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 Postdoc 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
Generalizing 2-vector spaces in the sense of Kapranov-Voevodsky
Searching for bad groups in the sense of Hopkins-Kuhn-Ravenel

At the moment, I am trying to find out whether Chetard's saturated and Totaro's geometric filtration on represention rings agree. I am also interested in formal verification via Isabelle/HOL both in math and in software engineering. Feel free to reach out if you are curious about any of that!

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 GitHub
"The Chow Ring of the 2-Sylow Subgroup of GL(4,2)" A computation of the mod-2 Chow ring of the classifying space of Syl_2 GL(4,2), extending methods of Burt Totaro to a more general computation strategy arXiv
"A Chow Ring of a Finite Group not generated by Chern Classes" A computation of the mod-2 Chow ring of SmallGroup(32,44), which is not generated by Chern classes, work in progress
"Integral Chow rings of Classifying Spaces. A computation of all intergal Chow rings of finite groups of order smaller than 32 with one exception, work in progress
"mu-recursive" An Isabelle/HOL project with the aim of formalizing µ-recursive functions with bounded minimization, providing a compiler to a simple stack machine and providing a formal verification of the correctness of the compiler, work in progress GitHub

Impressum