Resumen

In this talk, we discuss mutations of Jacobian algebras. Specifically, we show that (like other representation types) the notions of E-finiteness and E-tameness are invariant under mutations of quivers with potentials. Then we discuss classification of E-finite and E-tame finite-dimensional Jacobian algebras. More precisely, we demonstrate that (resp., except for a few cases,) a finite-dimensional Jacobian algebra J(Q,W) is E-finite (resp., E-tame) if and only if it is g-finite (resp., g-tame), if and only if it is representation-finite (resp., representation-tame), and this holds exactly when Q is of Dynkin type (resp., finite mutation type), as shown by Geiss, Labardini and Schröer. This also proves Demonet's conjecture for Jacobian algebras.