Alexander Ziegler

Arbeitsgruppe Topologie
Fachgruppe Mathematik und Informatik
Fakultät für Mathematik und Naturwissenschaften
Bergische Universität Wuppertal
Gaußstraße 20
42119 Wuppertal

Office: G16.06 at Campus Grifflenberg
Email: lastname@math.uni-wuppertal.de
Phone: +49 202 439-3478

Hi there! I am a PhD student in the topology group of the Bergische Universität Wuppertal. My advisor is Prof. Dr. Matthias Wendt.

I am currently trying to understand more about cohomology classes of classifying spaces of finite groups that are not (transfers of) Chern classes of representations. My goal is to relate these classes to a 2-categorical analogue of representations called 2-representions.

This endeavor comes in several flavors:

Furthering computational methods for the Chow ring of a motivic classifying space
Computing 2-representations of finite groups in search for pathological 2-characters
Searching for bad groups in the sense of Hopkins-Kuhn-Ravenel
Understanding the classifying space of 2-vector bundles to find a sensible notion of characteristic classes of 2-representations

At the moment I am trying to learn spectral algebraic geometry in the hopes of recasting the classifying space of 2-vector bundles as the ku-valued points of some spectral classifying stack.

My favorite finite group is SmallGroup(32,8).

Projects and Preprints

"Gamma Graded Character Rings" a tool set written in Sage and GAP to compute the associated graded algebra to the γ-filtration or geometric filtration on the complex representation ring of a finite group, work in progress
"Computing CH*(B(Syl_2(GL_4(F_2))))/2" a computation of the mentioned Chow ring including examples for (singular) cohomology classes that are not transfers of Chern classes of representations, work in progress

Impressum