In this first talk, I will explain the classical equivalence between 2-dimensional topological quantum field theories and commutative Frobenius algebras, touching also to operads and props.

Families of groups such as symmetric groups or general linear groups, and
families of spaces such as con guration spaces or certain moduli spaces of manifolds,
display a stability phenomenon in their homology. I'll describe this phenomenon and give an idea about how such theorems are proved.

Reading List:

First three sections of
 O. Randall-Willliams and N. Wahl, \Homological stability for autormorphism
groups", Advances in Mathematics, Vol. 318 (2017), pp. 534 - 626.