Clay Mathematics Institute Summer School on “Periods and Motives: Feynman amplitudes in the 21st century” will be held at the Instituto de Ciencias Matemáticas – ICMAT (Institute of Mathematical Sciences) in Madrid, Spain, from June 30 – July 25, 2014.

The deadline for complete applications is March 28, 2014. Graduate students and postdoctoral fellows who are within seven years of receipt of their Ph.D. are given preference for financial support. Support is decided on a competitive basis and may include accommodation plus funds towards the cost of economy travel.

Clay Mathematics Institute Summer School 2014

“Periods and Motives: Feynman amplitudes in the 21st century”

at ICMAT, Madrid, Spain

from June 30 – July 25, 2014.

The theory of motives originated from Grothendieck’s “universal cohomology theory”, and provides a conceptual framework for the study of periods. It is a vibrant area of current research in modern mathematics.

Feynman amplitudes date back to the early days of perturbative quantum field theory. They are highly intricate integrals over a large number of variables, and appear as coefficients of power expansions. The efficient calculation of Feynman amplitudes is of foremost importance for theoretical predictions in high energy physics. Thanks to the path-breaking work by Bloch, Connes, Esnault, Goncharov, Kreimer, Marcolli, and others, a beautiful relation between Feynman amplitudes and periods has emerged.

By bringing together leading expositors of the field, the school aims at training a new generation of graduate students and young researchers in the state of the art techniques behind these deep and important results.

This school will consist of three weeks of lecture courses supplemented by exercise and problem sessions. The aim of these courses is to provide a pedagogical introduction to the field as well as introducing advanced tools and techniques necessary to play an active role in current research. The main lecturers are:

Spencer Bloch (University of Chicago, USA)
— Lectures on the mathematics of Feynman amplitudes

José I. Burgos Gil (ICMAT-CSIC, Madrid, Spain)
— Motivic multiple zeta values

Hélène Esnault, Lars Kindler, Kay Rülling (Freie Universität Berlin, Germany)
— l-adic Galois representations of function fields over finite fields

Matilde Marcolli (California Institute of Technology, USA)
— Feynman integrals, periods and motives

The courses of the fourth week of this school aim at a higher level. In five mini-courses experts will present topics of great future promise as well as outline some open problems under current investigation.

For more information on the program and to apply, please visit: http://www.icmat.es/summerschool2014/