349 citations · 768 across the 43 of their papers we have counts for
47 papers
A unified approach to exotic cluster structures on simple Lie groups
Misha Gekhtman, Michael Shapiro, Alek Vainshtein
We propose a new approach to building log-canonical coordinate charts for any simply-connected simple Lie group $\G$ and arbitrary Poisson-homogeneous bracket on $\G$ associated wi…
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…
Introducing isodynamic points for binary forms and their ratios
Christian Hägg, Boris Shapiro, Michael Shapiro
The isodynamic points of a plane triangle are known to be the only pair of its centers invariant under the action of the Mobius group on the set of triangles. Generalizing this cla…
Finiteness of rank for Grassmann convexity
Nicolau C. Saldanha, Boris Shapiro, Michael Shapiro
The Grassmann convexity conjecture gives a conjectural formula for the maximal total number of real zeros of the consecutive Wronskians of an arbitrary fundamental solution to a di…
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 algebras from surfaces and extended affine Weyl groups
Anna Felikson, John W. Lawson, Michael Shapiro +1
We characterize mutation-finite cluster algebras of rank at least 3 using positive semi-definite quadratic forms. In particular, we associate with every unpunctured bordered surfac…