Complex Systems: Critical Phenomena

This lecture covers the concept of critical phenomena in complex systems, focusing on stochastic objects and percolation. It explores the emergence of tree-like structures and scale-free networks, discussing the behavior of complex systems. The instructor delves into disorder systems, glasses, and combinatorial optimization, illustrating examples and algorithms. The lecture concludes with a detailed explanation of the complexity theory, including the NP-complete problems and the concept of hardness. It also touches upon the Euler circuits and the reduction of problems to polynomial time complexity.