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This lecture delves into the analysis of extreme events related to climate change, focusing on the remaining carbon budget, emission metrics, and the Paris Agreement's goals. It covers the concepts of emission metrics, net zero emissions, and the implications of different metrics on temperature outcomes. The lecture also explores the definition and characteristics of extreme events, such as heatwaves, fires, floods, and cyclones, along with the challenges in defining and predicting these events. Additionally, it discusses the fitting of extreme value distributions to climate data, the probability of occurrence of extreme events, and the changes in the frequency of hot extremes under different global warming scenarios.