Intrinsic topologies on groups.

In this talk, we shall discuss intrinsic topologies on groups. In particular, various Zariski topologies generated by certain families of (semi)group polynomials as well as the Markov topology and its semigroup counterparts. We shall answer several questions by Dikranjan, Elliott, Mitchell, Peresse, Toller et al., and complement results of Banakh, Goffer, Greenfeld, Guran and Protasov.