Dates: October 19 & 21, 2026

Time: 4:00–5:00 pm ET

Location: Science Center – Zimmer Hall Lecture Hall D and via Zoom Webinar

In-person registration

Webinar Registration

Speaker: Daniel Litt, University of Toronto & Benedict H. Gross Distinguished Visitor, Harvard Mathematics Department

Monday, October 19, 2026

Lecture 1: The arithmetic of differential equations

Abstract: When does an algebraic differential equation have solutions which are themselves algebraic functions? This question goes back at least to Fuchs, in 1875. Its conjectural answer, due to Grothendieck and Katz in the linear case and Ekedahl-Shepherd-Barron-Taylor and Bost in general, situates it as one of number theory. I’ll explain these conjectures and some progress towards them, joint with Josh Lam, for isomonodromy differential equations. This class of differential equations includes, for example, the Painlevé VI equation. This work is in part an excuse to study “motivic” aspects of the space of all algebraic differential equations.

The Monday lecture will be followed by a reception in the Math Dept Austine & Chilton McDonnell Common Room, 4th floor

Wednesday, October 21, 2026

Lecture 2: Non-abelian motives

Abstract: Non-abelian Hodge theory, due to Corlette, Simpson, and others, develops structures on the space of representations of the fundamental group of a complex variety analogous to the structures on its cohomology. Taking this analogy seriously, we should expect *every* structure on cohomology to have an analogue in this “non-abelian” setting. I’ll discuss some work in this direction, as well as a number of related conjectures and new structures whose “abelian” analogues are less clear.

Harvard Mathematics Professor Raoul Bott (1923 – 2005), was a Hungarian-American mathematician known for numerous foundational contributions to geometry in its broad sense. He is best known for his Bott periodicity theorem, the Morse–Bott functions which he used in this context, and the Borel–Bott–Weil theorem.