Representation Theory and Topological Data Analysis (24w5241)

The Banff International Research Station will host the “Representation Theory and Topological Data Analysis” workshop in Banff from April 7 - 12, 2024.

A central problem in data-driven scientific inquiry is how to quantitatively describe the organizational structures intrinsic to large data sets. The field of algebraic topology provides a potential solution via the language of homology, which measures various features in a given topological space - such features being, loosely speaking, “holes” of different dimensions (e.g. connected components, loops, trapped volumes, etc.). In principle, these features can be located and studied explicitly.

In practice however, fundamental challenges in data analysis, such as the choice of scale or the presence of noise, make it necessary to go beyond the use of numerical summaries on a single topological space.

This need has given rise to the emerging area of topological data analysis, and to its mathematical foundations called persistence theory, whose aim is to define and study homological invariants for parametrized families of topological spaces.

While the one-parameter instance of persistence theory is by now well understood, there are fundamental mathematical and computational challenges associated with the development of its multi-parameter instance.

Recent advances have demonstrated that this new topic can greatly profit from using techniques developed in representation theory, in particular techniques based on homological algebra.

Therefore, the aim of this workshop is to bring together leading researchers as well as emerging scholars from topological data analysis and from representation theory, in order to enhance the growing connections between both areas, in particular, but not limited to, new methods in multi-parameter persistence.

The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station is located at The Banff Centre in Alberta and is supported by Canada’s Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF), Alberta’s Advanced Education and Technology, and Alberta Technology and Innovation.