Canonical paths and single valued iterated integrals

Canonical paths and single valued iterated integrals

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Sasha Shmakov, University of Georgia 

In joint work with Daniel Litt, we define a "canonical path" between any two points of a smooth connected complex variety X so that iterated integrals of 1-forms on X along the "canonical path" are single-valued (unlike iterated integrals along genuine paths). We show that many interesting examples of single-valued functions arise from this formalism. The talk will be self-contained and will discuss the theory of iterated integrals, why we care about them, and the mixed Hodge theory that governs them.