2024 Goncharov polylogarithms

Goncharov polylogarithms

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August undefined, 2024

WebGoncharov, A. \Polylogarithms and Motivic Galois groups," Proceedings of the AMS Research Summer Conference \Motives", Symposium in Pure Math-ematics, 55, 43 - 96, … 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.

Moduli spaces of local systems and higher Teichmüller theory

WebJan 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 … WebMar 8, 2001 · A. B. Goncharov We develop the theory of multiple polylogarithms from analytic, Hodge and motivic point of view. Define the category of mixed Tate motives … bob discount furniture white marsh

Geometry of configurations, polylogarithms and motivic …

WebGoncharov, A. B. (1995), "Geometry of configurations, polylogarithms, and motivic cohomology", Advances in Mathematics, 114 (2): 197–318, doi: … 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. 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]. bob discount furniture website outlet

Two-loop planar master integrals for the production of off-shell …

Alexander Goncharov - Wikipedia

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 ... bob discount furniture woodbridgeWeb• 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 … clip art breakfast sandwich

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Goncharov polylogarithms

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 … 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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WebJun 29, 2010 · Classical Polylogarithms for Amplitudes and Wilson Loops. Alexander B. Goncharov, Marcus Spradlin, C. Vergu, Anastasia Volovich. We present a compact … 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

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, … WebJan 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 …

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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 …

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]). clip art breakfast sausageWebof 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 bob discount goof proofWebOct 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 ... clipart breaking normalWebA.B. Goncharov A.B. Goncharov Scientific Council ofCybemetics Vavilova 40 117333 Moscow USSR MPI/91-64 Max-Planck-Institutfür Mathematik Gottfried-Claren-Straße26 … bob discount furniture yonkersWebGoncharov 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. clip art breakfast timeWebPolylogarithms 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 clipart breaking newsWebOct 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. bob discount lancaster