Călin Chindriş
University of Missouri, Columbia MO, USA

The Tame-Wild Dichotomy, a fundamental result due to Y. Drozd, asserts that every finite-dimensional algebra is of tame or wild representation type, and these types are mutually disjoint. This talk is aimed at capturing the Tame-Wild dichotomy within the framework of Geometric Invariant Theory ("GIT"). To this end, we introduce the class of GIT-finite algebras (among which are all representation-finite algebras) and that of GIT- tame algebras (among which are all GIT-finite algebras and all tame algebras). We will give a characterization of the GIT-finiteness/GIT-tameness of an algebra in terms of its weight spaces of semi-invariants/moduli spaces of representations. We will also present a string of conjectures about GIT-finite/GIT-tame algebras, Schur-finite/Schur-tame algebras, and rigidity in $\tau$-tilting theory.