Recent Developments in the Inverse Galois Problem

Part A. Explicit quotients of $G_{\mathbb Q}$ and $G_{\bar {\mathbb F}(t)}$: Explicit Galois realization of $C_{16}$-extensions of $A_n$ and $S_n$ by T. Crespo Topics in Galois theory by M. D. Fried Parametric solutions of embedding problems by B. H. Matzat Some projective linear groups over finite fields as Galois groups over $\mathbb Q$ by A. Reverter and N. Vila $K$-Admissibility of metacyclic $2$-groups by S. Liedahl and J. Sonn Embedding problems and the $C_{16}\rightarrow C_8$ obstruction by J. R. Swallow Cyclic covers of $\mathbb P^1$ and Galois action on their division points by H. Volklein Part B. Moduli spaces and the structure of $G_{\mathbb Q}$: Introduction to modular towers: Generalizing dihedral group-modular curve connections by M. D. Fried On Galois actions on profinite completions of braid groups by Y. Ihara and M. Matsumoto On the Galois image in the derivation algebra of $\pi_1$ of the projective line minus three points by M. Matsumoto Part C. The structure of $G_{\mathbb R(t)}, G_{\bar {\mathbb F}_q(t)}$, and $G_{\mathbb Q_p(t)}$: Covers of $\mathbb P^1$ over the $p$-adics by P. Debes Existence de points $p$-adiques pour tout $p$ sur un espace de Hurwitz by B. Deschamps Stable models by E. Dew Tout groupe fini est un groupe de Galois sur $\mathbb Q_p(T)$, d'apres Harbater by Q. Liu Specializations of coverings and their Galois groups by W. K. Seiler Rational points and canonical heights on K3-surfaces in $\mathbb P^1\times \mathbb P^1\times \mathbb P^1$ by L. Wang Part D. Group theory and geometric monodromy groups: Mathieu group coverings and linear group coverings by S. S. Abhyankar Fundamental groups for arbitrary categories by P. Feit Monodromy groups of branched coverings: The generic case by R. M. Guralnick and M. G. Neubauer Fundamental groups and embedding problems in characteristic $p$ by D. Harbater On free profinite groups of uncountable rank by M. Jarden Primitive monodromy groups of polynomials by P. Muller.