Degenerations and other orderings on the space of d-dimensional representations of associative algebras

This talk will be centered around the three related partial orderings on the space of d-dimensional representations of a finitely generated associative algebra over an algebraically closed field given by degenerations, what is called virtual degenerations and an order induced by the dimensions of the spaces of homomorphisms. These partial orders are on the outset of a geometrical nature. However, it is usually more convenient to express them in pure algebraic terms using homological properties. Therefore these notions can also be extended to the situation where the field is not algebraically closed, and some of the results can even be extended to the situation where one is considering algebras over a commutative artin ring. For the results which hold true in the most general situation the proofs become most elegant since they depend on using length arguments only and thereby forgetting about the nature of the field altogether. The notions will be introduced by using familiar examples from linear algebra and matrices, and some basic algebra.