Discrete and combinatorial homotopy theory
March 13 to March 17, 2023
American Institute of Mathematics,
San Jose, California
and Volkmar Welker
This workshop 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.
The main topics of this workshop are:
A-theory of graphs and simplicial complexes
Homotopy of digraphs
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.
Material from the workshop
A list of participants.
The workshop schedule.
A report on the workshop activities.