Higher Segal Spaces and their Applications to Algebraic K-Theory, Hall Algebras, and Combinatorics (24w5266)


(University of Virginia)

(Universitat Autònoma de Barcelona)

(University of Minnesota)


The Banff International Research Station will host the “Higher Segal Spaces and their Applications to Algebraic K-Theory, Hall Algebras, and Combinatorics” workshop in Banff from January 21 - 26, 2024.

Homotopy theory and combinatorics are two typically quite disparate areas of mathematics. Whereas combinatorics is concerned with discrete, enumerative problems, homotopy theory has its origins in a more geometric context and has in many ways become quite abstract. The emerging theory of higher Segal spaces provides a bridge between these two areas, allowing for the more theoretical tools of homotopy theory to be applied to combinatorial problems, as well as new homotopy-theoretic frameworks motivated by combinatorial constructions. Furthermore, higher Segal spaces provide a critical link between algebraic $K$-theory (a field which incorporates researchers in homotopy theory, algebra, and number theory) and Hall algebras (typically studied in representation theory and algebraic geometry).

The aim of our workshop is to bring together researchers in each of these areas: homotopy theory, combinatorics, algebraic $K$-theory, and Hall algebras, to help facilitate not only the study of higher Segal spaces themselves, but also the interplay between these different fields with the goal of opening new research directions and forming collaborations. The participants of this workshop will also be at a range of career stages, from graduate students to established researchers, from several different countries, and gender diverse.

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 Technology and Innovation.