# 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 3˛ + 4˛ = 5˛ ) 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.

### Lovász and Wigderson to share the Abel Prize

The Norwegian Academy of Science and Letters has decided to award the Abel Prize for 2021 to László Lovász of Alfréd Rényi Institute of Mathematics (ELKH, MTA Institute of Excellence) and Eötvös Loránd University in Budapest, Hungary, and Avi Wigderson of the Institute for Advanced Study, Princeton, USA,

“for their foundational contributions to theoretical computer science and discrete mathematics, and their leading role in shaping them into central fields of modern mathematics”

### The Honouring of the Abel Prize Laureates

Due to the uncertain development of the Covid-19 pandemic in Norway, all physical events are canceled. Instead, there will be three online events.

(07.04.2021) More### Announcement of the next Abel Prize laureate

The Abel Prize laureate for 2021 will be announced Wednesday March 17th at 12:00 (UTC/GMT+1).** **

### Isadore M. Singer, Abelprize laureate, dies at 96

Isadore M. Singer was the recipient together with Sir Michael Atiyah of the Abel Prize in 2004. They received the prize for their discovery and proof of the index theorem, one of the most significant discoveries in 20th century mathematics.

(12.02.2021) More