Towards intrinsic simplification: the landscape of topological complexity
Abstract
What can be inferred from a system's evolution towards a simpler topological state? This project aims at addressing this question, by developing a framework for minimising topological complexity. The proposed approach will merge diverse fields in pure and applied mathematics. It will represent a substantial breakthrough in core areas, with new results in geometric and computational topology and in measure theory. Outcomes include publications in top-tier maths journals, and the development of new software and computational approaches. Topology is increasingly being used to describe natural phenomena: in parallel to the theoretical novelty, benefits include applications in pressing problems in biophysics, computer and social sciences.
