AIM Workshop: Discrete and combinatorial homotopy theory

This workshop, sponsored by AIM and the NSF, will be devoted to homotopy theories developed for the study of discrete and combinatorial objects. Many different models of discrete homotopy have emerged in the past 20-30 years, developed largely in isolation from one another. In this workshop, we will study different perspectives on discrete homotopy and explore their connections and differences. Among our goals is to identify important applications, particularly to combinatorics, metric geometry, and geometric group theory. We will also investigate how ideas from abstract homotopy theory (model categories, simplicial and cubical homotopy, infinity categories, etc.) may be used to extend and consolidate the theories.

Topics: The main topics of this workshop are: A-theory of graphs and simplicial complexes; Homotopy of digraphs; Digital homotopy ; Discrete homotopy of metric spaces; Homotopy theory in topological categories; Applications of abstract homotopy theory to discrete homotopy; Applications of discrete homotopy to combinatorics, metric geometry, geometric group theory, and other areas.