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Publisher’s description: This book is the outcome of research initiatives formed during the special “Research trimester on multiple zeta values, multiple polylogarithms, and quantum field theory” at the ICMAT (Instituto de Ciencias Matemáticas, Madrid) in 2014. The activity was aimed at understanding and deepening recent developments where Feynman and string amplitudes on the one hand, and periods and multiple zeta values on the other, have been at the heart of lively and fruitful interactions between theoretical physics and number theory over the past few decades. In this book, the reader will find research papers as well as survey articles, including open problems, on the interface between number theory, quantum field theory and string theory, written by leading experts in the respective fields. Topics include, among others, elliptic periods viewed from both a mathematical and a physical standpoint; further relations between periods and high energy physics, including cluster algebras and renormalisation theory; multiple Eisenstein series and q-analogues of multiple zeta values (also in connection with renormalisation); double shuffle and duality relations; alternative presentations of multiple zeta values using Ecalle’s theory of moulds and arborification; a distribution formula for generalised complex and l-adic polylogarithms; Galois action on knots. Given its scope, the book offers a valuable resource for researchers and graduate students interested in topics related to both quantum field theory, in particular, scattering amplitudes, and number theory.
The articles of mathematical interest will be reviewed individually.
Indexed articles:
Todorov, Ivan, Perturbative quantum field theory meets number theory, 1-28 [Zbl 1444.81029]
Panzer, Erik, Some open problems on Feynman periods, 29-44 [Zbl 1444.81032]
Stieberger, S., Periods and superstring amplitudes, 45-76 [Zbl 1444.81034]
Schlotterer, Oliver, The number theory of superstring amplitudes, 77-103 [Zbl 1444.81033]
Matthes, Nils, Overview on elliptic multiple zeta values, 105-132 [Zbl 1444.81035]
Adams, Luise; Bogner, Christian; Weinzierl, Stefan, The elliptic sunrise, 133-143 [Zbl 1444.81017]
Vergu, Cristian, Polylogarithm identities, cluster algebras and the \(\mathcal{N} = 4\) supersymmetric theory, 145-172 [Zbl 1444.81037]
Bachmann, Henrik, Multiple Eisenstein series and \(q\)-analogues of multiple zeta values, 173-235 [Zbl 1455.11123]
Bachmann, Henrik; Kühn, Ulf, A dimension conjecture for \(q\)-analogues of multiple zeta values, 237-258 [Zbl 1444.81021]
Zhao, Jianqiang, Uniform approach to double shuffle and duality relations of various \(q\)-analogs of multiple zeta values via Rota-Baxter algebras, 259-292 [Zbl 1444.81023]
Singer, Johannes, \(q\)-analogues of multiple zeta values and their application in renormalization, 293-325 [Zbl 1444.81028]
Nikolov, Nikolay M., Vertex algebras and renormalization, 327-343 [Zbl 1444.81030]
Rejzner, Kasia, Renormalization and periods in perturbative algebraic quantum field theory, 345-376 [Zbl 1444.81025]
Malvenuto, Claudia; Patras, Frédéric, Symmetril moulds, generic group schemes, resummation of MZVs, 377-398 [Zbl 1444.81026]
Salerno, Adriana; Schneps, Leila, Mould theory and the double shuffle Lie algebra structure, 399-430 [Zbl 1444.81022]
Chapoton, F., On some tree-indexed series with one and two parameters, 431-443 [Zbl 1445.05027]
Ebrahimi-Fard, Kurusch; Gray, W. Steven; Manchon, Dominique, Evaluating generating functions for periodic multiple polylogarithms via rational Chen-Fliess series, 445-468 [Zbl 1456.11161]
Manchon, Dominique, Arborified multiple zeta values, 469-481 [Zbl 1459.11172]
Foissy, Loïc; Patras, Frédéric, Lie theory for quasi-shuffle bialgebras, 483-540 [Zbl 1464.16026]
Furusho, Hidekazu, Galois action on knots. II: Proalgebraic string links and knots, 541-591 [Zbl 1454.14071]
Nakamura, Hiroaki; Wojtkowiak, Zdzisław, On distribution formulas for complex and \(l\)-adic polylogarithms, 593-619 [Zbl 1456.11121]
Zudilin, Wadim, On a family of polynomials related to \(\zeta (2,1)=\zeta (3)\), 621-630 [Zbl 1455.11124]