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Goncharov polylogarithms

Web• Polylogarithms, Goncharov Program, Mixed Tate motives, Zagier conjecture. • Volumes of Non-Euclidean polytopes. • Cluster algebras and scattering amplitudes. PUBLICATIONS • Rational Elliptic Surfaces and the Trigonometry of … 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 ...

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WebTheir positive real points provide the two higher Teichmüller spaces related to G and S, while the points with values in the tropical semifields provide the lamination spaces. We define the motivic avatar of the Weil–Petersson form for one of these spaces. It is related to the motivic dilogarithm. Download to read the full article text. WebA.B. Goncharov A.B. Goncharov Scientific Council ofCybemetics Vavilova 40 117333 Moscow USSR MPI/91-64 Max-Planck-Institutfür Mathematik Gottfried-Claren-Straße26 … bunchoballoons code https://theros.net

Goncharov conjecture - Wikipedia

WebAlexander Goncharov. I am interested in several areas of Mathematics and Mathematical Physics: Arithmetic Algebraic Geometry: L-functions, mixed motives and motivic Galois groups, polylogarithms, periods, Hodge … 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. Webof the cluster polylogarithms associated with the Grassmannian cluster algebra Gr(4;n) determine much of the structure of the planar n-particle MHV amplitude. Because cluster algebras themselves are still new, and cluster polylogarithms newer still, there are many open physical and mathematical questions about these structures. The bunchoballoons.com splash to win

Geometry of configurations, polylogarithms and motivic …

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Goncharov polylogarithms

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http://users.math.yale.edu/users/goncharov/4717 WebJun 29, 2010 · Classical Polylogarithms for Amplitudes and Wilson Loops. Alexander B. Goncharov, Marcus Spradlin, C. Vergu, Anastasia Volovich. We present a compact …

Goncharov polylogarithms

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WebClassical polylogarithms for amplitudes and Wilson loops. AB Goncharov, M Spradlin, C Vergu, A Volovich. Physical review letters 105 (15), 151605, 2010. 638: 2010: Cluster … 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 …

WebMay 21, 2014 · The U.S. Department of Energy's Office of Scientific and Technical Information WebPOLYLOGARITHMS IN ARITHMETIC AND GEOMETRY A.B.GONCHAROV The classical polylogarithms were invented in correspondence of Leibniz with Joh.Bernoulli in 1696 ( …

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 … 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

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.

WebNov 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. half life of actiniumWebGeneralized 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]). bunch o balloons grenadeWebAdvancing research. Creating connections. half life of alcohol in bodyWebPolylogarithms 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 half life of alendronateWebA. 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, … half life of alpha lipoic acidhalf life of alcohol in bloodWebJan 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 … bunch o balloons dual launcher