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Goncharov polylogarithms

WebSep 1, 2024 · The very existence of deep connections between polylogarithms and cluster varieties is surprising. It will have many applications far beyond Algebraic Geometry and …

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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. 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 … harry potter 3 streaming vf hds https://teschner-studios.com

Algorithms for the symbolic integration of hyperlogarithms with ...

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. 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 … 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 charlene kingsley obit

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Category:Triangulations, Polylogarithms, and Grassmannian Cluster …

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Goncharov polylogarithms

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

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 … 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 …

Goncharov polylogarithms

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http://www-personal.umich.edu/~jbourj/jacob_bourjaily_cv.pdf WebA numerical realization of multiple polylogarithm (or Goncharov polylogarithm, generalized polylogarithm) in pure Mathematica based on the algorithm given in this paper 0410259. These polylogarithms are …

WebJun 22, 2024 · When formulated in twistor space, the D-instanton corrected hypermultiplet moduli space in \( \mathcal{N} = {2} \) string vacua and the Coulomb branch of rigid \( \mathcal{N} = {2} \) gauge ... 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

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. WebA.B. Goncharov A.B. Goncharov Scientific Council ofCybemetics Vavilova 40 117333 Moscow USSR MPI/91-64 Max-Planck-Institutfür Mathematik Gottfried-Claren-Straße26 …

WebNumerical evaluations of multiple polylogarithms. A numerical realization of multiple polylogarithm (or Goncharov polylogarithm, generalized polylogarithm) in pure Mathematica based on the algorithm given in this paper 0410259. These polylogarithms are widely used in the calculation of Feynman integrals and amplitudes.

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 propagators in terms of Goncharov polylogarithms of up to transcendental weight six. We also present analytic results for physical kinematics for the ladder-box family and the two … harry potter 3 subtitrat in romana onlineWebGeneralized 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]). harry potter 3 thuyet minh tieng vietWebA. 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, … charlene keys husband