This expository paper is a slightly expanded version of the final talk I gave at the group rings conference celebrating the 25th anniversary of the Institute of Mathematics and Statistics at the University of São Paulo. The talk concerned an application of ultraproducts to the solution of the semiprimitivity problem for group algebras K[G] of locally finite groups G. It explained why the specia...

Group signatures are a modern cryptographic primitive that allow a member of a specific group (e.g., “the White House staff” or “employees of Corporation X that publish press releases”) to sign messages on behalf of the group as a whole; i.e., without revealing their individual identities and thus providing them with a certain degree of anonymity and privacy. They have quite a number of potenti...

In this paper we compute in some new cases the cardinalities of fibers certain natural fibrations that appear analysis configuration space Heisenberg ring. This is done by means cyclic group actions on subsets restricted partitions.