Part I: What is tilting theory? Part II: Convex geometry for fans of tilting theory. In Part I, we will use modules over a polynomial ring in one variable to illustrate how quiver representations provide a concrete method for understanding
I will describe a connection between multiple polylogarithms on tori and the Steinberg module of rationals, and show how this connection can be used to prove that all multiple polylogarithms of a given weight and depth can be expressed via