Residual properties of 1-relator groups

This is a survey of two papers joint with A. Borisov and a paper joint with I. Spakulova. It is based on my lectures at the conference "Groups St. Andrews 2009", Bath (August 2009). We prove that almost all 1-related groups with at least 3 generators are virtually residually (finite p-)groups for almost all primes p, and coherent. The proof involves methods from combinatorial group theory (the congruence extension property of certain subgroups of free groups) algebraic geometry (dynamics of polynomial maps over finite and p-adic fields) and probability theory (convex hulls of Brownian bridges).Comment: 19 pages

The Rapid Decay property and centroids in groups

This is a survey of methods of proving or disproving the Rapid Decay property in groups. We present a centroid property of group actions on metric spaces. That property is a generalized (and corrected) version of the property (**)-relative hyperbolicity" from our paper with Cornelia Drutu, math/0405500, and implies the Rapid Decay (RD) property. We show that several properties which are known to imply RD also imply the centroid property. Thus uniform lattices in many semi-simple Lie groups, Artin groups of large type and the mapping class groups have the centroid property. We also present a simple "non-amenability-like" property that follows from RD, and give an easy example of a group without RD and without any amenable subgroup with superpolynomial growth, some misprints in other sections are corrected.Comment: 27 pages; v2: Section 2 corrected, added a reference to Olshansii's preprint arXiv:1406.0336 in Section 4. v3: Section 3.6 on graph products of groups is added. v3: Small correction in the proof of Theorem 2.3, estimate slightly improve

Current Issues in Evaluating Structural Reforms within the Lisbon Process; comments and recommendations about the Lisbon Methodology (LIME) Working Group. Bruegel Policy Contribution/February 2007

In 2005, shortly after taking office, the Barroso Commission replaced the failed Lisbon process initiated in 2000 (Lisbon 1) by a new one (Lisbon 2) which gave centre stage to the National Reform Programmes (NRPs). A year later, in a paper written at the request of the Austrian Presidency, Jean Pisani-Ferry and I critically reviewed the new process and concluded that “the outcome is mixed at best”. In particular, we emphasised that “There is no explicit methodology behind the evaluation of the NRPs by the Commission.