Explore the mathematical concepts behind generators of C0-semigroups of composition operators and their weighted counterparts in this 52-minute lecture by Eva Gallardo-Gutiérrez from Complutense University Madrid & ICMAT. Delve into the intricacies of semigroups, their generators, and natural assumptions before examining the proofs and consequences. Investigate weighted composition operators, including the latest developments, and uncover key ideas and conditions that drive this field of study. Gain insights from a comprehensive overview of the topic, complete with relevant references, as part of the Focus Program on Analytic Function Spaces and their Applications at the Fields Institute.