• 14:00-14:50 CM221 Ian Leary (Southampton) Subgroups of almost finitely presented groups

In the late 1940's, Higman-Neumann-Neumann showed that every countable group embeds in a 2-generator group. In the early 1960's Higman characterized which finitely generated groups embed in finitely presented groups: they are the recursively presented groups. `Almost finitely presented' or FP_2 lies somewhere between finitely generated and finitely presented, so it is natural to ask for a characterization of the groups that embed in almost finitely presented groups. I shall define FP_2 groups, state my embedding theorem, and indicate why it has only been discovered 55 years after Higman's embedding theorem.

• 15:05-15:55 CM221 Alexander Veselov (Loughborough) Conway's topograph, PSL(2,Z) and two-valued groups

In 1990s John H. Conway proposed "topographic" approach to describe the values of the binary quadratic forms, which can be applied also to the description of the celebrated Markov triples. In the talk I will review it from the point of view of the theory of two-valued groups. The first important examples of such groups were discovered by Buchstaber and Novikov in algebraic topology, which was developed further by Buchstaber and Rees. Classification results in the theory of two-valued groups emphasize again the role of the modular group PSL(2,Z) and present a novel view on the results of Conway, Markov and Mordell. The talk is based on a joint work with V.M. Buchstaber

16:00-16:30 common room Tea

• 16:30-17:20 CM221 Nick Gilbert (Heriot-Watt University) Presentations and rewriting systems

Presentations of groups by rewriting systems (that is, by monoid presentations), have been fruitfully studied by encoding the rewriting system in a 2-complex - the Squier complex - whose fundamental groupoid then describes the derivation of consequences of the rewrite rules. We describe a reduced form of the Squier complex, investigate the structure of its fundamental groupoid, and show that the approach can also be adapted to presentations of inverse monoids.

There will be a dinner in Durham. Please e-mail Anna Felikson if you plan to attend.

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Room CM221 is on the first floor of the maths department, to the left from the stairs.