The basic question which underpins the project is as follows: when can we find simple structures, which we understand, within complex geometric objects? For instance, the above geometric object may be a representation of data gathered by a company or individual, depending on thousands of variables. After applying some ‘tests', one may determine that in fact this data depends on, or is well approximated by something which depends on, only 10 variables. The task of analysing this data further now becomes far easier. The project ‘quantitative differentiability and rectifiability in metric spaces' — carried out at the University of Jyväskylä — seeks to find these 'tests', by developing new tools and techniques to establish the existence of certain simple structures in a variety of geometric objects. Special attention is paid to geometries which do not adhere to our usual intuition (metric spaces), which can appear naturally, for example, in the geometry of data.

2024

2028