The arithmetic of differential equations

When can an algebraic differential equation be solved by algebraic functions? Daniel Litt discusses a question dating to Fuchs in 1875 and the number-theoretic perspective supplied by conjectures of Grothendieck and Katz for linear equations, and of Ekedahl, Shepherd-Barron, Taylor and Bost more generally. Joint work with Josh Lam provides progress for isomonodromy differential equations, a class that includes Painlevé VI. These results also motivate the study of motivic structures in the space of algebraic differential equations.