ERC Consolidator Grant · 2016
Galois theory of periods and applications.
A period is a complex number defined by the integral of an algebraic differential form over a region defined by polynomial inequalities. Examples include: algebraic numbers, elliptic integrals, and Feynman integrals in high-energy physics. Many problems in mathematics can be cast as a statement involving periods. A deep idea, based on Grothendieck's philosophy of motives, is that there should be a Galois theory of periods, generalising classical Galois theory for algebraic numbers. This reposes on inaccessible conjectures in transcendence theory, but these can be circumvented in many important cases using an elementary notion of motivic periods. This allows one to set up a working Galois…
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