On the Converse to Eisenstein's Last Theorem

Explore the intricacies of Eisenstein's last theorem and its converse in this comprehensive lecture by Daniel Litt from the Institute for Advanced Study. Delve into the 1852 proof by Eisenstein regarding algebraic functions and their Taylor expansions. Examine ongoing joint research with Josh Lam, investigating the extent to which the converse of this theorem holds. Discover the conjecture that functions satisfying non-linear algebraic ODEs with Taylor expansion coefficients in finitely-generated Z-algebras are algebraic. Learn about proven cases for linear ODEs, including Picard-Fuchs equations with algebraic cycle initial conditions. Investigate results for non-linear ODEs, focusing on "isomonodromy" ODEs with "Picard-Fuchs" initial conditions. Explore motivic corollaries and their connection to the Grothendieck-Katz p-curvature conjecture in this in-depth Joint IAS/PU Arithmetic Geometry presentation.