North British Geometric Group Theory

Spring meeting 2010, York, Wednesday March 10

Timetable

• 13:00: Lunch, Roger Kirk building.
• 14:15: Tom Brady (Dublin). Climbing elements in finite Coxeter groups.
  • Suppose we have a fixed total order on the reflections of a finite Coxeter group W. We will call an element w in W a climbing element if w has a reduced expression whose corresponding sequence of reflections is increasing in the total order. We give a characterisation of climbing elements for certain fixed total orders. This is joint work with Aisling Kenny and Colm Watt.
• 15:30: Caroline Series (Warwick). Top terms of trace polynomials in Kra's plumbing construction.
  • Kra's plumbing construction manufactures a surface S by `plumbing' together a suitable family of triply punctured spheres. This gives a natural pants decomposition of S, together with a projective structure for which the associated holonomy representation ρ depends on the `plumbing parameters' τ. In particular Trace ρ(γ), for γ in the fundamental group of S, is a polynomial in the τ. Simple curves on S can be described in terms of their Dehn-Thurston coordinates relative to the pants decomposition. After explaining the construction, we show that if γ is simple there is a remarkably easy formula relating the coefficients of the top terms of ρ(γ) and its Dehn-Thurston coordinates. The proof involves a rather interesting result on matrix products. Joint work with Sara Maloni.
• 16:30 coffee
• 17:15: Thomas Mueller (Queen Mary). A class of groups universal for free R-tree actions.
  • I report on a new construction in group theory giving rise to a kind of continuous analogue of free groups. More explicitly, given any (discrete) group G, we construct a group RF(G) equipped with a natural (real-valued) Lyndon length function, and thus with a canonical action on an associated R-tree XG, which turns out to be transitive. Analysis of these groups RF(G) is difficult. However, conjugacy of hyperbolic elements is understood, as are the centralizers and normalizers of hyperbolic elements; moreover, we show that RF-groups and their associated R-trees are universal (with respect to inclusion) for free R-tree actions. Furthermore, we determine |RF(G)|, and that non-trivial normal subgroups of RF(G) contain a free subgroup of rank |RF(G)|, as well as a number of further structural properties of RF(G) and its quotient by the span of the elliptic elements. 
• 18:45 Dinner 

All talks are in Vanburgh College room V/120

Geography

• Click here for a web-friendly map of the University of York main (Heslington) campus. The Mathematics department is located in James (formerly called Goodricke) College near the center-left of the map. The Roger Kirk Centre, adjacent, is the amenity building for the college. 
• All the talks will take place in Vanbrugh College room V/120, which you can find on this map.
• Coffee will be in the Mathematics department coffee room, labelled J2 on this map.
• The map also highlights the car parks. Parking is available in any of the four General Car Parks (North, South, West or Central), of which South is most convenient, but be sure to feed the Pay and Display machine: £2 for 4 hours or £4 for 10 hours.
• Click here for a map of the university in relation to the local main roads.
• Click here for a map of the university in relation to the City of York, including the location of York railway station. The distance from the station to campus is about 1.5 miles and is walkable. Alternatively the bus you want is the FTR (the long purple bendy one) which stops just outside the station. Get off on University Road under the bridge. It runs roughly every 10 minutes and costs (approximately) £1.80 for a single and £3.90 return.

Earlier meetings at York

• GeNERators I, November 2003. Ilya Kazatchkov (Omsk), Ian Leary (Southampton), Martin Bridson (Imperial).
• GeNERators IV, December 2004. Steve Pride (Glasgow), Daan Krammer (Warwick), Dan Segal (Oxford).
• NBGGT, December 2008. Sarah Rees (Newcastle), Eddy Godelle (Caen), Meinholf Geck (Aberdeen).