We are seeking to appoint two Undergraduate Studies Administrators to join our friendly and established Academic Administration team to deliver a varied, complex and stimulating workstream on a permanent, full-time basis. These posts present a great opportunity to get involved in supporting a thriving academic department to achieve its vision of a workplace where all staff and students can achieve their full potential.
I will report on a joint work with Pablo Destic and Nuno Hultberg, about some applications of Globally Valued Fields (GVFs) and I will describe a density result that we needed, which turns out to be connected to Riemann-Zariski and Berkovich spaces.
I will present a recent work with G. Kocharyan, where we show the undecidability of the following two problems: given a finitely generated subgroup G of GL(n,Q), a) determine whether G has a non-identity element whose (i,j) entry is equal to zero, and b) determine whether the stabilizer of a given vector in G is non-trivial. Undecidability of problem b) answers a question of Dixon from 1985. The proofs reduce to the undecidability of the word problem for finitely presented groups.
I'll talk about the Morse local-to-global property and try to convince you that is a good property. There are three reasons. Firstly, it is satisfied by many examples of interest. Secondly, it allows to prove many theorems. Thirdly, it sits nicely in the larger program of classifying groups up to quasi-isometry and it has connections with open questions.
