Rune Haugseng (MPIM Bonn): Enriched Infinity-Categories Abstract: Categories enriched in symmetric monoidal categories such as spectra turn up in various places in algebraic topology. Unfortunately these can be difficult to work with in a homotopically meaningful way, which suggests that for many purposes it would be better to work with less rigid structures, where composition is only associative up to coherent homotopy. In this talk I will introduce a general theory of such weak or homotopy-coherent enrichment, built using a non-symmetric variant of Lurie's infinity-operads. I will describe how the correct homotopy theory of these enriched infinity-categories can be constructed as a localization of a homotopy theory defined using infinity-operads (this is joint work with David Gepner), and also discuss some comparison results.