## ESI Program – The interrelation between mathematical physics, number theory and non-commutative geometry

Over the past few years, the newly discovered relation between Feynman integrals in quantum field theory and Grothendieck’s theory of motives of algebraic varieties has become a topic of growing importance in the panorama of theoretical and mathematical physics. In particular, the field has developed along different parallel lines, and one of the pressing needs at the moment is to create more interaction between researchers involved in the various different aspects of this area of research. In particular, we single out four different directions among which we hope to stimulate new interactions:

- Motives and periods in perturbative quantum field theory
- Amplitudes and super Yang–Mills theory
- Algebraic structures in renormalization
- Quantum field theory on noncommutative spacetimes

There will be a **one week Master Class** followed by a **one week Research Meeting** in which these topics will be the focus.

During the first week there will be lectures by

**Raimar Wulkenhaar****Jacob Bourjaily****Stefan Weinzierl****Karen Yeats**

**Pierre Vanhove** (IHÉS) will give a **Erwin Schrödinger Lecture** on Wednesday March 4 (17:00).

**Alain Connes** (IHÉS/Collège de France) will give a lecture series on “The Arithmetic Site” (March 5, 10 and 11). These lectures take place in cooperation with Collège de France.