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WS 2017/2018

07.11.2017 um 14:15 Uhr in 69/E15:

Martin Frankland (Universität Osnabrück)

Towards the dual motivic Steenrod algebra in positive characteristic

14.11.2017 um 14:15 Uhr in 69/E15:

Manfred Stelzer (Universität Osnabrück)

Andre-Quillen cohomology and simplicial coalgebras

28.11.2017 um 12:15 Uhr in 69/E15:

Dr. Peter Arndt (Heinrich-Heine-Universität Düsseldorf)

From GAG to NAG: On Durov's and Haran's approaches to F1-geometry

I will give a quick introduction to Durov's "Generalized Algebraic Geometry" (GAG) and Haran's "Non-additive Geometry" (NAG), both of which are generalizations of algebraic geometry in which one glues more general objects than rings. I will present the compactifications of Spec Z that both authors construct. There is an inclusion from Durov's into Haran's F1-schemes, known to both authors. I will construct a left adjoint to this inclusion and compute it for Haran's compactification of Spec Z.

28.11.2017 um 14:15 Uhr in 69/E15:

Dr. Frederico Binda (Universität Regensburg)

Cycles with modulus, regulators and applications

In this talk we will survey some recent results involving the so-called (higher) Chow groups with modulus for a pair (X,D), where X is a smooth variety over a field k and D is a (possibly non reduced) effective Cartier divisor on X, generalizing Bloch-Esnault additive Chow groups studied by Rülling, Park and Krishna as well as the Chow groups of zero cycles with modulus introduced by Kerz and Saito. These groups are a modified version of Bloch's higher Chow groups and are related to several non A¹-homotopy invariant objects.
This is a joint work with Shuji Saito.

05.12.2017 um 14:15 Uhr in 69/E15:

Glen M. Wilson (Universitetet Oslo)

Motivic homotopy groups of spheres over finite fields

12.12.2017 um 14:15 Uhr in 69/E15:

Paul Arne Østvær (University of Oslo)

Motivic Landweber exact theories and etale cohomology

19.12.2017 um 14:15 Uhr in 69/E15:

Arun Kumar (Universität Osnabrück)

Hermitian K-theory

09.01.2018 um 14:15 Uhr in 69/E15:

Hadrian Heine (Universität Osnabrück)

Infinity categories with duality

16.01.2018 um 14:15 Uhr in 69/E15:

Toan M. Nguyen (Universität Osnabrück)

Orbifold motivic cohomology and K-theory

In this talk, I will discuss about new algebraic invariants for algebraic orbifolds: orbifold motivic cohomology and K-theory. These invariants come out as a consequence of the obstruction bundles and the virtual fundamental classes in Gromov-Witten theory. I will also explain how these invariants relate to motivic cohomology and K-theory of (crepant) resolutions of singularities of the coarse moduli spaces of orbifolds.

23.01.2018 um 14:15 Uhr in 69/E15:

Somayeh Habibi (Institute for Research in Fundamental Sciences, Tehran, Iran)

Motives of fibrations and application to the moduli of G-Shtukas

30.01.2018 um 14:15 Uhr in 69/E15:

Bogdan Gheorghe (Wayne State University, USA)

A topological construction of cellular motivic homotopy over Spec C

This is current work in progress with Achim Krause, Dan Isaksen and Nicolas Ricka. Motivic homotopy theory over the complex numbers is becoming a popular tool for attacking classical problems in algebraic topology. For example, recent work of Isaksen & collaborators extended the calculation of classic stable homotopy groups of spheres, and Behrens & collaborators made progress towards the telescope conjecture at p=2 and n=2. In this talk, I will show a construction of the category of motivic spectra over Spec C, independent from Morel and Voevodsky's construction, in fact, even without mentionning schemes at all. We will illustrate how this new model seems more appropriate for computations, by computing the Steenrod algebra. 

06.02.2018 um 14:15 Uhr in 69/E15:

Drew Heard (Haifa University, Israel)

Stratification for homotopical groups

We generalize Quillen's F-isomorphism theorem, Quillen's stratification theorem, Chouinard's theorem, and the finite generation of cohomology rings from finite groups to homotopical groups. As a consequence, we show that the category of module spectra over C*(BG,\F_p) is stratified for any p-local compact group G, thereby giving a support-theoretic classification of all localizing subcategories of this category. No prior knowledge of stratifications or the theory of homotopical groups will be assumed. Joint work with Barthel, Castellana, and Valenzuela

13.02.2018 um 14:15 Uhr in 69/E15:

José Carrasquel Vera (Adam Mickiewicz University of Poznań, Poland)

Rational sectional category à la Sullivan

Schwarz's sectional category is an invariant of the homotopy type of maps which generalizes Lusternik-Schnirelmann category. If we restrict it to some category of rational spaces, thanks to Sullivan's theory of rational homotopy, sectional category can be described in terms of algebraic objects called Sullivan models.
In this talk we introduce Sullivan models and outline how they can be used to model sectional category.