Abstract:
We study the behavior of the Nil-subgroups of K-groups under localization. As a consequence we obtain that the relative assembly map from the family of finite subgroups to the family of virtually cyclic subgroups is rationally an isomorphism. Combined with the equivariant Chern character we obtain a complete computation of the rationalized source of the K-theoretic assembly map in terms of group homology and the K-groups of finite cyclic subgroups.

Abstract:
For a space X, we define Frobenius and Verschiebung operations on the nil-terms NA^{fd} (X) in the algebraic K-theory of spaces, in three different ways. Two applications are included. Firstly, we obtain that the homotopy groups of NA^{fd} (X) are either trivial or not finitely generated as abelian groups. Secondly, the Verschiebung defines a Z[N_x]-module structure on the homotopy groups of NA^{fd} (X), with N_x the multiplicative monoid. We also we give a calculation of the homotopy groups of the nil-terms NA^{fd} (*) after p-completion for an odd prime p as Z_p[N_x]-modules up to dimension 4p-7. We obtain non-trivial groups only in dimension 2p-2, where it is finitely generated as a Z_p[N_x]-module, and in dimension 2p-1, where it is not finitely generated as a Z_p[N_x]-module.

Abstract:
Recent developments in the measurement of precision electroweak measurements are summarised, notably new results on the mass of the top quark and mass and width of the W boson. Predictions of the Standard Model are compared to the experimental results which are used to constrain the input parameters of the Standard Model, in particular the mass of the Higgs boson. The agreement between measurements and expectations from theory is discussed. Invited talk presented at the EPS HEP 2007 conference Manchester, England, July 19th to 25th, 2007

Abstract:
The status of published and preliminary precision electroweak measurements as of winter 2002/03 is presented. The new results on the mass of the W boson as measured at LEP-2 and on atomic parity violation in Caesium are included. The experimental results are compared with the predictions of the minimal Standard Model and are used to constrain its parameters, including the mass of the Higgs boson. The agreement between measurements and expectations from theory is discussed.

Abstract:
This paper contains a review of recent precision measurements of electroweak observables and resulting tests of the electroweak Standard Model.

Abstract:
Recent published and preliminary precision electroweak measurements are reviewed, including new results on the mass of the top quark and mass and width of the W boson. The experimental results are compared with the predictions of the Standard Model and are used to constrain its free parameters, notably the mass of the Higgs boson. The agreement between measurements and expectations from theory is discussed. (Invited talk presented at the EPS HEPP conference, Lisboa, Portugal, July 21st to 27th, 2005)

Abstract:
The status of precision electroweak measurements as of summer 2002 is reviewed. The recent results on the anomalous magnetic moment of the muon and on neutrino-nucleon scattering are discussed. Precision results on the electroweak interaction obtained by the experiments at the SLC, LEP and TEVATRON colliders are presented. The experimental results are compared with the predictions of the minimal Standard Model and are used to constrain its parameters, including the mass of the Higgs boson. The final LEP results on the direct search for the Higgs boson of the Standard Model are presented.

Abstract:
We show that the outer automorphism group of a polycyclic-by-finite group is an arithmetic group. This result follows from a detailed structural analysis of the automorphism groups of such groups. We use an extended version of the theory of the algebraic hull functor initiated by Mostow. We thus make applicable refined methods from the theory of algebraic and arithmetic groups. We also construct examples of polycyclic-by-finite groups which have an automorphism group which does not contain an arithmetic group of finite index. Finally we discuss applications of our results to the groups of homotopy self-equivalences of K(\Gamma, 1)-spaces and obtain an extension of arithmeticity results of Sullivan in rational homotopy theory.

Abstract:
We consider discontinuous operations of a group $G$ on a contractible $n$-dimensional manifold $X$. Let $E$ be a finite dimensional representation of $G$ over a field $k$ of characteristics 0. Let $\mathcal{E}$ be the sheaf on the quotient space $Y=G \setminus X$ associated to $E$. Let $H^{\bullet}_{\textbf{!}}(Y;\mathcal{E})$ be the image in $H^{\bullet}(Y;\mathcal{E})$ of the cohomology with compact support. In the cases where both $H^{\bullet}_{\textbf{!}}(Y;\mathcal{E})$ and $H^{\bullet}_{\textbf{!}}(Y;\mathcal{E}^*)$ ($\mathcal{E}^*$ being the the sheaf associated to the representation dual to $E$) are finite dimensional, we establish a non-degenerate duality between $H^{m}_{\textbf{!}}(Y;\mathcal{E})$ and $H^{n-m}_{\textbf{!}}(Y;\mathcal{E}^{\ast})$. We also show that this duality is compatible with Hecke operators.

Abstract:
A group G is called subgroup conjugacy separable (abbreviated as SCS), if any two finitely generated and non-conjugate subgroups of G remain non-conjugate in some finite quotient of G. We prove that the free groups and the fundamental groups of finite trees of finite groups with some normalizer condition are SCS. We also introduce the subgroup into-conjugacy separability property and prove that the above groups have this property too.