# 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.

### Sir Vaughan F.R. Jones, outstanding mathematician and incoming member of the Abel committee, has passed away

(11.09.2020) More### The Norwegian Academy of Science and Letters calls for nominations of candidates for the Abel Prize 2021

(03.07.2020) More### The Honouring of the 2020 Abel Prize Laureates

All events in connection to the Abel Prize Week in May are cancelled due to the Corona pandemic. The 2020 Abel Prize Laureates Hillel Furstenberg and Gregory Margulis will be honoured, together with the Abel Prize Laureate(s) of 2021 during next year’s Abel Prize Ceremony, May 25 2021.

### Furstenberg and Margulis to share the Abel Prize

The Abel Prize for 2020 goes to Hillel Furstenberg, Hebrew University of Jerusalem, Israel and Gregory Margulis, Yale University, New Haven, CT, USA, for “pioneering the use of methods from probability and dynamics in group theory, number theory and combinatorics.”

(13.03.2020) More### President of the Academy announces Abel Prize winner

The President of the Norwegian Academy of Science and Letters, Hans Petter Graver will announce the winner of the 2020 on March 18. The Academy's choice of laureate is based on the Abel Committee's recommendation.

**The event will be in an all-digital format and streamed live from this location**