
Arbeitsgruppen Navigation Arbeitsgruppe Prof. Dr. Rüdiger Göbel Dr. Daniel Herden Dipl.-Math. Christian Müller Dipl.-Math. Katrin Leistner Jasmin Matz PD Dr. Lutz Strüngmann Dr. Stefan Friedenberg Ehemalige Mitglieder Ehemalige Arbeitsgruppe Dr. Sebastian Pokutta Dr. Simone Wallutis Dr. Nicole Hülsmann

PD Dr. Lutz Strüngmann Research Visits Publications Projects Attended conferences Organised conferences Talks and Preprints Curriculum Vitae Teaching Evaluation Private News/Press

Here are my recent projects and those which are submitted

The Interplay Between Algebra and Logic

DFG-Research project with Professor Ralf Schindler (Münster), Dr. Gunter Fuchs (Münster) and Professor Rüdiger Göbel (Duisburg-Essen, Campus Essen)

In this project we focus on the interplay between algebra and set theory. Over the last decades algebraists have used infinite combinatorics and set-theoretic as well as model-theoretic methods to solve long-standing open problems in algebra by showing their consistency with, respectively independence of the usual set theory given by the Zermelo-Fraenkel axioms and the axiom of choice (ZFC). The construction (for instance by the method of forcing) of models of set theory in which large cardinals exist (respectively do not exist) or certain combinatorial properties like uniformization principles, prediction principles etc. hold, played an essential role. Very often algebraic properties are equivalent to set-theoretic axioms or to certain cardinal conditions like the (non-)validity of the (generalized) continuum hypothesis. It is the aim of this project to further investigate this interplay between algebra and set theory. In particular we shall focus on the structure of infinite rank Butler modules, large cardinals, the automorphism tower problem and dual groups in various
models of ZFC obtained by (proper, improper) forcing.

For the duration of 2 years (2008-2010) this project is supported by the German Research Foundation. We will have an advanced seminar with the University of Münster that takes place every two weeks on fridays during the semester. We take turns which means that we will be in Essen and Münster every 4 weeks.

Solving Problems from Module Theory using Recent Results from Logic and Model Theory

GIF-Research project with Professor Saharon Shelah (Jerusalem) and Professor Rüdiger Göbel (Duisburg-Essen, Campus Essen)

The project is based on various problems from module theory which are of interest to algebraists working on modules of infinite rank over commutative rings. It is the aim to apply a machinery of (recently) developed results and techniques from from axiomatic set theory in connection with infinite combinatorial arguments. Main topics are as follows:
o The theory of E(R)-algebras and its natural environment
o The existence of absolutely indecomposable groups/modules
o Cotorsion modules, classes and pairs
o Singular compactness for universal modules
o Commutative noetherian rings and slender modules
o On minimal groups and automorphism groups
o אn-free abelian groups and modules
o Questions on the existence of domains R with strange module decompositions.

For the duration of three years this project is supported by the German Israeli Foundation GIF (2010-2012).

PPP-project funded by the DAAD (Germany) and AWTR (Chech Republic) on Methods from model theory, logic and set theory in the structure theory of modules over commutative rings

The project focuses on the following topics:
o The investigation of cellular covers and related topics from homotopy theory;
o E-rings (including the non-commutative ones, using recent deep results of S.Shelah);
o Model theory of groups (connecting logic with fundamental problems of classification of Abelian groups);
o Model and set-theoretic methods for investigation of the roots of Ext (abstract elementary classes of the roots and the problem of their finite character, bounds for deconstruction of the roots of Ext);
o Cotorsion modules and cotorsion additive functors (structure, generalizations to localization in triangulated categories);
o Drinfeld modules (structure and approximation properties of flat Mittag-Leffler modules, connections to non-commutative geometry).

This project is supported by the DAAD for two years (2010-2011).

How to measure the complexity of algebraic problems and how to solve them by flipping a coin

ERC-Starting grant. Application submitted in October 2010.

In this project we intend to find new ways to measure the complexity of algebraic problems. In particular we focus on infinte structures and try to extend an approach based on Borel equivalence relations and Borel reduction as well as combinatorial methods. As a simplest case we will consider structures that are presentable by finite automata.

Knowing the complexity we then try to solve problems by using a random approach; thus simplifying algebraic methods and tools in order to obtain random versions that apply to more general settings.

Team members are gabor Braun, Daniel Herden, Katrin Leistner, Jan Saroch, and Jan Stovicek

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