Conference abstracts

Plenary talk

July 28, 10:30 ~ 11:20

## $A_{\infty}$-algebras in representation theory and homological algebra

### Université Grenoble Alpes - Universidad de Buenos Aires - CONICET, France - Argentina   -   Estanislao.Herscovich@ujf-grenoble.fr

In this talk I will recall the basic theory of $A_{\infty}$-algebras, which were introduced by J. Stasheff in 1963. Even though they appeared within the realm of algebraic topology, I will present several examples of their use in representation theory and in homological algebra. In particular, in the last part of the talk I will show that the torsion theory of $A_{\infty}$-algebras naturally allows to compute the cup and cap products on Hochschild cohomology and homology of any nonnegatively graded connected algebra, respectively.