I will present a joint work with Michael Lipnowski in which we describe an
algorithm to compute the cohomology of an arbitrary compact arithmetic
manifold equipped with the action of Hecke operators, and analyse its
complexity. A key ingredient is to use the equidistribution of Hecke orbits
to produce a good cover of the manifold.
Links:
[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/node/3444
[3] http://www.mpim-bonn.mpg.de/node/246