The notion of a discriminant plays an important role in various settings in algebraic number theory, algebraic geometry, combinatorics, and noncommutative algebra. We will give an overview of this subject and present three general results on discriminants of noncommutative algebras arising from (1) Poisson geometry, (2) cluster algebras and (3) representation theory.

This talk is based on joint work with Ken Brown (Glasgow), Bach Nguyen (Temple) and Kurt Trampel (LSU).