Bousfield localization on finite lattices

A central theme in algebraic topology is the study of spaces under different notions of equivalence. This can be made precise from a categorical perspective via the formalism of model categories, which consists of additional structure on a category. Bousfield localization is a way of obtaining new model category structures from previous ones in a controlled way. In this talk I will introduce this formalism and describe model structures on finite lattices and their Bousfield localizations in terms of a combinatorial object called a transfer system.