This is the first volume of the lectures presented at the Clay Mathematics Institute 2014 Summer School, Periods and Motives: Feynman amplitudes in the 21st century, which took place at the Instituto de Ciencias MatemįticasICMAT (Institute of Mathematical Sciences) in Madrid, Spain. It covers the presentations by S. Bloch, by M. Marcolli and by L. Kindler and K. Rülling.
The main topics of these lectures are Feynman integrals and ramification theory. On the Feynman integrals side, their relation with Hodge structures and heights as well as their monodromy are explained in Blochs lectures. Two constructions of Feynman integrals on configuration spaces are presented in Ceyhan and Marcollis notes. On the ramification theory side an introduction to the theory of l -adic sheaves with emphasis on their ramification theory is given. These notes will equip the reader with the necessary background knowledge to read current literature on these subjects.
| Preface |
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vii | |
| Foreword |
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xi | |
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Feynman Integrals in Mathematics and Physics |
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1 | (34) |
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Feynman integrals and periods in configuration spaces |
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35 | (68) |
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Introductory course on -adic sheaves and their ramification theory on curves |
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103 | |
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K. Ebrahimi-Fard, Norwegian University of Science and Technology, Trondheim, Norway.
J. I. Burgos Gil, Institute of Mathematical Sciences, Spanish National Research Council, Madrid, Spain.
D. Manchon, CNRS et Universite Clermont-Auvergne, Aubiere, France
