Topological Data Analysis (TDA) – Theory, Computation and Application (Oxford) & The Persistence of topology in big data analysis (Edinburgh)

Oxford, 10 -11 September, 2015

Main organisers: Peter Grindrod, Heather Harrington, Ulrike Tillman, Patrick Wolfe

In the last decade there has been an explosion of work and interest in topological data analysis, and in particular in persistent homology. Typically to a data cloud one associates as sequence of shapes, each depending on a resolution parameter. These shapes are then analysed by algebraic topological means. The resulting bar code is a simple summary and footprint of the underlying shape of the data.

By now there is an ever evolving sophisticated theory of persistent homology and its variants, some combining powerful tools from other branches of the mathematical sciences, such as statistics and probability. The computation of persistent homology for large data sets remains a challenge, but several prototype software implementations are now available and have been tested on real data. This has led to interesting applications in fields ranging from computer vision to medicine, network analysis and cell biology.

The aim of the workshop is to bring participants from across the mathematical sciences together to discuss the future of the field — theory, applications and software development — starting from basic definitions and aims, and advancing to current research questions through to a prioritisation of future ones.

The following key-questions will be addressed: How can topological data analysis help us to ask and answer data-driven questions?  What are the most important and highest-priority challenges in theory. for computation and application? How can the existing expertise in the UK best address these questions through the Alan Turing Institute? Which areas should be prioritised to maximise impact in the short, medium and and longer terms?

International speakers include:
Omer Bobrowski, Herbert Edelsbrunner,  Robert Ghrist, Michael Kerber, Ezra Miller, Konstantin Mischaikow