Theory and computation of vineyards and vineyard modules. Vineyards and vineyard modules are mathematical objects calculated from topological measurements of continuous one-parameter families of data.

Description

Theory and computation of vineyards and vineyard modules. Vineyards and vineyard modules are mathematical objects calculated from topological measurements of continuous one-parameter families of data. This project aims to develop theory and computational tools for the use of vineyards and vineyard modules with a particular focus on time-varying point clouds and planar subsets as data input. The project expects to generate new knowledge relating to the algebraic and geometric structures within vineyards and vineyard modules, as well as develop new code for computing vineyards and distances between vineyards. Expected outcomes and benefits include enhanced data analysis tools, research training with increased capacity within the mathematical sciences, and increased international collaboration. . Scheme: ARC Future Fellowships. Field: 4904 - Pure Mathematics. Lead: A/Prof Katharine Turner