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.

Symmetric groups, braid groups, certain mapping class groups and general linear groups are examples of families of groups known to display a stability phenomenon in their homology. In my talks, I will give an answer to the following questions: What do these examples have in common? When should one expect that a family of groups satisfies homological stability? and how does one check that such a family does indeed stabilize?