Explore the positivity of Meijer G-functions on the positive half-line in this 43-minute lecture by Thomas Simon from the Institut des Hautes Etudes Scientifiques (IHES). Delve into results and conjectures focusing on non-trivial cases where the underlying random variable is not an independent product of quotients of beta random variables. Gain insights into the concepts of logarithmic infinite divisibility and quasi infinite divisibility. Time permitting, examine potential extensions to Fox H-Functions. This talk, presented by Thomas Simon from Paul Painlevé Lab at the Université de Lille, offers a deep dive into advanced mathematical concepts for those interested in complex analysis and special functions.