Curvature of higher direct images
Friday, 3.2.17, 10:15-11:15, Raum 404, Eckerstr. 1
The differential geometric properties of the classical Hodge bundles were\nfirst studied by Griffiths in the context of the period map and variation of\nHodge structures. This can be used to show the hyperbolicity of the moduli\nspace of polarized Calabi-Yau manifolds. In the talk we consider generalized\nHodge bundles which are twisted by a relative ample line bundle. An intrinsic\ncurvature formula can be given. This generalizes a result of Berndtsson on\nthe\nNakano positivity of the direct image of the ample twisted relative canonical\nbundle of a fibration as well as the curvature formula for higher direct\nimages\nof Schumacher in the canonically polarized case.
tba.
Friday, 10.2.17, 10:15-11:15, Raum 404, Eckerstr. 1
Arithmetic hyperbolicity
Friday, 10.2.17, 10:15-11:15, Raum 404, Eckerstr. 1
I will explain what it means for a variety to be arithmetically hyperbolic. I will then explain that Lang-Vojta's conjecture implies that any variety with an immersive period map is arithmetically hyperbolic. In this joint work with Daniel Loughran we extend the latter statement to algebraic stacks by rigidifying stacky period maps.
Segal approach for algebraic structures
Friday, 10.2.17, 14:00-15:00, Raum 125, Eckerstr. 1
Abstract: The operads are considered today as a conventional tool to describe homotopy algebraic structures. However, for the original problem of delooping, another formalism exists, bearing the name of Segal. This approach has proven advantageous in certain situations, such as, for example, modelling higher categories.\n\nIn this talk, we will discuss how one can illuminate and arguably simplify the proof of Deligne conjecture, the existence of E_2-structure on Hochschild cochains, using the language of Segal objects and operator categories of Barwick. We will then elaborate on our solution to the problem of extending the Segal approach to arbitrary monoidal structures, which employs the language of Grothendieck fibrations and an extension of Reedy theorem to families of model categories.\n\nWhile the second part of the talk is technical, the first one will require only basic knowledge of categories and topology.\n