Seminar

Mohamed Barakat: "Doctrine-specific ur-algorithms"

Abstract: Various constructions of categories have a universal property expressing the freeness/initiality of the construction within a specific categorical doctrine. Expressed in an algorithmic framework, it turns out that this universal property is in a certain sense a doctrine-specific “ur-algorithm” from which various known categorical constructions/algorithms (including spectral sequences of bicomplexes) can be derived in a purely computational way. This can be viewed as a categorical version of the Curry-Howard correspondence to extract programs from proofs.

Holger Brenner: "Module schemes in invariant theory"

Abstract: Let G be a finite group acting linearly on the polynomial ring with invariant ring R. If the action is small, then a classical result of Auslander gives in dimension two a correspondence between linear representations of G and maximal Cohen-Macaulay R-modules. We establish a correspondence  for all linear actions, in particular for actions of a group generated by reflections, between representations and objects over the invariant ring by looking at quotient module schemes (up to modification) instead of the modules of covariants.