Watch a 26-minute lecture exploring the mathematical concepts of quadratic differentials and degenerate eigenvalues, presented by Dmitrii Rachenkov at the International Centre for Theoretical Sciences. Part of a comprehensive program on discrete integrable systems, the lecture delves into mathematical physics concepts related to difference equations, cluster algebras, and probabilistic models. Learn about integrable systems' exact solvability properties and their conserved quantities, connecting topics from theoretical physics, statistical physics, string theory, combinatorics, representation theory, geometry, and probability. The presentation is part of a broader two-week program featuring mini-courses, problem sessions, and workshops, designed for both junior and senior researchers interested in discrete integrable systems and related mathematical fields.