The so-called Ax-Lindemann theorem asserts that the Zariski closure of a certain subset of a homogeneous variety (typically abelian or Shimura) is itself a homogeneous variety. This theorem has recently been proven in full generality by Klingler-Ullmo-Yafaev and Gao. This statement leads to a variety of questions about topological and Zariski closures of certain sets in  homogeneous varieties which can be approached by both ergodic and o-minimal techniques.  In a series of recent papers with E. Ullmo, we formulate conjectures and prove a certain number of results  of this type.  In this talk I will present these conjectures and results and explain the ideas of proofs
 

One of many overlaps between logic and topology is duality: Stone duality links Boolean algebras with zero-dimensional compact Hausdorff spaces, and gives a useful topological way of describing certain phenomena in first order logic; and there are generalisations that allow one to study infinitary logics also. We will look at a couple of ways in which this duality theory is useful.'

The smooth representation theory of a p-adic reductive group G with characteristic zero coefficients is very closely connected to the module theory of its (pro-p) Iwahori-Hecke algebra H(G). In the modular case, where the coefficients have characteristic p, this connection breaks down to a large extent. I will first explain how this connection can be reinstated by passing to a derived setting. It involves a certain differential graded algebra whose zeroth cohomology is H(G). Then I will report on a joint project with R. Ollivier in which we analyze the higher cohomology groups of this dg algebra for the group G = SL_2.

Inverse problems are ubiquitous in many areas of Science and Engineering and, once discretised, they lead to ill-conditioned linear systems, often of huge dimensions: regularisation consists in replacing the original system by a nearby problem with better numerical properties, in order to find meaningful approximations of its solution. In this talk we will explore the regularisation properties of many iterative methods based on Krylov subspaces. After surveying some basic methods such as CGLS and GMRES, innovative approaches based on flexible variants of CGLS and GMRES will be presented, in order to efficiently enforce nonnegativity and sparsity into the solution.

Thin glass sheets are used in smartphone, battery and semiconductor technology, and may be manufactured by first producing a relatively thick glass slab (known as a preform) and subsequently redrawing it to a required thickness. Theoretically, if the sheet is redrawn through an infinitely long heater zone, a product with the same aspect ratio as the preform may be manufactured. However, in reality the effect of surface tension and the restriction to factories of finite size prevent this. In this talk I will present a mathematical model for a viscous sheet undergoing redraw, and use asymptotic analysis in the thin-sheet, low-Reynolds-number limit to investigate how the product shape is affected by process parameters. 

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.