the boardman-vogt tensor product of operads encodes the notion of interchanging algebraic structures. a classic result of dunn tells us that the tensor product of two little cube operads is equivalent to a little cube operad with the dimensions added together. as models for $\mathbb{e}_k$-operads, this reflects a defining property of these operads.
in this talk, we will explore some equivariant generalizations to dunn’s additivity. along the way, we will play with little star-shaped operads, question if we really need group representations for equivariant operads, and learn to love (and hate) the tensor product.