×

Amplitudes, Hodge theory and ramification. From periods and motives to Feynman amplitudes. Lectures presented at the Clay Mathematics Institute 2014 summer school, “Periods and Motives: Feynman amplitudes in the 21st century”, Madrid, Spain, June 30 – July 25, 2014. (English) Zbl 1446.81001

Clay Mathematics Proceedings 21. Providence, RI: American Mathematical Society (AMS); Cambridge, MA: Clay Mathematics Institute (ISBN 978-1-4704-4329-0/pbk). xiv, 229 p. (2020).

Show indexed articles as search result.

Publisher’s description: 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.
The articles of this volume will be reviewed individually.
Indexed articles:
Bloch, Spencer, Feynman integrals in mathematics and physics, 1-34 [Zbl 1448.81325]
Ceyhan, Özgür; Marcolli, Matilde, Feynman integrals and periods in configuration spaces, 35-102 [Zbl 1456.81192]
Manin, Yuri I., Foreword, xi-xiv [Zbl 1452.14004]
Kindler, Lars; Rülling, Kay, Introductory course on \(\ell\)-adic sheaves and their ramification theory on curves, 103-229 [Zbl 1455.11156]

MSC:

81-03 History of quantum theory
01A61 History of mathematics in the 21st century
81Q30 Feynman integrals and graphs; applications of algebraic topology and algebraic geometry
81T18 Feynman diagrams
14C15 (Equivariant) Chow groups and rings; motives
14D07 Variation of Hodge structures (algebro-geometric aspects)
11S15 Ramification and extension theory
00B25 Proceedings of conferences of miscellaneous specific interest
PDFBibTeX XMLCite