The Seventeenth Colloquiumfest was centered around algebra and model theory.

Arno Fehm: Elementary equivalence of profinite groups
Abstract: Jarden and Lubotzky had shown in 2008 that if two finitely generated profinite groups are elementarily equivalent in the language of groups, then they are in fact already isomorphic. Around the same time, Frohn had studied the theory of abelian profinite groups in the Cherlin-van den Dries-Macintyre language of inverse systems and reached a similar conclusion for so-called small abelian profinite groups. I will explain these results and discuss some related questions concerning elementary equivalence and isomorphism.

Lorna Gregory: Ziegler spectra of modular lattices?
Abstract: The Ziegler spectrum of a ring R is a topological space attached to its category of right R-modules. I will explain how to construct the Ziegler spectrum of a ring from its lattice of pp-formulas in 2 variables. The construction indicates that it is likely to also work for a larger class of modular lattices. We hope that leaving the context of modules over a ring will give us greater insight into various open questions about Ziegler spectra of rings. This is work in progress.

Immi Halupczok: A new notion of minimality in valued fields
Abstract: In the reals, o-minimality has been very successful. Various analogues exist in various valued field setting. I will present a new trial to come up with a good notion of minimality in valued fields, which hopefully one day will work in any valued field where model theory is known to behave well.

Franz-Viktor Kuhlmann: Valuations on rational function fields that are invariant under permutation of the variables - and the unusual story behind them
Abstract: We study and characterize the class of valuations on rational functions fields that are invariant under permutation of the variables and can be extended to valuations with the same property whenever a finite number of new variables is adjoined. The Gauss valuation is in this class, which constitutes a natural generalization of the concept of Gauss valuation. We will also tell the unusual story that triggered this joint work with Katarzyna Kuhlmann and Catalina Visan (Bucharest).

Rob Leek: Convergence properties in high-order objects: a structural viewpoint
Abstract: Topological spaces that are constructed from categorial dualities typically consist of high-order objects, such as ultrafilters of a Boolean algebra or prime ideals of a commutative ring. As such, convergence properties in these spaces are often difficult to parse in algebraic language. In this talk I will introduce spoke systems, which characterise certain convergence properties (radial, Frechet-Urysohn) in all topological spaces. Using these, I will show how translate these properties into corresponding algebraic properties of the structure.

Dugald Macpherson: Metrically homogeneous graphs
Abstract: A countably infinite graph is `metrically homogeneous' if it is homogeneous in the sense of Fraisse once binary relation symbols are added to be interpreted by distance between vertices; that is, any isomorphism between finite induced subgraphs (in the language with these distance predicates) extends to an automorphism. I will describe joint work with Amato and Cherlin classifying metrically homogeneous graphs of diameter 3.

David Towers: The generalised nilradical of a Lie algebra
Abstract: A solvable Lie algebra L has the property that its nilradical N contains its own centraliser. This is interesting because gives a representation of L as a subalgebra of the derivation algebra of its nilradical with kernel equal to the centre of N. We consider how to find a generalised nilradical with this same property for any Lie algebra.

Marcus Tressl: Interpreting formulas of abelian L-groups in latices of zero sets
Abstract: An abelian L-group is essentially a group of functions from a set X to the ordered abelian group of real numbers that is closed under taking finite infima and suprema. E.g. G could be the semi-linear functions defined in the plane or the continuous functions on a topological space. I will show how the group can be interpreted (in a weak sense) in its lattice of zero sets and give applications, using model theory of these lattices.

Last update: May 2, 2024 --------- created and maintained by Franz-Viktor Kuhlmann