Georgia Institute of Technology College of Sciences

I will talk about how tropical geometry can be used for implicitization and elimination problems. Implicitization is the problem of finding the defining equations (implicit equations) of an algebraic variety from a given parameterization. Elimination is the problem of finding the defining equations of a projection of an algebraic variety. In some instances such as the case when the polynomials involved have generic coefficients, we give a combinatorial construction of the tropical varieties without actually computing the defining polynomials. Tropical varieties can then be used to compute invariants of the original varieties.