5 citations · 5 across the 3 of their papers we have counts for
6 papers
Integrable Systems and Rank One Conditions for Rectangular Matrices
Michael Gekhtman, Alex Kasman
We provide a determinantal formula for tau-functions of the KP hierarchy in terms of rectangular, constant matrices , and satisfying a rank one condition. This result is…
Cluster algebras and Weil-Petersson forms
Michael Gekhtman, Michael Shapiro, Alek Vainshtein
In our previous paper we have discussed Poisson properties of cluster algebras of geometric type for the case of a nondegenerate matrix of transition exponents. In this paper we co…
Cluster algebras and Poisson geometry
M. Gekhtman, M. Shapiro, A. Vainshtein
We introduce a Poisson variety compatible with a cluster algebra structure and a compatible toric action on this variety. We study Poisson and topological properties of the union o…
The number of connected components in the double Bruhat cells for nonsimply-laced groups
Michael Gekhtman, Michael Shapiro, Alek Vainshtein
We compute the number of connected components in a generic real double Bruhat cell for series and and an exceptional group .
Poisson brackets on rational functions and multi-Hamiltonian structure for integrable lattices
L. Faybusovich, M. Gekhtman
We introduce a family of compatible Poisson brackets on the space of rational functions with denominator of a fixed degree and use it to derive a multi-Hamiltonian structure for a…
On billiard weak solutions of nonlinear PDE's and Toda flows
Mark Alber, Roberto Camassa, Michael Gekhtman
A certain class of partial differential equations possesses singular solutions having discontinuous first derivatives ("peakons"). The time evolution of peaks of such solutions is…