Los Encuentros en Teoría de Grupos son organizados bianualmente por la Red Ibérica en Teoría de Grupos. Esta décima edición tendrá lugar en el Instituto Universitario de Investigación de Matemáticas de la Universidad de Sevilla (IMUS), entidad que colabora con la organización.

On limit groups over partially commutative groups
Ilya Kazachkov
(University of Oxford)

The class of limit groups can be likened to the classical coordinate algebras in algebraic geometry. Limit groups admit extremely rich and diverse characterizations and this versatile nature makes them a fine example of the connection between Group Theory, Algebra, Geometry, and Model Theory. Its importance from each of the different perspectives has led to an intensive study of these groups in recent years.

The class of partially commutative groups is a prominent class of groups which is widely studied in different branches of mathematics and computer science. Most recently, partially commutative groups became key to solving some well-known problems in group theory and topology, like Baumslag's conjecture on residual finiteness of one-relator groups with torsion and the virtually fibred conjecture for 3-manifolds.

In this talk, I will describe a universe for the class of limit groups over partially commutative groups. I will then explain how this result can be used to study algorithmic problems. This is joint work in progress with A. Duncan and M. Casals-Ruiz

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