Outline Introduction Lax pairs in the continuous case Symmetry approach in the continuous case Lax pairs in the semidiscrete case Symmetry approach in the semidiscrete case Semidiscrete Toda lattices Sergey V. Smirnov Moscow State University Matrix Models, Tau functions and Geometry University of Glasgow March 3, 2012 Sergey V. Smirnov Semidiscrete To da ... Symmetry x y provides another Lax presentation: x (j ) = -h(j - 1)(j - 1) . ...