Carlos D'Andrea, U.C. Berkeley
Classical resultants and subresultants of two univariate polynomials were originally introduced by Sylvester in 1853. They have been used in order to give an efficient and parallelizable algorithm for computing the greatest common divisor of two polynomials.
Recently, subresultants have been extended to the multivariate case and have been used in computational algebra for polynomial system solving as well as for providing explicit formulas for the representation of rational functions. The study of their properties is an active area of research.
In this talk, we will review the definition and basic properties of multivariate subresultants as well as some of their applications.