Geometry of Operads in Equivariant Homotopical Algebra – Location: SC 1312
A space with an action by a finite group -admits corresponding actions on its homotopy, homology, and cohomology groups. In equivariant homotopy theory, by keeping track of fixed point loci of subgroups, one obtains far richer algebraic structures than sets, groups, and rings with -action. We will review this on the levels of equivariant analogues of sets, groups, and rings. Graduating to the topological case, we examine the special roles of little disk and linear isometry operads in equivariant homotopy theory and some of their convenient geometric properties, including some recent discoveries. We will discuss how these properties are particularly helpful for study of Thom spectra and the Fujii—Landweber Real bordism spectrum in particular.