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Explore the fascinating concept of phase transitions in combinatorial structures through this 47-minute seminar talk by Tomasz Łuczak, part of the MUNI Seminar Series. Delve into the origins of phase transition in physics and its application to discrete combinatorial systems. Discover how small parameter changes can dramatically alter system behavior, examining both physically-inspired phenomena and naturally emerging transitions in combinatorial studies. Gain insights into rigorous analyses of these rapid structural transformations across various examples.