Ivan Fesenko (University of Nottingham )
I.Fesenko@maths.nottingham.ac.uk Some observers might think that modern arithmetic geometry has reached the level when almost everything important which can realistically be done at the level of finite sums has been done; so maybe it is time to try infinite sums and convergence methods (for instance when working with K-groups or homologies of objects which in a sense are complete). It happens that in higher dimensions most groups are not topological groups with respect to the right topology on them; but still the multiplication is sequentially continuous. This could change our point of view on the real significance of harmonic analysis and integration on compact groups. In the talk I shall discuss sequential topologies and their applications in higher local fields and class field theory which sometimes provide the only existing proof of algebraically stated results.