48 citations · 85 across the 11 of their papers we have counts for
11 papers · 1 filter
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 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…
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})…