The project described here consists of two related topics. The first is the construction and exploration of
exponential motivic homotopy theory, a variant of motivic homotopy theory for varieties with potentials.
The second is centered around the geometric and homotopical theory of foliations and higher differential
Galois theory, and its application to the study of motives and algebraic cycles. Exponential connections
and the twisted de Rham complex play a central role in both areas.