Fibered Derivators, (Co)homological Descent and the Six-Functor Formalism
Friday, 8.11.13, 10:15-11:15, Raum 404, Eckerstr. 1
Derivators have been introduced by Grothendieck, as one of his last mathematical contributions, to simplify, extend, and conceptually clarify the\nnotions of derived and triangulated categories. Extended to the context of fibered (multi-)categories (e.g. any kind of sheaves of abelian groups on spaces, schemes, stacks etc.)\nthe notion allows for a neat solution to problems of cohomological descent as well as homological descent. This gives an elegant way\nof extending the six-functor formalism of Grothendieck (which encodes, among other things, dualities like e.g. Serre duality, Poincar'e-Verdier duality)\nto stacks.
Nichthomogene affine Flächen mit riesiger Automorphismengruppe
Friday, 15.11.13, 10:15-11:15, Raum 404, Eckerstr. 1
A diagram algebra for categorifying gl(1|1)
Friday, 22.11.13, 10:15-11:15, Raum 404, Eckerstr. 1
Friday, 29.11.13, 10:15-11:15, Raum 404, Eckerstr. 1
The geometry of singularities in the Minimal Model Program and applications to singular spaces with trivial canonical class
Friday, 29.11.13, 10:15-11:15, Raum 404, Eckerstr. 1
This talk surveys recent results on the singularities of\nthe Minimal Model Program and discusses applications to the study of\nvarieties with trivial canonical class. Comparing the étale fundamental\ngroup of a klt variety with that of its smooth locus, we show that any\nflat holomorphic bundle, defined on the smooth part of a projective\nklt variety is algebraic and extends across the singularities. This\nallows to generalise a famous theorem of Yau, which states that any\nRicci-flat Kähler manifold with vanishing second Chern class is an\nétale quotient of a torus.\n\nThis is joint work with Daniel Greb and Thomas Peternell\n