Goncharov polylogarithms

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August undefined, 2024

WebA. B. Goncharov, Polylogarithms, regulators and Arakelov motivic complexes, J. Amer. Math. Soc., 18 (2005), no. 1, 1–6; math.AG/0207036. A. B. Goncharov and Yu. I. Manin, … WebClassical polylogarithms have been studied extensively since pioneering work of Euler and Abel. It is known that they satisfy lots of functional equations, but in weight >4 these equations are not known yet. Even in the weight 4 they were first found using heavy computer-assisted computations. ... The talk is based on joint work with A. Goncharov.

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WebGeneralized polylogarithms [1, 2] (also known as Goncharov polylogarithms, generalized harmonic polylogarithms, or hyperlogarithms) are a class of functions that frequently show up in results for Feynman integrals, as they appear in high energy physics (for overview articles, see e.g. refs. [3, 4]). WebDec 31, 1994 · They showed up again in such different subjects as quantum groups [Dr] (the Drinfeld associator), Zagier’s studies [Z1-2], the Kontsevich integrals for Vassiliev knot invariants, mixed Tate motives over Spec Z [G1-2], and, recently, in computations in quantum field theory [B], [Kr]. The multiple polylogarithms were studied in [G1-4]. research topic on smartphone

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WebPolylogarithms and motivic Galois groups A.B. Goncharov This paper is an enlarged version of the lecture given at the AMS con-ference \Motives" in Seattle, July 1991. More details can be found in [G2]. My aim is to formulate a precise conjecture about the structure of the Galois group Gal (M T(F)) of the category M T(F) of mixed Tate motivic WebA.B. Goncharov A.B. Goncharov Scientific Council ofCybemetics Vavilova 40 117333 Moscow USSR MPI/91-64 Max-Planck-Institutfür Mathematik Gottfried-Claren-Straße26 … WebGoncharov was an Invited Speaker at the 1994 International Congress of Mathematicians and gave a talk Polylogarithms in arithmetic and geometry. In 2024, Goncharov was appointed the Philip Schuyler Beebe Professor of Mathematics at Yale University, as well as the Gretchen and Barry Mazur Chair at the Institut des hautes études scientifiques. research topic in stem strand

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Planar three-loop master integrals for 2 → 2 processes with one ...

WebMar 15, 2024 · The result can be expressed in terms of multiple Goncharov polylogarithms. We also employ a more restricted class of hexagon functions which have the correct branch cuts and certain other restrictions on their symbols. We classify all the hexagon functions through transcendental weight five, using the coproduct for their Hopf … Webﬁrst systematically studied by Arakawa-Kaneko, Deligne, Goncharov and Racinet (see [5, 6, 15, 17, 22, 23, 42]). Since then they have been also studied by a lot of ... tiple polylogarithms, we solved both the MZV’s and AMZV’s version of the Zagier-Hoﬀman’s conjectures in positive characteristic. We mention that the latter is much research topic ideas technology research topic meaning in research

"WebOct 8, 2024 · Abstract. We compute the two-loop four-point form factor of a length-3 half-BPS operator in planar N = 4 SYM theory, which belongs to the class of two-loop five-point scattering observables with one off-shell color-singlet leg. A new bootstrapping strategy is developed to obtain this result by starting with an ansatz expanded in terms of master ... " - Goncharov polylogarithms

Goncharov polylogarithms

http://users.math.yale.edu/users/goncharov/4717 WebAug 1, 2024 · Nature of problem: Numerical evaluation routine for generalised (or Goncharov [1]) polylogarithms that is fast enough for Monte Carlo integration. Solution method: Implementing the algorithm presented by Vollinga and Weinzierl [2] in Fortran 90, providing a Fortran module and a Mathematica interface.

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WebA.B.Goncharov Contents 1 Introduction 1 2 Construction of Chow polylogarithms 2 3 Properties of Chow polylogarithm functions 6 4 Cocycles for all continuous cohomology … WebSep 22, 2024 · Differential equations for the one-loop vertex diagram in heavy quark effective theory (HQET) with arbitrary self-energy insertions and arbitrary residual energies are reduced to the $ϵ$ form and used to obtain the $ϵ$ expansion in terms of Goncharov polylogarithms.

WebOct 13, 2024 · The final expressions for the master integrals are given in terms of Goncharov polylogarithms. These results allow us to extract the two-loop short-distant matching coefficients between quark quasi and lightcone PDFs in LaMET, and are valuable to improve the determination of the nucleon PDFs from first principles in future. WebApr 4, 2024 · A bstract Elliptic multiple polylogarithms occur in Feynman integrals and in particular in scattering amplitudes. They can be characterized by their symbol, a tensor product in the so-called ...

WebGoncharov and Levin. We want to give evidence for the claim that polygons and their internal structure are very (mixed Tate) motivic, at least if we work over a ﬁeld. Deﬁnition 1.1. Let R be a set. An R-deco polygon π is an oriented polygon with a distinguished root side and a decoration {sides of π} → R. WebApr 8, 2001 · By Goncharov's inversion formula [Gon01, (34)], each inverted polylogarithm Li k (x −1 ) is a rational polynomial in regular polylogarithms Li k (x), logarithms log(x i ) and powers of πi. The ...

WebarXiv:2304.03349v1 [math.NT] 6 Apr 2024 Relations for the diﬀerence of two dilogarithms Jean-Christophe Pain1 ,2∗ 1CEA, DAM, DIF, F-91297 Arpajon, France 2Université Paris-Saclay, CEA, Laboratoire Matière en Conditions Extrêmes, 91680 Bruyères-le …

WebApr 22, 2024 · We present analytic results for the two tennis-court integral families relevant to 2 → 2 scattering processes involving one massive external particle and massless … prosperity affiliatesWebGoncharov, A. \Polylogarithms and Motivic Galois groups," Proceedings of the AMS Research Summer Conference \Motives", Symposium in Pure Math-ematics, 55, 43 - 96, … research topic in nursingWebPOLYLOGARITHMS IN ARITHMETIC AND GEOMETRY A.B.GONCHAROV The classical polylogarithms were invented in correspondence of Leibniz with Joh.Bernoulli in 1696 ( … research topic in radiologic technologyWebNov 6, 2013 · The boundary conditions are also particularly transparent in this setup. We identify the class of functions relevant to this problem to all orders in ϵ. We present the results up to weight four for all except one integrals in terms of a subset of Goncharov polylogarithms, which one may call two-dimensional harmonic polylogarithms. research topic managementhttp://www-personal.umich.edu/~jbourj/jacob_bourjaily_cv.pdf research topic on cloud computingWebJan 21, 2024 · The results obtained by using the known expressions of the integral functions involve complicated combinations of Goncharov multiple polylogarithms, but we show that much simpler expressions can in fact be derived using the symbol of transcendental functions. For n=3 we find a very compact remainder function expressed in terms of … research topic on machine learningWebJan 17, 2014 · In this paper we study motivic amplitudes — objects which contain all of the essential mathematical content of scattering amplitudes in planar SYM theory in a completely canonical way, free from the ambiguities inherent in any attempt to choose particular functional representatives. We find that the cluster structure on the kinematic … prosperity and depression quizlet