Goncharov polylogarithms

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August undefined, 2024

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 … 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

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

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]). 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. top cities in delaware

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 … 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. 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 … top cities in egypt

HOPF ALGEBRAS AND ALTERNATING MULTIPLE ZETA VALUES …

Moduli spaces of local systems and higher Teichmüller theory

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 ... http://users.math.yale.edu/users/goncharov/4717 top cities in idahoWebHOLOMORPHIC POLYLOGARITHMS AND BLOCH COMPLEXES CHRISTIANK.ZICKERT Abstract. Foranintegern 2 wedeﬁneapolylogarithmLb n,whichisaholomorphicfunction ontheuniversalabeliancoverofC nf0;1gdeﬁnedmodulo(2ˇi)n=(n 1)!. Weusetheformal properties of its functional relations to deﬁne groups Bb k(Fb) lifting Goncharov’s Bloch … top cities in england

"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 … " - Goncharov polylogarithms

Goncharov polylogarithms

Geometry of configurations, polylogarithms and motivic …

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 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. 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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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. 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.

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 … WebMay 21, 2014 · The U.S. Department of Energy's Office of Scientific and Technical Information

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 … 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.

WebFeb 17, 2002 · Periods and mixed motives. A. B. Goncharov. We define motivic multiple polylogarithms and prove the double shuffle relations for them. We use this to study the motivic fundamental group of the multiplicative group - {N-th roots of unity} and relate it to geometry of modular varieties. In particular we get new information about the actionof the ...

WebCite this paper. Goncharov, A.B. (1995). Polylogarithms in Arithmetic and Geometry. In: Chatterji, S.D. (eds) Proceedings of the International Congress of Mathematicians. pics reponseWebGoncharov, A. B. (1995), "Geometry of configurations, polylogarithms, and motivic cohomology", Advances in Mathematics, 114 (2): 197–318, doi: … top cities in hawaiiWebMar 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 … pics reminderWebClassical polylogarithms for amplitudes and Wilson loops. AB Goncharov, M Spradlin, C Vergu, A Volovich. Physical review letters 105 (15), 151605, 2010. 638: 2010: Cluster … pics resizerWebJan 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 … top cities in france to visitWebNov 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. pics related to tsunamiWebJun 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 ... top cities in florida