WebMoreover, these iterated integrals have an explicit geometric description, built out of the (usual) de Rham complex on X. We put this framework to use in two independent ways. … WebIterated integrals Iterated integrals on Riemann surfaces Higher-genus KZB-connections Motivatingexamples Multiplepolylogarithms Multi-valuedfctsonM= Conf n(P1(C) nf0;1;1g) (conf.spaceofn pointsonP1(C) nf0;1;1g)inducedbyhomotopy-inv.iteratedintegrals. Ellipticmultiplepolylogarithms Multi-valuedfunctionsonM= Conf n((C=Z+ ˝Z) nf0g) inducedby
Introduction - University of Oxford
Webthe Kontsevich integral for knots developed in [14]. We review basic facts about such iterated integrals of logarithmic 1-forms in a general situation of the complement of a hyperplane arrangement. We give a criterion so that iterated integrals of logarithmic 1-forms depend only on the homotopy class of loops. Web7 Symbols and iterated integrals of modular forms29 ... 11 Conclusions46 A Hopf algebras and comodules47 B Homotopy-invariant iterated integrals48 C The total di erential of eMPLs50 D The coaction and symbols for ordinary MPLs54 E Modular forms56 F q-expansion for the functions g(n) 59 1 Introduction pelham nh football
Application of Iterated Integrals to Number Theory and Algebraic Geometry
Webbornotopy-equivalence i: Y —> Y', and a coarse homotopy h':X x [0, 1] -> Y' such that the obvious diagram is bornotopy commutative (see [8, Section 3]). Thus any functor F which is both coarse homotopy invariant and bornotopy invariant will be invariant under generalized coarse homotopies, at least on the subcategory of path spaces. Webaa r X i v : . [ m a t h . AG ] D ec Iterated integrals on affine curves. Martin T. Luu, Albert Schwarz. Abstract. Motivated by amplitude calculations in string theory we establish basic properties of homotopy invariant iteratedintegrals on affine curves. To Dmitry Fuchs, with warmest wishes for his 80th birthday Web1 jun. 2016 · The program is based on homotopy invariant iterated integrals on moduli spaces M0,nof curves of genus 0 with nordered marked points. It includes the symbol map and procedures for the analytic computation of period integrals on M0,n. It supports the automated computation of a certain class of Feynman integrals. Program summary … pelham nh election 2022