Explore a 28-minute lecture on the characterization of generators for various positive maps in quantum information theory. Delve into the study of k-positive and k-super positive maps, inspired by the renowned Lindblad, Kossakowski, Gorini, and Sudarshan's (LKGS) theorem. Discover a Schoenberg-type correspondence for non-unital semigroups of operators and its application to different cones of positive operators in L(M_n, M_n). Learn how this research contributes to re-establishing the LKGS theorem as a corollary. Presented by Purbayan Chakraborty from the Université de Bourgogne-Franche-Comté at the Institut des Hautes Etudes Scientifiques (IHES), this talk offers valuable insights into advanced concepts in quantum information and operator theory.