70 citations · 395 across the 55 of their papers we have counts for
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Lagrangian configurations and symplectic cross-ratios
Charles Conley, Valentin Ovsienko
We consider moduli spaces of cyclic configurations of lines in a -dimensional symplectic vector space, such that every set of consecutive lines generates a Lagrangian s…
-deformed rationals and -continued fractions
Sophie Morier-Genoud, Valentin Ovsienko
We introduce a notion of -deformed rational numbers and -deformed continued fractions. A -deformed rational is encoded by a triangulation of a polygon and can be computed…
Farey boat I. Continued fractions and triangulations, modular group and polygon dissections
Sophie Morier-Genoud, Valentin Ovsienko
We reformulate several known results about continued fractions in combinatorial terms. Among them the theorem of Conway and Coxeter and that of Series, both relating continued frac…
Cluster algebras with Grassmann variables
Valentin Ovsienko, Michael Shapiro
We develop a version of cluster algebra extending the ring of Laurent polynomials by adding Grassmann variables. These algebras can be described in terms of `extended quivers' whic…