North British Geometric Group Theory Seminar

Wednesday 31st October 2018, University of Newcastle

• Bob Gilman (Stevens Tech, Hoboken NJ), Algorithmic randomness in group theory

  We apply Kolmogorov complexity to group theory. (1) It is well known that two randomly chosen permutations generate the alternating or symmetric group with asymptotic probability 1. This is bad news if you would like to sample 2-generator permutation groups. We present a sampling method which avoids this problem. (2) Generic case complexity is often used to estimate the efficacy of group theoretic algorithms, but these estimates may depend on the choice of generators. We discuss an alternative which is not sensitive to choice of generators.

• David Hume (Oxford), The geometric subgroup problem

  One central aspect of Geometric Group Theory is the study of finitely generated groups; specifically relating their algebraic and geometric properties. Geometrically, we consider groups up to quasi-isometry and we possess a wealth of tools to distinguish different quasi-isometry classes of groups. Algebraically, groups are studied via their subgroup structue. However, there are very few geometric properties of groups which pass to all their (finitely generated) subgroups. I will introduce a new collection of geometric properties which are inherited by subgroups, and demonstrate that they do give new insight, particularly in the case of subgroups of hyperbolic groups.

• Ana Lecuona (Glasgow), Complexity and Casson-Gordon invariants

  Homology groups provide bounds on the minimal number of handles needed in any handle decomposition of a manifold. We will use Casson-Gordon invariants to get better bounds in the case of 4-dimensional rational homology balls whose boundary is a given rational homology 3-sphere. This analysis can be used to understand the complexity of the discs associated to ribbon knots in S^3. This is a joint work with P. Aceto and M. Golla.

• 1200 onwards. Informal meeting for lunch, at Courtyard restaurant on the University of Newcastle campus (That's in the Old Library Building, and the entrance is opposite Merz Court. If you walk onto campus from haymarket metro, you need to walk through the archway and into the main quadrangle, then out of it on the far righthand side; the door you want is immediately on your right).
• 1330-1430 Bob Gilman
• 1445-1545 David Hume
• 1545-1615 Tea
• 1615-1715 Ana Lecuona
• 1745 onwards. Early dinner at restaurant close to station. (I suggest the Ottoman in Clayton street, but am open to suggestions.)

  Lectures will be in room TR4 on the fourth floor of the Herschel buildings (home of the School of Mathematics and Statistics, next to Haymarket) at Newcastle University.

  Please let us know if you plan to stay for dinner, since the restaurant needs an idea of numbers.

  The meeting is funded by grants from the London Mathematical Society and the Glasgow Mathematical Journal Learning and Research Support Fund.

  

  Organiser: Sarah Rees (SarahDOTReesATnclDOTacDOTuk), Tel: 0191 208 7236