17 03 2023 1 Andrei Jaikin- On recent advances on the profiniterigidity of free and surface groups.

I will discuss recent results about the Profinite Rigidity of free and surface groups. In particular I will explain the proofs of the following two results:
1) Let φ : F → G be an injective map from a free group to a residually finite group inducing an isomorphism of profinite completions. Then φ is an isomorphism.
2) Let G be a residually finite one-relator group having the same profinite completion as a surface group. Then G is surface. (joint with Ismael Morales)