Georgia Institute of Technology College of Sciences

In this talk we discuss a recent paper by Andrew Chan and Diane Maclagan on Groebner bases for fields, where the valuation of the coefficients is taken into account, when defining initial terms. For these orderings the usual division algorithm does not terminate, and ideas from standard bases needs to be introduced. Groebner bases for fields with valuations play an important role in tropical geometry, where they can be used to compute tropical varieties of a larger class of polynomial ideals than usual Groebner bases.