# 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.

### Yakov G. Sinai gives lecture at "Abel in Pittsburgh"

The Department of Mathematical Sciences at Carnegie Mellon University is hosting the "Abel in Pittsburgh" conference where Yakov G. Sinai who received the Abel Prize in 2014 is one of the speakers. The conference is organized by professor and member of the Abel commitee Irene Fonseca and will take place on the 11th of January 2019. "Abel in Pittsburgh" will be the 9th edition of a one-day conference with lectures aimed at a mathematically educated and interested audience, with the objective of increasing public awareness.

(05.11.2018) More### The Abel Symposium 2019

Abel Symposium 2019 will take place at Scandic Parken Hotel Ålesund, 23-29 June 2019. The title of the symposium is: Geometry, Lie Theory and Applications.

(02.11.2018) More### Who will be the next Abel Laureate?

The Abel Committee has embarked on the long journey in search of the next Abel Laureate. The committee which consists of five distinguished mathematicians has had its first meeting at the Norwegian Academy of Science and Letters in Oslo the 2nd and 3rd of October. The next meeting will take place in Pittsburgh, Pennsylvania early next year.

(03.10.2018) More### Record turnout for Atiyah’s Abel Lecture at ICM in Rio

1250 mathematicians from all over the world filled the big conference hall in Rio de Janeiro on Monday the 6^{th} of August to listen to Sir Michael Atiyah’s Abel Lecture, “The Future of Mathematical Physics: New ideas in old bottles”.

### Sir Michael Atiyah gives Abel lecture at ICM in Rio

Sir Michael Atiyah who receiced the Abel Prize in 2004, shared with Isadore Singer, will give the Abel Lecture at ICM in Rio on the 6th of August. He has titled the lecture: "The Future of Mathematical Physics: new ideas in old bottles". Atiyah will be introduced by Jacob Palis, former president of the International Mathematical Union and a member of the Abel Committee.

(26.07.2018) More