Higher Segal Spaces and Applications

Featuring proceedings from a January 2024 workshop in Banff, this volume explores cutting-edge insights into higher Segal spaces and their versatile roles in algebra, geometry, combinatorics, and beyond. Expertly crafted expository papers bridge homotopy theory and higher category theory for both newcomers and specialists. This volume contains the proceedings of the Workshop on Higher Segal Spaces and their Applications to Algebraic $K$-Theory, Hall Algebras, and Combinatorics, held from January 21 to 26, 2024, at the Banff International Research Station, Banff (AB), Canada. This book is a collection of ten expository papers providing an introduction to the theory and applications of higher Segal spaces, a rather new topic in the interface between homotopy theory and higher category theory, finding applications in homological algebra, representation theory, geometry, combinatorics, algebraic $K$-theory, and other areas. The papers are written by experts on the various topics, in an engaging style welcoming newcomers to the field, and are also designed to help specialists in one application area make the transition to another.