Equivariant elliptic cohomology and mapping stacks

Equivariant elliptic cohomology is an equivariant cohomology theory associated to an elliptic curve. After a review of its complexified incarnation, introduced by Grojnowski in 1994, we will give a new perspective on this invariant which involves derived mapping stacks. This naturally gives rise to an algebraic avatar of equivariant elliptic cohomology, that we call (equivariant) elliptic Hochschild homology. Based on joint work with Nicolò Sibilla.