For free atomic Hermitian operators p and q, the boundary heuristic for the Brown measure of X = p + iq implies the boundary is an algebraic curve, and the paper provides an explicit resultant-based algorithm to produce the defining polynomial.
Support of the Brown measure of the product of a free unitary Brownian motion by a free self-adjoint projection
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Quaternionic Green's Function and the Brown Measure of Atomic Operators
For free atomic Hermitian operators p and q, the boundary heuristic for the Brown measure of X = p + iq implies the boundary is an algebraic curve, and the paper provides an explicit resultant-based algorithm to produce the defining polynomial.