Single-valued hyperlogarithms, correlation functions and closed string amplitudes
We give new proofs of a global and a local property of the integrals which compute closed
string theory amplitudes at genus zero. Both kinds of properties are related to the newborn …
string theory amplitudes at genus zero. Both kinds of properties are related to the newborn …
Zagier-Hoffman's conjectures in positive characteristic II
Zagier-Hoffman's conjectures predict the dimension and a basis for the $\mathbb Q $-vector
spaces spanned by $ N $ th cyclotomic multiple zeta values (MZV's) of fixed weight where …
spaces spanned by $ N $ th cyclotomic multiple zeta values (MZV's) of fixed weight where …
Semiclassical Hodge theory for log Poisson manifolds
A Lindberg, B Pym - arXiv preprint arXiv:2408.16685, 2024 - arxiv.org
We construct a mixed Hodge structure on the topological K-theory of smooth Poisson
varieties, depending weakly on a choice of compactification. We establish a package of tools …
varieties, depending weakly on a choice of compactification. We establish a package of tools …
Logarithmic morphisms, tangential basepoints, and little disks
We develop the theory of``virtual morphisms''in logarithmic algebraic geometry, introduced
by Howell. It allows one to give algebro-geometric meaning to various useful maps of …
by Howell. It allows one to give algebro-geometric meaning to various useful maps of …
The Expansion ⋆ mod ō (ℏ4) and Computer-Assisted Proof Schemes in the Kontsevich Deformation Quantization
R Buring, AV Kiselev - Experimental Mathematics, 2022 - Taylor & Francis
The Kontsevich deformation quantization combines Poisson dynamics, noncommutative
geometry, number theory, and calculus of oriented graphs. To manage the algebra and …
geometry, number theory, and calculus of oriented graphs. To manage the algebra and …
Grothendieck-Teichmüller group, operads and graph complexes: a survey
S Merkulov - arXiv preprint arXiv:1904.13097, 2019 - arxiv.org
arXiv:1904.13097v3 [math.QA] 18 Jul 2021 Page 1 arXiv:1904.13097v3 [math.QA] 18 Jul
2021 GROTHENDIECK-TEICHMULLER GROUP, OPERADS AND GRAPH COMPLEXES: A …
2021 GROTHENDIECK-TEICHMULLER GROUP, OPERADS AND GRAPH COMPLEXES: A …
Deformations of path algebras of quivers with relations
S Barmeier, Z Wang - arXiv preprint arXiv:2002.10001, 2020 - arxiv.org
Let $ A=\Bbbk Q/I $ be the path algebra of any finite quiver $ Q $ modulo any two-sided ideal
$ I $ of relations and let $ R $ be any reduction system satisfying the diamond condition for …
$ I $ of relations and let $ R $ be any reduction system satisfying the diamond condition for …
Webs by conics on del Pezzo surfaces and hyperlogarithmic functional identities
L Pirio - arXiv preprint arXiv:2212.02556, 2022 - arxiv.org
For $ d $ ranging from 2 to 6, we prove that the web by conics naturally defined on any
smooth del Pezzo surface of degree $ d $ carries an interesting functional identity whose …
smooth del Pezzo surface of degree $ d $ carries an interesting functional identity whose …
Kontsevich's star-product up to order 7 for affine Poisson brackets: where are the Riemann zeta values?
R Buring, AV Kiselev - Open Communications in Nonlinear …, 2024 - ocnmp.episciences.org
The Kontsevich star-product admits a well-defined restriction to the class of affine–in
particular, linear–Poisson brackets; its graph expansion consists only of Kontsevich's graphs …
particular, linear–Poisson brackets; its graph expansion consists only of Kontsevich's graphs …
Hyperlogarithmic functional equations on del Pezzo surfaces
AM Castravet, L Pirio - Advances in Mathematics, 2024 - Elsevier
Abstract For any d∈{1,…, 6}, we prove that the web of conics on a del Pezzo surface of
degree d carries a functional identity whose components are antisymmetric hyperlogarithms …
degree d carries a functional identity whose components are antisymmetric hyperlogarithms …