ИСТИНА

Totally positive matrices [1] form the basis of the modern intensively developing field of cluster algebras, have applications in integrable models of statistical physics, representation theory of quantum algebras, diophantine equations and many other fields. However, they arose in the context of the classical problem of small oscillations of linear elastic continuums [2]. The talk will be focused on the origin of these structures and some applications in the modern theory of electrical networks. 1. Postnikov A. Total positivity, Grassmannians, and networks, arXiv:math/0609764 2. Gantmacher F. R., Krein M. G., Oscillation matrices and kernels and small vibrations of mechanical systems. AMS CHELSEA PUBLISHING American Mathematical Society.