GTA Seminar: Tang -- Short Curves on Flat Surfaces and the Curve Graph

Speaker: Dr. Robert Tang (Sydney)

http://homepages.warwick.ac.uk/~mariam/

Time: Thursday, March 6, 12NOON--1PM. 

Room: Carslaw 707A. 

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Title: Short Curves on Flat Surfaces and the Curve Graph

Abstract: on a flat torus, any simple closed curve has an 
arbitrarily short geodesic representative upon applying a 
suitable SL(2,R)-deformation to the flat metric. For a 
given flat metric on higher genus surface, however, the 
same is not true. We will study the set of curves which 
can be made short on some metric obtainable under some 
SL(2,R)-deformation. This ’short curve’ set has some 
interesting coarse geometric properties when viewed as 
a subset of the curve graph - a combinatorial tool which 
has been used to study mapping class groups, Teichmuller 
space and hyperbolic 3-manifolds. I will also describe 
nearest point projection properties to the short curve 
set within the curve graph. This is a joint work with 
Richard Webb. 

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Seminar website:

http://www.maths.usyd.edu.au/u/SemConf/Geometry/