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Department of Mathematical Sciences

Seminar Archives

On this page you can find information about seminars in this and previous academic years, where available on the database.

Pure Maths Colloquium: Betti numbers of random manifolds

Presented by Michael Farber, University of Durham

13 November 2006 16:00 in CM221

In various fields of applications, such as topological robotics,
configuration spaces of mechanical systems depend on a large
number of parameters, which typically are only partially known and
often can be considered as random variables. Since these
parameters determine the topology of the configuration space, the
latter can be viewed in such a case as a random topological
space or a random manifold. One of the most natural notion to investigate is the mathematical
expectation of the Betti numbers of random manifolds. Clearly,
these average Betti numbers encode valuable information for
engineering applications; for instance they provide an average
lower bound for the number of critical points of a Morse function
(i.e. observable) on such manifolds.

In the talk I will present a recent joint work with T. Kappeler
in which we studied mathematical expectations of Betti numbers of
configuration spaces of planar linkages, viewing the lengths of
the bars of the linkage as random variables. Our main result gives
explicit asymptotic formulae for these expectations in the case of two distinct probability measures describing the
statistics of the length vectors when the number of links tends to
infinity.

Contact anna.felikson@durham.ac.uk for more information