Abstract: We talk on efficiently computing resultants of composed polynomials. By the resultant of several polynomials in several variables (one fewer variables than polynomials) we mean an irreducible polynomial in the cofficients of the polynomials that vanishes if they have a common zero. By a composed polynomial we mean the polynomial obtained from a given polynomial by replacing each variable by a polynomial.

We report on four results:

• M. Minimair, "Dense Resultant of Composed Polynomials",
• H. Hong and M. Minimair, "Sparse Resultant of Composed Polynomials I",
• M. Minimair, "Sparse Resultant of Composed Polynomials II" and
• M. Minimair, "Sparse Resultant under Vanishing Coefficients".

The preprints are available at http://www.math.ncsu.edu/~mminima .