# About the Lectures

John Milnor gave his prize lecture at the University of Oslo. Curtis McMullen and Michael Hopkins were invited speakers. The aim of the Abel Lectures is to give a general audience a glimpse of the mathematics of the Abel Laureate and to convey to the general mathematician the importance and impact of his work. The Science Lecture was delivered by Etienne Ghys.

**Etienne Ghys: A guided tour of the seventh dimension**

One of the most amazing discoveries of John Milnor is an exotic sphere in dimension 7. For the layman, a sphere of dimension 7 may not only look exotic but even esoteric... It took a long time for mathematicians to gradually accept the existence of geometries in dimensions higher than 3. One may wonder how topologists can develop some intuition about these geometries. How can they work "in" these abstract worlds? In this talk, I'll describe some historical developments of higher dimensional geometries, starting of course with the fourth dimension. Then, I'll try to convey some intuition about high dimension. Finally, I want to present Milnor's 7 dimensional jewel, hoping to demystify it. I'll do my best to avoid any kind of sophisticated mathematical background.

**Curtis McMullen: Manifolds, topology and dynamics**

This talk will focus on two fields where Milnor's work has been especially influential: the classification of manifolds, and the theory of dynamical systems. To illustrate developments in these areas, we will describe how topological objects such as exotic spheres and strange attractors arise naturally in the classical world of algebraic varieties and polynomial maps.

**Michael Hopkins: Bernoulli numbers, homotopy groups, and Milnor**

In his address at the 1958 International Congress of Mathematicians Milnor described his joint work with Kervaire, relating Bernoulli numbers, homotopy groups, and the theory of manifolds. These ideas soon led them to one of the most remarkable formulas in mathematics, relating fundamental quantities from three different fields. This talk will describe this formula, and the many remarkable developments associated to each of its terms.