215 citations · 1.2k across the 39 of their papers we have counts for
40 papers
Symplectic groupoid and cluster algebras
Leonid Chekhov, Michael Shapiro
We consider the symplectic groupoid of pairs with unipotent upper-triangular matrices and being such that $\widetilde {\mathbb A}=B{\mathbb…
Virtual Euler characteristics via topological recursion
Leonid O. Chekhov
We use Seiberg--Witten-like relations in the topological recursion framework to obtain virtual Euler characteristics for uni- and multicellular maps for ensembles of classic orthog…
Characteristic equation for symplectic groupoid and cluster algebras
Leonid O. Chekhov, Michael Shapiro, Huang Shibo
We use the Darboux coordinate representation found by two of the authors (L.Ch. and M.Sh.) for entries of general symplectic leaves of the -groupoid of upper-triangul…
Cluster variables for affine Lie--Poisson systems
Leonid O. Chekhov
We show that having any planar (cyclic or acyclic) directed network on a disc with the only condition that all sources are separated from all sinks, we can construc…
Symplectic structures on Teichmüller spaces and cluster algebras
Leonid O. Chekhov
We recall the fat-graph description of Riemann surfaces and the corresponding Teichmüller spaces with holes and bordered cusps in the…
Quantised Painlevé monodromy manifolds, Sklyanin and Calabi-Yau algebras
Leonid Chekhov, Marta Mazzocco, Volodya Rubtsov
In this paper we study quantum del Pezzo surfaces belonging to a certain class. In particular we introduce the generalised Sklyanin-Painlevé algebra and characterise its PBW/PHS/Ko…