Stable representations of posets and derivation

In this talk, I aim to discuss recent results concerning (semi)-stable representations of posets. Nazarova and Roiter originally defined poset representations as a tool for studying representations of specific algebras and as an approach to the Brauer-Thrall conjecture. They introduced an efficient algorithm, the differentiation procedure, which Kleiner used to describe posets of finite representation types. Later, Gabriel formulated this procedure in a functorial way. Similar to the quiver language approach (as done by King), one can construct a moduli space of poset representations by studying semi-stable objects in corresponding categories. One of the main objectives of the talk is to explain how the differentiation functor acts on stable representations. In certain cases, the obtained results allow us to characterize the Schurian dimensions of the derived posets.