48 citations · 85 across the 11 of their papers we have counts for
15 papers
Pentagram relations
Nikita Markarian
We study the cohomology of iterated Kummer extensions on the moduli space of five-pointed rational curves, continuing [arXiv:2609.19341, arXiv:2609.21356]. A two-dimensional shrink…
Double shuffle relations via the Hodge defect
Nikita Markarian
We interpret the convolution constructions of [arXiv:2604.26357] in Hodge-theoretic terms, extending the Hodge defect calculation of [arXiv:2609.19341]. For Hodge--Tate modules on…
The Drinfeld associator and functors
Nikita Markarian
We compare two mixed Hodge structures attached to a unipotent variation of mixed Hodge--Tate structures on : the cohomology of its e…
Harmonic sums and the Galois group of the Mellin-KZ difference equation
Nikita Markarian
We identify the universal Galois group of the difference equation obtained by the Mellin transform of the Knizhnik-Zamolodchikov equation with the prounipotent group associated wit…
Multiplicative convolution and double shuffle relations
Nikita Markarian
We develop a geometric approach to the regularized double shuffle relations for multiple zeta values, based on convolution of perverse sheaves on and inspired by the…
Multiplicative convolution and double shuffle relations: convolution
Nikita Markarian
This is the first of two parts of a project devoted to a geometric interpretation of the Deligne-Terasoma approach to regularized double shuffle relations. The central fact of this…
On Conormal Lie Algebras of Feigin-Odesskii Poisson Structures
Leonid Gorodetsky, Nikita Markarian
The main result of the paper is a description of conormal Lie algebras of Feigin-Odesskii Poisson structures. In order to obtain it we introduce a new variant of a definition of a…
Compatible Feigin-Odesskii Poisson brackets
Nikita Markarian, Alexander Polishchuk
We prove that several Feigin-Odesskii Poisson brackets associated with normal elliptic curves in are compatible if and only if they are contained in a scroll or in…
On algebra of big zeta values
Nikita Markarian
The algebra of big zeta values we introduce in this paper is an intermediate object between multiple zeta values and periods of the multiple zeta motive. It consists of number seri…
On generalized stuffle relations between cell-zeta values
Nikita Markarian
We introduce a family of linear relations between cell-zeta values that have a form similar to product map relations and jointly with them imply stuffle relations between multiple…
Weyl n-algebras and the Swiss cheese operad
Nikita Markarian
We apply Weyl -algebras to prove formality theorems for higher Hochschild cohomology. We present two approaches: via propagators and via the factorization complex. It is shown t…
Weyl n-algebras and the Kontsevich integral of the unknot
Nikita Markarian
Given a Lie algebra with a scalar product, one may consider the latter as a symplectic structure on a -scheme, which is the spectrum of the Chevalley--Eilenberg algebra. In the…
Manifoldic homology and Chern-Simons formalism
Nikita Markarian
The aim of this note is to define for any -algebra and a compact parallelizable n-manifold without borders a morphism from the homology of homotopy Lie algebra $A[n-1]…
The Atiyah class, Hochschild cohomology and the Riemann-Roch theorem
Nikita Markarian
We develop a formalism involving Atiyah classes of sheaves on a smooth manifold, Hochschild chain and cochain complexes. As an application we prove a version of the Riemann--Roch t…
A note on the symplectic structure on the space of G-monopoles
Michael Finkelberg, Alexander Kuznetsov, Nikita Markarian +1
Let be a semisimple complex Lie group with a Borel subgroup . Let be the flag manifold of . Let be the projective line. Let $α\in H_2(X,{\Bbb Z})…