# Abel Lectures at the University of Oslo

Abel Laureate Pierre Deligne will give his prize lecture at the University of Oslo. This will be followed by Abel Lectures by leading mathematicians Nicholas Katz and Claire Voisin. Ravi Vaki will give the popular science lecture.

### Pierre Deligne:

Hidden symmetries of algebraic varieties

**Abstract:**

If a complex algebraic variety is defined by equations with rational coefficients, the set of its points whose coordinates are in that is are algebraic numbers, carries an action of the Galois group Gal ( / ), the symmetry group of . This, and related symmetries, have a strong influence on the topology of complex algebraic varieties, and a mysterious connection with Hodge theory.

### Nicholas Katz

**Princeton University:**

### Life Over Finite Fields

**Abstract:**

We will discuss some of Deligne's work and its diophantine applications.

### Professor Claire Voisin

École Polytechnique and CNRS

### Mixed Hodge structures and the topology of algebraic varieties

**Abstract:**

Deligne proved that the cohomology of a complex algebraic variety carries a functorial "mixed Hodge structure", which generalizes the previously known results for smooth projective complex varieties. Formal properties of morphisms of Mixed Hodge structures then allowed him to deduce a number of important consequences, including the "theorem of the fixed part". I will describe these fundamental results, and some applications to the study of Hodge classes.

**Science Lecture**:

### Ravi Vakil

Stanford University

### Algebraic geometry and the ongoing unification of mathematics

**Abstract:**

When we look carefully at nature, we can discover surprising coincidences, which suggest deeper underlying structure. The centrality of mathematics comes in part from the fact that seemingly unrelated ideas are often unified by some grand theory, which is far more powerful than the sum of its parts. Mathematics is most exciting when different ideas come together unexpectedly to give a new point of view. This is typified in algebraic geometry, and in the work of Deligne in particular, which brings together many themes in mathematics, including geometry, number, shape (topology), algebra, and more. This magic is the reason I became an algebraic geometer. For example, the theory of Pythagorean triples (such as 3² + 4² = 5² ) connects geometry to the theory of numbers by way of algebra. This ancient example grows up to be the Weil conjectures, a wondrous prediction whose proof was finally completed by Deligne.

I will try to share a glimpse of this strange unification of many different ideas. This talk is aimed at a general audience, and no particular background will be assumed.

### 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