A Kähler group is a group which can be realised as fundamental group of a compact Kähler manifold. I shall begin by explaining why such groups are not arbitrary and then address Delzant-Gromov's question of which subgroups of direct products of surface groups are Kähler. Work of Bridson, Howie, Miller and Short reduces this to the case of subgroups which are not of type $\mathcal{F}_r$ for some $r$. We will give a new construction producing Kähler groups with exotic finiteness properties by mapping products of closed Riemann surfaces onto an elliptic curve. We will then explain how this construction can be generalised to higher dimensions. This talk is independent of last weeks talk on Kähler groups and all relevant notions will be explained.

Let S be a set of monic degree 2 polynomials over a finite field and let C be the compositional semigroup generated by S. In this talk we establish a necessary and sufficient condition for C to be consisting entirely of irreducible polynomials. The condition we deduce depends on the finite data encoded in a certain graph uniquely determined by the generating set S. Using this machinery we are able both to show examples of semigroups of irreducible polynomials generated by two degree 2 polynomials and to give some non-existence results for some of these sets in infinitely many prime fields satisfying certain arithmetic conditions (this is a joint work with A.Ferraguti and R.Schnyder). Time permitting, we will also describe how to use character sum techniques to bound the size of the graph determined by the generating set (this is a joint work with D.R. Heath-Brown).

Code based Cryptography had its beginning in 1978 when Robert McEliece
demonstrated how the hardness of decoding a general linear code up to
half the minimum distance can be used as the basis for a public key
crypto system.  At the time the proposed system was not implemented in
practice as the required public key was relatively large.

With the realization that a quantum computer would make many
practically used systems obsolete coding based systems became an
important research subject in the area of post-quantum cryptography.
In this talk we will provide an overview to the subject.

In addition  we will report on recent results where the underlying
code is a disguised Gabidulin code or more generally a subspace
code and where the distance measure is the rank metric respecively the
subspace distance.