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Tuesday, October 27, 2015

**Abstract:** When studying objects with additional algebraic structure, e.g. algebras over an operad, it can be helpful to consider cell decompositions adapted to these algebraic structures. I will talk about joint work with Jeremy Miller on the relationship between E_n-cells and homological stability. Using this theory, we prove a local-to-global principle for homological stability, as well as give a new perspective on homological stability for various spaces including symmetric products and spaces of holomorphic maps.