Clay Mathematics Institute

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Vol 21. Amplitudes, Hodge Theory and Ramification: From Periods and Motives to Feynman Amplitudes

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 Matemáticas–ICMAT (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 Bloch's lectures. Two constructions of Feynman integrals on configuration spaces are presented in Ceyhan and Marcolli's 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.



CMI/AMS publication. 2020. 229 pp. Softcover, List price: $120.00, AMS members: $96.00, Order code: CMIP/21. Students: $96.00, Order code: CLAYMATH. Available at the AMS Bookstore

Editors:  Karusch Ebahimi-Fard (Norwegian University of Science and Technology), Jose Ignacio Burgos Gil (Institute of Mathematical Sciences, Spanish National Research Council), Dominique Manchon (CNRS, Université Clermont-Auvergne)

Authors:  Spencer Bloch, Matilde Marcolli, Lars Kindler, Kay Rüling

Not yet published.  Expected publication date November 8, 2020