Non-abelian motives
Seminar · Oct 21, 2026
Harvard Center of Mathematical Sciences and Applications — Math Science Lectures in Honor of Raoul Bott
Seminar, Hosted by Harvard Center of Mathematical Sciences and Applications — Math Science Lectures in Honor of Raoul Bott
The arithmetic of differential equations
University of Toronto; Benedict H. Gross Distinguished Visitor, Harvard Mathematics Department
Abstract
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.
Topics
- algebraic differential equations, broader topic: differential equations
- algebraic functions, search World Wide
- Fuchs, search World Wide
- isomonodromy differential equations, broader topic: differential equations
- Painlevé VI, search World Wide
- motivic structures, search World Wide
- linear equations, search World Wide