Tue, 5 April 2022, 1 pm MDT

For a while now, Peter Mayr and I have been looking at properties of direct and subdirect products in algebra, often motivated by some well known or particularly nice results from combinatorial group theory. The topics include finite generation, finite presentability, residual finiteness, infinite subdirect powers, etc. A fairly rich landscape has emerged over the years. Perhaps unsurprisingly the most general results can be obtained in the context of congruence permutable or modular varieties. This then leaves semigroups outside, and I have been working on such questions in parallel with some of my PhD students. In this talk I will try to sketch this landscape, not so much by means of a systematics introduction, but a few selected strands, results and comparisons.