Department of Pure Mathematics, the University of Sheffield.
This was a working meeting with the usual time for participant discussion.
14 May 2009
First I will survey two different notions of equivalence for Seifert surfaces. Then I will show how sutured Floer homology helps in the classification of minimal genus Seifert surfaces under both types of equivalence.
Betti numbers of configuration spaces of mechanical linkages (known also as polygon spaces) depend on a large number of parameters – the lengths of the bars of the linkage.
Motivated by applications in topological robotics, statistical shape theory and molecular biology, we view these lengths as random variables and study asymptotic values of the average Betti numbers as the number of links n tends to infinity. We establish a surprising fact that for a reasonably ample class of sequences of probability measures the asymptotic values of the average Betti numbers are independent of the choice of the measure.
The meeting was partially supported by a Scheme 3 grant from the London Mathematical Society.