Logarithmic Hochschild homology and cohomology

In this thesis, we explore a Hochschild homology and cohomology-like notion for logarithmic schemes. We prove preliminary results towards the definition of these invariants, prove the logarithmic analogue of known results in Hochschild homology and cohomology, and specialise to the case of logarithmic schemes arising from pairs. Then we restrict to a special case of derived equivalences to prove derived invariance. Finally, we explore the situation for orbifolds, providing explicit computations some examples.