Researchers, thesis students and ex-thesis students of CI²MA had an outstanding participation in the XXXII Jornada de Matemática de la Zona Sur, which was held at the University of Magallanes, in Punta Arenas, from April 24 to 26, 2019. This congress, organized by the Department of Mathematics and Physics of that university, had as its main purpose (like all previous versions) to generate new dissemination spaces for the most recent results obtained by researchers and students from universities of southern Chile. In this event, the researcher of CI²MA, Mauricio Sepúlveda, delivered the plenary lecture entitled "Stability Analysis and Numerical Methods for Damped Dispersive Equations". In turn, the researcher also of CI²MA, Rommel Bustinza, organized the Invited Session on Numerical Analysis, in which there were presentations by: the postdoc David Zorío, who is supervised by the Vice-Director of CI²MA, Raimund Bürger; the thesis students of our Doctorate in Applied Sciences with major in Mathematical Engineering, Paul Méndez (supervised by Raimund Bürger as well), Nestor Sánchez (supervised by the researcher of CI²MA, Manuel Solano), Cristian Cárcamo (supervised by the researcher of CI²MA, Rodolfo Araya), and Iván Velásquez (supervised by the researchers of CI²MA, David Mora and Rodolfo Rodríguez); the researcher of CI²MA, Luis Miguel Villada, and finally Rommel Bustinza himself. In addition to the above, a short course entitled "Introduction to numerical calculation in mathematical modelling", was given by the graduated of our Doctorate in Applied Sciences with major in Mathematical Engineering, Emilio Cariaga.