# Geometry and Topology Seminar

## Warwick Mathematics Institute, Term II, 2012-2013

Please contact Saul Schleimer or Caroline Series if you would like to speak or suggest a speaker.

 Thursday January 24, 15:00, room MS.03 Alexander Wickens (Warwick) A topological proof of Klarreich's theorem Abstract: Klarreich's theorem, that the Gromov boundary of the curve complex is homeomorphic to the space of ending laminations, relates two topological objects but was previously proved using Teichmüller theory. I will sketch a new proof that uses train tracks and is almost entirely topological

 Thursday January 31, 15:00, room MS.03 Brian Bowditch (Warwick) Coarse median spaces Abstract: By a "coarse median" we mean a ternary operation on a path metric space, satisfying certain conditions which generalise those of a median algebra. It can be interpreted as a kind of non-positive curvature condition and is applicable, for example, to finitely generated groups. It is a consequence of work of Behrstock and Minsky that the mapping class group of a surface satisfies this condition. We aim to give some examples, results and applications concerning coarse medians.

 Thursday February 7, 15:00, room MS.03 TBA (TBA) TBA Abstract: TBA

 Thursday February 14, 15:00, room MS.03 Brian Bowditch (Warwick) Coarse median spaces: II Abstract: The second half.

 Thursday February 21, 15:00, room MS.03 Rafael Torres (Oxford) Smooth structures on non-orientable 4-manifolds and orientation-reversing involutions Abstract: We describe how to construct inequivalent smooth structures for every closed non-orientable 4-manifold with fundamental group of order two that admits a Pin+-structure. A study of the smooth structure on the universal cover of the manifolds constructed yield examples of exotic involutions. These results serve as a good excuse to review and exemplify the process of unveiling exotic smooth structures.

 Thursday February 28, 15:00, room MS.03 Richard Evan Schwartz (Brown and Oxford) The density of shapes in barycentric subdivision Abstract: One can apply barycentric subdivision, iteratively, to a simplex and produce an infinite collection of smaller simplices. One can ask whether this process produces a dense set of shapes of simplices. The answers is yes in dimension 2, thanks to Beardon, Barany and Carne, yes in dimensions 3 and 4, thanks to me, and otherwise not known. I'll sketch proofs in the 3 cases I know, and explain how the problem and its solution are related to CAT(0) geometry, hyperbolic geometry, and sphere coverings.

 Thursday March 7, 15:00, room MS.03 Danielle O'Donnol (Imperial) Legendrian Graphs Abstract: We investigate Legendrian graphs in $(\mathbb{R}^3, \xi_{\tiny\mbox{std}})$. We extend the classical invariants, Thurston-Bennequin number and rotation number to Legendrian graphs. In this talk I will discuss a number of realization and classification results.

 Thursday March 14, 15:00, room MS.03 Agelos Georgakopoulos (Warwick) A new homology for infinite graphs and metric continua Abstract: We generalise a fundamental graph-theoretical fact, stating that every element of the cycle space of a graph is a sum of edge-disjoint cycles, to arbitrary continua. To achieve this we replace graph cycles by topological circles, and replace the cycle space of a graph by a new homology group for continua which is a quotient of the first singular homology group $H_1$. This homology seems to be particularly apt for studying spaces with infinitely generated $H_1$, e.g. infinite graphs or fractals.

Information on past talks. This page was last touched Sunday, 6 January 2013 18:03:49 GMT.