Abstract:The classical (multiple) polylogarithm functions play, through their special values, a prominent role in a number of arithmetic questions related to periods and motives. Crucially, these functions satisfy an algebraic differential equation, the KZ equation, from which many of their properties are derived. In particular, they can be written as iterated integrals of certain algebraic di...
PrerequisiteMulti-variable Calculus, Basic Partial Differential Equation, Basics of Riemannian Geometry(optional)AbstractThe course introduces hyperbolic partial differential equations and conservation laws from both historical and modern perspectives, focusing on important examples rather than general theory. The classical concepts such as characteristics and Riemann invariant plays an indispe...