**Seminario teoría de grupos UAM-ICMAT**

**Miercoles 16 de Octubre, 12:30, Aula 420 (cambio de Aula), UAM **

**Ashot Minasyan (U. Southampton)**

** Title: Virtual retraction properties in groups**

** Abstract. A subgroup $H$ is said to be a virtual retract of a group $G$ if $H$ is a retract of some finite index subgroup $K$ of $G$ (i.e., $H leqslant K$ and there is a homomorphism $phi:K to H$ such that that $phi(h)=h$ for all $h in H$). Virtual retracts are important in Group Theory, as they inherit many properties of the ambient group. They play a prominent role in the theory of virtually special groups of Haglund and Wise, which was fundamental in Agol's resolution of the virtual Haken Conjecture. **

** During the talk I will give examples of discrete groups in which ``many'' subgroups are virtual retracts. Various applications and related results will also be discussed.**