05.04.2016 um 14:15 Uhr in 69/E15:
Holger Brenner/Oliver Röndigs (Universität Osnabrück)
Introduction to the cancellation problem
12.04.2016 um 14:15 Uhr in 69/E15:
Ismaël Soudères (Universität Osnabrück)
Overview over the proof
19.04.2016 um 14:15 Uhr in 69/E15:
Markus Wageringel (Universität Osnabrück)
The counter-example in positive characteristic ( after Gupta)
26.04.2016 um 14:15 Uhr in 69/E15:
Sean Tilson (Universität Osnabrück)
The very weak 5-lemma
10.05.2016 um 14:15 Uhr in 69/E15:
Girja Tripathi (Universität Osnabrück)
17.05.2016 um 14:15 Uhr in 69/E15:
Konrad Voelkel (Universität Freiburg)
From division algebras to motivic cellularity
We will recast how the classical division algebras of real, complex, quaternionic and octonionic numbers give rise to projective spaces in algebraic geometry. The affine algebraic varieties that we construct via Jordan algebras are exactly the infinite families in the classification of simple rank 1 spherical homogeneous spaces, which gives us a connection to representation theory. We discuss ways to endow these spaces with motivic cell structures which give rise to motivic decompositions and result in connectivity properties. We use the Jordan algebra viewpoint to construct equivariant completions and use a Dynkin-diagram description to compute the motives.
24.05.2016 um 14:15 Uhr in 69/E15:
Oliver Röndigs (Universität Osnabrück)
The Brower degree in motivic cohomology theory
31.05.2016 um 14:15 Uhr in 69/E15:
Hongyi Chu (Universität Osnabrück)
07.06.2016 um 14:15 Uhr in 69/E15:
Tom Bachmann (Ludwig-Maximilians-Universität München)
SH(k)2- and the Real Étale Topology
All objects in SH(k)2-(the subcategory of 2-local and eta-local objects in the stable motivic homotopy category) satisfy real étale descent. We explain what this means and give a - perhaps slightly idiosyncratic - proof of this fact. We also explain how to obtain the following corollary: the Ayoub-Morel category of "motives without transfers" and the Ananyevskiy-Levine-Panin category of Witt motives coincide away from 2 and eta: DA(k)2-=DM_W(k)2.
14.06.2016 um 14:15 Uhr in 69/E15:
Markus Spitzweck (Universität Osnabrück)
12.07.2016 um 14:15 Uhr in 69/E15:
Elden Elmanto (Northwestern University)
Nonabelian Poincare Duality in A1-Homotopy
In recent years, there has been at least two instances when homotopical ideas have been useful in studying geometry, construed broadly. The first is through a homology theory for En algebras (factorization homology), as developed by Lurie and Ayala-Francis, which is used to study manifolds and configuration spaces of them. The second is through A1-homotopy theory, as developed by Morel and Voevodsky, which brings topological thinking into algebraic geometry.
This talk is a progress report on a fusion of these two areas. We will motivate why such an endeavor might be profitable, with reference to classical theorems in topology (Dold-Thom, Atiyah-Bott). We then give a definition of factorization homology in this context, and sketch the first calculation: an A1-local analogue of nonabelian Poincare duality, inspired by recent work of Gaitsgory-Lurie. This talk will include a brief sampler to the techniques of factorization homology and the A1 homotopy theory of schemes.
19.07.2016 um 14:15 Uhr in 69/E15:
David Carchedi (George Mason University)
A new approach to etale homotopy theory
Etale homotopy theory, as originally introduced by Artin and Mazur in the late 60s, is a way of associating to a suitably nice scheme a pro-object in the homotopy category of spaces, and can be used as a tool to extract topological invariants of the scheme in question. It is a celebrated theorem of theirs that, after profinite completion, the etale homotopy type of an algebraic variety of finite type over the complex numbers agrees with the homotopy type of its underlying topological space equipped with the analytic topology. We will present work of ours which offers a refinement of this construction which produces a pro-object in the infinity-category of spaces (rather than its homotopy category) and applies to a much broader class of objects, including more general schemes and all algebraic stacks. We will also present a generalization of the previously mentioned theorem of Artin-Mazur, which holds in much greater generality than the original result.