Tobias Dyckerhoff

TL;DR: In this article, a quasi-equivalence between matrix factorizations and differential graded (dg) derived categories of an explicitly computable dg algebra has been established, and the Hochschild chain and cochain complexes of these categories are derived.

TL;DR: In this paper, the first paper in a series on higher categorical structures called higher Segal spaces is presented. The starting point of the theory is the observation that Hall algebras, as previously studied, are only the shadow of a much richer structure governed by a system of higher coherences captured in the datum of a 2-Segal space.

TL;DR: In this paper, the category of matrix factorizations associated to the germ of an isolated hypersurface singularity is studied and a quasi-equivalence between matrix factorization and the dg derived category of an explicitly computable dg algebra is deduced.

TL;DR: In this article, the Kapustin-Li duality pairing on the morphism complexes in the matrix factorization category of an isolated hypersurface singularity has been studied as an explicit description of a local duality isomorphism obtained by using the basic perturbation lemma and Grothendieck residues.

TL;DR: For a triangulated category A with a 2-periodic dg-enhancement and a marked surface S, the authors showed that F(S,A) admits a canonical action of the mapping class group up to essentially unique Morita equivalence, based on general properties of cyclic 2-Segal spaces.