Shadows and THH of ∞-Categories

Topological Hochschild Homology (THH) was originally conceived as a generalization of Hochschild homology to ring spectra. However, it has since been generalized to many other settings. Here are just some of the many examples:
> A generalization of THH to enriched categories and their profunctors that has been used, particularly by Ponto, in the study of fixed point theorems.
> An ∞-categorical approach to THH of ring spectra, which for example has been used successfully by Scholze and Nikolaus in their study of cyclotomic actions.
> Finally, there is now a notion of THH of enriched ∞-categories, due to Berman.

In this talk we want to discuss ongoing work, joint with Kathryn Hess, with the goal of reconciling the various notions of THH using an ∞-categorical approach. In particular, after giving some motivation, we will focus on comparing the axiomatic approach to THH introduced by Ponto, shadow functors, with the enriched ∞-categorical approach to THH due to Berman. 

If time permits, we will illustrate how the ∞-categorical approach can help us recover classical results, such as Morita invariance of THH, using far more formal techniques.