Pham Ngoc Ánh: Factorizations of noncommutative polynomials and finite-dimensional representations over digraphs

This is a report on a work in progress with F. Mantese on a threefold relations between noncommutative polynomials and either finite-dimensional representations of quiver algebras or finitely presented modules of finite length over the extended digraphs. The result extends the classical factorization theory of polynomials in one variable to one in several non-commuting variables.