Hablicsek Márton (Leiden/BME): Categorical shadows of logarithmic Hochschild (co)homology

Hochschild homology is a foundational invariant for associate algebras, schemes, stacks, etc. For instance, for smooth, complex, projective varieties X, Hochschild homology and its variants, like cyclic homology, are closely related to Hodge cohomology and to de Rham cohomology. In this talk, via a geometric approach, we extend Hochschild homology to logarithmic schemes, in particular to compactifications, i.e, to pairs (X,D) where X is a smooth and proper variety and D is a simple normal crossing divisor. Even though the definition is not categorical, this geometric approach allows us to see categorical shadows: 1) formulae for blow-ups, orbifolds, 2) extension to cyclic homology, 3) some weak functoriality with respect to Fourier-Mukai transformations. 

The work is joint with Leo Herr and Francesca Leonardi.