7 citations · 10 across the 6 of their papers we have counts for
9 papers
Cluster Reductions, Mutations, and -Painlevé Equations
Mikhail Bershtein, Pavlo Gavrylenko, Andrei Marshakov +1
We propose an extension of the Goncharov-Kenyon class of cluster integrable systems by their Hamiltonian reductions. This extension allows us to fill in the gap in cluster construc…
Classifying fermionic states via many-body correlation measures
Mykola Semenyakin, Yevheniia Cheipesh, Yaroslav Herasymenko
Understanding the structure of quantum correlations in a many-body system is key to its computational treatment. For fermionic systems, correlations can be defined as deviations fr…
Topological string amplitudes and Seiberg-Witten prepotentials from the counting of dimers in transverse flux
Mykola Semenyakin
Important illustration to the principle ``partition functions in string theory are -functions of integrable equations'' is the fact that the (dual) partition functions of $…
A brief introduction to quantum groups
Pavel Etingof, Mykola Semenyakin
These are lecture notes of a mini-course given by the first author in Moscow in July 2019, taken by the second author and then edited and expanded by the first author. They were al…
Solution of tetrahedron equation and cluster algebras
Pavlo Gavrylenko, Mykola Semenyakin, Yegor Zenkevich
We notice a remarkable connection between Bazhanov-Sergeev solution of Zamolodchikov tetrahedron equation and certain well-known cluster algebra expression. The tetrahedron transfo…
Cluster integrable systems and spin chains
A. Marshakov, M. Semenyakin
We discuss relation between the cluster integrable systems and spin chains in the context of their correspondence with 5d supersymmetric gauge theories. It is shown that $\mathfrak…