Effective Bounds For Finite Differential-Algebraic Varieties (Part I)
University of California, Berkeley
Given a differential algebraic variety over a partial differential field, can one give bounds for the degree of the Zariski closure which depend only on the order and degree of the differential polynomials (but not the parameters) which determine the variety? We will discuss the general theory of prolongations of differential algebraic varieties as developed by Moosa and Scanlon, and use this theory to reduce the problem to a combinatorial problem (which will be discussed in detail in the second part of the talk). Along the way we will give numerous examples of the usefulness of the result, some of an arithmetic flavor. We will also describe some other applications of the theory of prolongations.
This is joint work with Omar Sanchez.