Primitives of algebraic functions
Speaker:
Jacob Tsimerman, University of Toronto
Date and Time:
Friday, December 17, 2021 - 12:30pm to 1:30pm
Location:
Fields Institute, Room 230
Abstract:
Given an algebraic function $f_0(x)$, when can a primitive of it be constructed by means of algebraic oper-ations and taking primitives of some other given algebraic functions $f_1(x),\dots,f_m(x)$? When the only primitive allowed is the logarithm, this is the question of elementary integrability and a decision procedure has been given by Risch. We will present a general decision procedure for deciding this question, based on a new result of Ax-Schanuel type for primitives of differential forms on curves.
This is Joint work with Jonathan Pila.