From 29th July-2nd August Rosemary Bailey, Peter Cameron, and Siavash Lashkarighouchani attended the British Combinatorial Conference at the University of Birmingham. Peter organised a mini-symposium on Designs and Latin Squares, at which Rosemary spoke on ‘Substitutes for the non-existent square lattice design for 36 treatments’. Peter also contributed a talk on ‘Hall-Paige and synchronization’. At the conference business meeting, Peter was re-elected chair of the British Combinatorial Committee, a position he has held for 25 years.
CIRCA members took part in the Research Day, held in the School of Mathematics and Statistics on 24th January 2019. The speakers were Rosemary Bailey, Collin Bleak, Peter Cameron, Martyn Quick, Louis Theran, and Peter Cameron. Olexandr Konovalov and Michael Torpey presented a poster.
The next major release of GAP, version 4.10.0, has been announced in November 2018. You can find further information and links to the release announcement and an overview of new features in this post on the CoDiMa website.
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.
In the coming semester, CIRCA lunchtime seminars will be on Thursday 1pm in odd weeks in Maths Theatre C (note the change of venue). The first one will be on Thursday, February 1st. Jon Fraser and Shayo Olukoya will be speaking.