# Abel Lectures at the University of Oslo

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.

**Abel Lectutes and Science: Lecture Place: The University of Oslo **

**Time: 25th of May**

10.00 Welcome by Rector Ole Petter Ottersen, University of Oslo and Øyvind Østerud, President of the Norwegian Academy of Science and Letters

10.10 John Milnor, "Spheres"

11.00 Coffee break

11.30 Curtis McMullen, "Manifolds, topology and dynamics"

12:30 Lunch

13.30 Michael Hopkins, "Bernoulli numbers, homotopy groups, and Milnor"

14:15 Coffe break

14:30 Science Lecture: Etienne Ghys, "A guided tour of the seventh dimension"

15.15 Closing session

### The Abel lectures 2018

Abel Laureate Robert Langlands gave his prize lecture titled "*On the geometric theory" *at the University of Oslo on the 23th of May. John Rognes, chair of the Abel committee, introduced Langlands to an almost full auditorium. Langlands' lecture was followed by two others talks, by Jim Arthur and Edward Frenkel. Watch the lectures live

### Robert P. Langlands received the Abel Prize from H.M. King Harald

In the University Aula in Oslo, surrounded by Munch's paintings and a diverse mathematical audience, Robert P. Langlands was today, May 22, awarded the Abel Prize for 2018 by H.M. King Harald. Langlands received the award of 6 million NOK “for his visionary program connecting representation theory to number theory.” The Langlands program is frequently described as a grand unified theory of mathematics.

(22.05.2018) More### Would you like to attend the 2018 Abel Prize award ceremony?

The Abel Prize award ceremony takes place at 22 may 2018, 14:00 in the University Aula in Oslo, Norway. His Majesty King Harald V will present the prize to this year’s laureate, Robert P. Langlands. The ceremony is open, but requires registration. For registration, click here.

(11.04.2018) More### AMS President congratulates Robert P. Langlands

"It is my great pleasure to congratulate Professor Robert P. Langlands, winner of the 2018 Abel Prize. Robert Langlands is one of the most distinguished mathematicians alive today and a towering figure in the history of modern mathematics. His insights, which grew out of penetrating technical work early in his career, have transformed and enriched both number theory and representation theory. The deep relations between the two subjects that he predicted and probed have guided the work of countless mathematicians over the last 50 years."

- Kenneth A. Ribet, AMS President, University of California, Berkeley

### Robert P. Langlands receives the Abel Prize

The Norwegian Academy of Science and Letters has decided to award the Abel Prize for 2018 to Robert P. Langlands of the Institute for Advanced Study, Princeton, USA “for his visionary program connecting representation theory to number theory.”

(19.03.2018) More