From logarithms to motives

Berkay Kebeci
Koç Üniversitesi, Türkiye

A period is a number that can be expressed as an integral of a rational function over a domain cut out by polynomial inequalities with rational coefficients. Among the most interesting examples are polylogarithms (evaluated at rational numbers). For a more geometric viewpoint, we will examine Aomoto polylogarithms.

Motives are expected to form a (conjectural) Tannakian category, proposed by Grothendieck as a universal framework for Weil cohomology theories. Motives provide a conceptual way to organize periods by their cohomological origin. In this talk, we will consider motives in the sense of Nori.

Finally, we will discuss a conjecture of Beilinson predicting that the Hopf algebra of mixed Tate motives is isomorphic to the bialgebra of Aomoto polylogarithms.