\( \newcommand{\SL}{\operatorname{SL}} \newcommand{\Pin}{\operatorname{Pin}} \newcommand{\ZZ}{\mathbb{Z}} \)

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



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.