Hodge theory and formality
Freitag, 1.12.17, 10:15-11:15, Hörsaal FRIAS, Albertsstr. 19
Given a differential graded algebra or any algebraic structure\nin chain complexes, one may ask if it is quasi-isomorphic to its\nhomology equipped with the zero differential. This property is called\nformality and has important consequences in algebraic topology. For\ninstance, if the de Rham algebra of a manifold is formal, then certain\nhigher operations in cohomology, called Massey products, are known to\nvanish. In this talk, I will first discuss the notion of formality and\nits consequences in different algebraic and topological contexts. Then,\nI will explain how mixed Hodge theory and Galois actions can be used to\nprove formality, for algebraic structures arising from the category of\ncomplex algebraic varieties.
Recent results and open problems about Oeljeklaus-Toma manifolds
Freitag, 8.12.17, 10:15-11:15, Hörsaal FRIAS, Albertsstr. 19
Oeljeklaus - Toma manifolds are compact complex manifolds associated to number fields with at least one real and and at least one complex place. The construction is similar to tori, but it involves not only the lattice of integers but also a suitable group of units. We investigate how the number-theoretic properties influence their geometric properties: existence of special metrics, existence of closed subvarieties, etc. The talk is based mainly on joint work with L.Ornea and M. Verbitsky.
1-Motives
Donnerstag, 14.12.17, 11:15-12:15, Hörsaal FRIAS, Albertstr. 19
In this expository talk we want to present Deligne's category of 1-motives and its realisations. This ties up\nwith the talk of Wüstholz on Friday, but the two talks\nwill be independent of each other.
Period domains
Freitag, 15.12.17, 10:30-11:30, Hörsaal FRIAS, Albertstr. 19