorems, asymptotics.
Additional Information
The CMS is organizing mini-courses to add more value to meetings and make them attractive for students and researchers to attend. The mini-courses will be held on Friday, May 31 and include topics suitable for graduate students, postdocs, and other interested parties.
Partial funding may be available for students, postdocs, and early-career researchers to attend the Applied Topology minicourses. To receive more information and apply for this opportunity, please fill out this google form. For full consideration, please apply by May 1 using this form: https://forms.gle/v5FEVmcYC4w2nyXw5
For registration, please complete the Google form for funding above and then enrol through the CMS website.