Goncharov polylogarithms

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August undefined, 2024

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 … 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 ...

Geometry of configurations, polylogarithms and motivic …

http://users.math.yale.edu/users/goncharov/4717 WebJACOB 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: meaning of songs website

Publications of Alexander Goncharov

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 … 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, … meaning of song your woman

Classical polylogarithms, cluster algebras and Zagier conjecture.

WebWe provide algorithms for symbolic integration of hyperlogarithms multiplied by rational functions, which also include multiple polylogarithms when th… WebMay 21, 2014 · The U.S. Department of Energy's Office of Scientific and Technical Information meaning of song wildfire by michael murphyWebGoncharov was an Invited Speaker at the 1994 International Congress of Mathematicians and gave a talk Polylogarithms in arithmetic and geometry. In 2024, Goncharov was … pediatric gynecologist in maryland

"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. " - Goncharov polylogarithms

Goncharov polylogarithms

GitHub - munuxi/Multiple-Polylogarithm: Numerical Multiple

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 … 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.

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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 ... 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

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

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 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 …

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. meaning of songs of solomonWebPOLYLOGARITHMS IN ARITHMETIC AND GEOMETRY A.B.GONCHAROV The classical polylogarithms were invented in correspondence of Leibniz with Joh.Bernoulli in 1696 ( … pediatric gynecologist los angelesWebJun 29, 2010 · Classical Polylogarithms for Amplitudes and Wilson Loops. Alexander B. Goncharov, Marcus Spradlin, C. Vergu, Anastasia Volovich. We present a compact … meaning of sonship in the bibleWebOct 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. pediatric growth chart male pdfWebApr 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 … pediatric gynecologist queens nyWebA 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 … meaning of soonWebGeneralized 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]). meaning of soot in hindi