EVENT DETAILS AND ABSTRACT

Title: Dynamical systems and diagrams
Speaker: Rick Jardine
Speaker Info: University of Western Ontario
Brief Description:
Special Note:
Abstract:

A dynamical system is a map of spaces $X \times S \to X$, and a map of dynamical systems $X \to Y$ over $S$ is an $S$-equivariant map. There are both injective and a projective model structures for the resulting category.

These model structures are special cases of homotopy theories for space-valued diagrams $X$ defined on a fixed category $A$ enriched in simplicial sets. Simultaneously varying the parameter category $A$ (or parameter space $S$) along with the diagrams $X$ up to weak equivalence is more interesting, and requires new model structures for $A$-diagrams having weak equivalences defined by homotopy colimits, as well as a generalization of Thomason's model structure for small categories to a model structure for simplicial categories.