Abstract: The notion of discriminant plays an important role in various algebraic,
geometric and combinatorial settings. In the area of Noncommuntative
Algebra, discriminants provide an invariant with applications to the
representation theory of the algebra, the automorphism and isomorphism
problems for families of algebras, and the study of maximal orders. We
will present three general results for computing discriminants of
noncommutative algebras based on (1) Poisson geometry, (2) Cluster
Algebras and (3) Representation Theory. Some of applications to concrete
families of algebras will be also described. The first 2 theorems are
joint work with Bach Nguyen and Kurt Trampel (LSU), and the third with
Kenneth Brown (Glasgow Univ).