On the converse to Eisenstein’s last theorem

I’ll explain a conjectural characterization of algebraic solutions to (possibly non-linear) algebraic differential equations, in terms of the arithmetic of the coefficients of their Taylor expansions, strengthening the Grothendieck-Katz p-curvature conjecture. I’ll give some evidence for the conjecture coming from algebraic geometry: in joint work with Josh Lam, we verify the conjecture for algebraic differential equations (both linear and non-linear) and initial conditions of algebro-geometric origin. In this case the conjecture turns out to be closely related to basic conjectures on algebraic cycles, motives, and so on.

Daniel has also kindly agreed to give a pretalk on algebraic differential equations from 2:00-2:45pm in SC 530. We especially encourage younger students to attend and ask questions!