The next CIRCA Lunchtime Seminar will be on Thursday 15th February in Maths Lecture Theatre C at 1pm. Ian Gent and Markus Pfeiffer will be speaking.
There will be a seminar on Wednesday February 7th, 2018 at 1pm in Lecture Theatre D: Peter Cameron will speak on Reed–Muller codes and Thomas’ conjecture.
Abstract: A countable first-order structure is countably categorical if its automorphism group has only finitely many orbits on n-tuples of points of the structure for all n. (Homogeneous structures over finite relational languages provide examples.) For countably categorical structures, we can regard a reduct of the structure as a closed overgroup of its automorphism group. Simon Thomas showed that the famous countable random graph has just five reducts, and conjectured that any countable homogeneous structure has only finitely many reducts. Many special cases have been worked out but there is no sign of a general proof yet. In order to test the limits of the conjecture, Bertalan Bodor, Csaba Szabo and I showed that a vector space over GF(2) of countable dimension with a distinguished non-zero vector has infinitely many reducts. The proof can most easily be seen using an infinite generalisation of the binary Reed–Muller codes.
There will be a workshop on Groups, Generalisations and Applications at the ICMS in Edinburgh on the afternoon of Wednesday 8 November. Organisers are Jim Howie (Heriot-Watt), Ben Martin (Aberdeen) and Colva Roney-Dougal (St Andrews). Further details are available here.
Martyn Quick attended the joint meeting of the Edinburgh Mathematical Society and Societat Catalana de Matemàtiques (27-29 September 2017) held at the ICMS in Edinburgh. He was invited to speak at the special session on Geometric Group Theory at this meeting and delivered a talk titled “Presentations for Thompson’s group V and its generalisations”. Colva Roney-Dougal and Colin Campbell also attended.
Peter Cameron spoke at a summer school for PhD students on Permutation Groups in Marienheide, Germany, run by the Experimental and Constructive Algebra Group at RWTH Aachen. He gave an introduction to permutation groups and applications to semigroups, and also ran the problem session (which was held outdoors, as the weather was warm).
Ian Gent, Chris Jefferson and Peter Nightingale have shown that the n-Queens puzzle (given a chessboard of size n x n, place n queens so that no two queens attack each other) is NP-Complete. Their paper “Complexity of n-Queens Completion” was published in the Journal of Artificial Intelligence Research on August 30. See these two articles: “Simple” chess puzzle holds key to $1m prize and n-Queens Completion is NP-Complete for further details.