2024 Goncharov polylogarithms

Goncharov polylogarithms

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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. 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.

Moduli spaces of local systems and higher Teichmüller theory

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 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 … automan season 1

Folding Amplitudes into Form Factors: An Antipodal Duality

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

Polylogarithms in Arithmetic and Geometry (1995) Alexander Goncharov …

Alexander Goncharov - Yale University

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. WebGoncharov, A. \Polylogarithms and Motivic Galois groups," Proceedings of the AMS Research Summer Conference \Motives", Symposium in Pure Math-ematics, 55, 43 - 96, … gb05235/04WebA 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 … gb058629

"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 … " - Goncharov polylogarithms

Goncharov polylogarithms

Planar three-loop master integrals for 2 → 2 processes …

http://www-personal.umich.edu/~jbourj/jacob_bourjaily_cv.pdf 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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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

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 … 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 ...

http://users.math.yale.edu/users/goncharov/4717 WebGoncharov, A. B. (1995), "Geometry of configurations, polylogarithms, and motivic cohomology", Advances in Mathematics, 114 (2): 197–318, doi: …

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 …

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 automan season 1 episode 1WebJACOB LEWIS BOURJAILY: vitae J. Bourjaily, Determining the Actual Local Density of Dark Matter Particles, Eur.Phys.J. C Direct (2005),[astro-ph/0410470]. J. Bourjaily, Weighing the Dark Matter Halo, “IDM 2004: The 5th International Workshop on the Identiﬁcation of Dark Matter,” eds. N. Spooner et al.,[astro-ph/0411409]. Books: gb0544WebMay 21, 2014 · The U.S. Department of Energy's Office of Scientific and Technical Information gb0505Web• 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 … automan seasonWebMar 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 … gb061WebGeneralized 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]). automan season 1 episode 8WebClassical polylogarithms for amplitudes and Wilson loops. AB Goncharov, M Spradlin, C Vergu, A Volovich. Physical review letters 105 (15), 151605, 2010. 638: 2010: Cluster … gb05235/05