Global equivariant Thom spectra

The aim of this talk is to explain a systematic formalism to construct and manipulate Thom spectra in global equivariant homotopy theory. The upshot is a colimit preserving symmetric monoidal global Thom spectrum functor from the infinity-category of global spaces over BOP to the infinity-category of global spectra. Here BOP is a particular globally-equivariant refinement of the space Z x BO, which simultaneously represents equivariant K-theory for all compact Lie groups.

I plan to give two applications of the formalism. Firstly, a specific and much studied morphism  mU--> MU between two prominent equivariant forms of the complex bordism spectrum is a localization, in the infinity-category of commutative global ring spectra, at the "inverse Thom classes". Secondly, by joint work with Gepner and Nikolaus, the infinity-category of global spectra can be described as a pushout of parameterized symmetric monoidal infinity categories along the global Thom spectrum functor.