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Monday, March 5, 2018

**Abstract:** I will introduce the idea of multiplicative norms in equivariant and motivic homotopy theories. This is a necessary structure behind the theory of genuine rings, which are supposed to be like E_\infty algebras with additional multiplication structure. For example, in equivariant orthogonal spectra, norms help us establish a model structure on commutative rings that plays well with restriction along the inclusion of a subgroup. In motivic homotopy theory, there is a formulation of norms in terms of infinity-categorical Grothendieck construction. I will show that although this is a nice way to package the story, it is difficult to work with in terms of computations.