ABHYANKAR 82nd BIRTHDAY CONFERENCE SPEAKER: Nathan Moses (Purdue) TITLE: Explicit Multivariable Meromorphic Series ABSTRACT: In pursuit of an explicit representation of meromorphic series in more than one variable, we investigate a lexicographic ordering or the exponents of the variables. This creates a new set of functions, which we call the lexomorphic field, and we compare the lexomorphic field to the meromorphic field. It will be shown that there are infinitely many lexomorphic functions that are algebraically independent over the meromorphic field. This is a joint work with Shreeram Abhyankar and Nicholas Fireman.