FB 6 Mathematik/Informatik

Institut für Mathematik


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SS 2018

17.04.2018 um 14:15 Uhr in 69/E15:

Lyne Moser (École polytechnique fédérale de Lausanne)

Injective and projective model structures on enriched diagram categories

R. Garner, K. Hess, M. Kedziorek, E. Riehl, and B. Shipley have developed methods to induce model structures from an adjunction. The injective and projective model structures on categories of diagrams in accessible model categories can be induced from specific Kan extension adjunctions using these methods. In this talk, I will explain how to adapt this result to an enriched setting, in order to prove the existence of injective and projective model structures on categories of enriched diagrams in enriched model categories, which satisfy some enriched accessibility and enriched local presentability conditions.

22.05.2018 um 14:15 Uhr in 69/E15:

Brad Drew (Universität Freiburg)

Lisse motives and their underlying variations of mixed Hodge structure

Using techniques of higher algebra, we construct a realization functor from the full subcategory of Voevodsky's category of mixed motives over a complex variety S spanned by the lisse objects to the category of variations of mixed Hodge structure on S. After reinterpreting some classical results in mixed Hodge theory through the lens of this realization functor, we will explore some connections with the more general theory of mixed Hodge modules.

29.05.2018 um 14:15 Uhr in 69/E15:

Daniel Harrer  (Universität Essen)

An explicit realization functor between motives

We construct an explicit comparison functor from Voevodsky's geometric motives to the bounded derived category of Nori motives. It is triangulated, monoidal and compatible with the Betti realization on both sides. The argument uses the following three main ingredients:
(a) translating finite correspondences to multi-valued morphisms (after Rydh, Suslin, Voevodsky and others),
(b) a theory of étale/Nisnevich covers on diagrams of finite correspondences (generalizing results by Friedlander),
(c) Nori's (co)homological analogue of topological cell-structures on both varieties and finite correspondences (extending on work by Nori, Huber and Müller-Stach).

05.06.2018 um 14:15 Uhr in 69/E15:

Adeel Khan (Universität Regensburg)

The motivic Pontrjagin-Thom isomorphism

We will explain an analogue in motivic homotopy theory of (a generalized form of) the Pontrjagin-Thom isomorphism, computing stable homotopy groups of spheres in terms of framed bordisms.

12.06.2018 um 14:15 Uhr in 69/E15:

Konrad Voelkel (Universität Osnabrück)

Log differentials

03.07.2018 um 14:15 Uhr in 69/E15:

Manh Toan Nguyen (Universität Osnabrück)

Kato-Nakayama spaces

In this talk, I will discuss about the construction of the Kato-Nakayama space (or Betti realization) associated to a fine and saturated log scheme X which is locally of finite type over the field of complex numbers.
This is a topological space whose singular cohomology computes the log étale cohomology and log de Rham cohomology of X.

10.07.2018 um 14:15 Uhr in 69/E15:

Holger Brenner (Universität Osnabrück)

Crystalline cohomology