The Tenth Barcelona Weekend in Group Theory took place on May 27th, 2015.
- 10:00 Montse Casals (Euskal Herriko Unibertsitatea, Universidad del País Vasco, Bilbao, Spain)
Embeddability between right-angled Artin groups and its relation to model theory and geometry.
Abstract: In this talk we will discuss when a right-angled Artin group is a subgroup of another one, and explain how this basic algebraic problem may provide answers to questions in geometric group theory and model theory such as classification of right-angled Artin groups up to quasi-isometries and universal equivalence.
- 11:15 Jim Howie (Heriot-Watt University, Edinburgh, Scotland)
Weight of groups and surgery on knots.
Abstract: The weight of a group G is the smallest integer n such that some subset of size n generates G as a normal subgroup of itself. In particular, any n-knot group has weight 1 for any n, as it is the normal closure of a meridian element. Hence, many problems arising from knot surgery reduce to questions about whether certain groups can have weight 1. I will talk about some interesting examples of such questions.
- 12:30 Yash Lodha (EPFL, Lausanne, Switzerland)
A nonamenable finitely presented group of piecewise projective homeomorphisms.
Abstract: I will describe a finitely presented subgroup of Monod’s group of piecewise projective homeomorphisms of the real line. This provides a new example of a finitely presented group which is nonamenable and yet does not contain a nonabelian free subgroup. The example is torsion free and of type F∞. A portion of this is joint work with Justin Moore.
- 16:00 Jianchun Wu (Soochow University, Suzhou, China)
- 17:15 Lawrence Reeves (Melbourne University, Melbourne, Australia)
Coxeter groups and limit roots.
Abstract: Limit roots were recently introduced by Hohlweg, Labbe and Ripoll to study the asymptotic distribution of roots in a based root system. I will describe some recent work with Xiang Fu on the set of limit roots associated to an infinite Coxeter group.
Fixed subgroups are compressed in surface groups.
Abstract: For a compact surface $\Sigma$ (orientable or not, and with boundary or not) we show that the fixed subgroup, $\fix\B$, of any family $\B$ of endomorphisms of $\pi_1(\Sigma )$ is compressed in $\pi_1(\Sigma )$ i.e., $\rk(\fix\B)\leqslant \rk(H)$ for any subgroup $\fix\B\leqslant H\leqslant \pi_1(\Sigma )$. On the way, we give a partial positive solution to the inertia conjecture, both for free and for surface groups. We also investigate direct products, $G$, of finitely many free and surface groups, and give a characterization of when $G$ satisfies that $\rk(\fix \phi)\leqslant \rk(G)$ for every $\phi\in \aut(G)$.