Online Talk 

Elliptic cohomology has many different incarnations, and in this talk, we will discuss the functoriality of some classical and contemporary constructions. In particular, we will describe how spectral algebraic geometry leads to a tangible theory of stable operations on elliptic cohomology, and also to generalised versions of Baker‘s Hecke operators. We will save a bit of time at the end to prove some properties of these operations and discuss some immediate applications.