Advances in the geometric analysis of Smith maps (25rit043)

The Banff International Research Station will host the “Advances in the geometric analysis of Smith maps” Research in Teams program in Banff from October 12 - 19, 2025.

This research project aims to study a special class of maps (functions) between geometric spaces that come equipped with special extra structure. Such maps play an important role in constructing "invariants" of such spaces, which allow us to distinguish them geometrically. These maps are the natural higher-dimensional generalizations of holomorphic maps, which are the special maps arising in the study of spaces modelled on the complex numbers. Questions which are to be considered include how "badly behaved" such maps can be (that is, how non-smooth can they be), and can such maps be deformed in a natural way in families. These are vital questions to be able to construct "invariants" using such maps.

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), and Alberta’s Advanced Education and Technology.