Recently, the winners of the 2019 National Grant Competitionfor the Installation in the Academy, PAI Program (Program of Attraction and Insertion of Advanced Human Capital) of CONICYT have been announced. This program seeks to contributing to the institutional strengthening of Chilean universities through the installation of researchers who are starting their independent careers. One of the beneficiaries of this initiative -41 at national level- is Sergio Caucao. He is currently performing a postdoctoral stay at the University of Pittsburgh (United States), after having obtained the highest academic degree in the Doctorate Program in Applied Sciences with a minor in Mathematical Engineering of Universidad de Concepción in 2018, under the guidance of the Director of the Center for Research in Mathematical Engineering, CI²MA, Gabriel Gatica and the researcher of the Center, Ricardo Oyarzúa.

This state funding initiative has a duration of three years and, in the case of Caucao, it will start running on March, when he becomes a member the Department of Applied Mathematics and Physics, at Universidad Católica de la Santísima Concepción, UCSC. The research project that Caucao will develop in that period is entitled Finite Element Methods for Models of Fluid Interaction-Poroelastic Structure and Related Problems. “The main idea of this research project is to continue developing the problems addressed in my postdoctoral studies, which have arisen from the desire of analyzing the coupling of Brinkman-Forchheimer and Biot equations, the latter motivated by some physical phenomena where the fluid flow considers high Reynolds numbers”, the researcher explains.

The stay that Caucao is currently performing in the United States began in January of this year and will last until February 2020, which fits perfectly with its incorporation in the UCSC from next March. “I am performing a postdoctoral stay at the Department of Mathematics, University of Pittsburgh, under the supervision of Professor Ivan Yotov,” the researcher details about this stay which is also funded by CONICYT through the Becas Chile Postdoctoral Fellowship outside Chile, call 2018. “My research project is entitled Numerical Methods for Fluid-Poroelastic Structure Interaction Models, which consists of studying, analyzing and developing new numerical methods for the coupling of Stokes equations (Navier-Stokes) and Biot, and other related models. In particular, we are interested indeveloping the well-posedness, stability and error analyses of the proposed schemes. All this motivated by the study of physical phenomena such as processes related with the flow of groundwater in aquifers, the extraction of oil and gas, and arterial flows”, Caucao says.

In the formulation of the project participated Professor Luis Gatica. He is an  academician and Director of the Master's Program in Applied Mathematics at UCSC, and associate researcher at CI²MA. “With the award of this insertion project, as institution, we seek to establish stable academic cadres with young researchers having, among other aspects, a high potential of scientific productivity, ability to lead Fondecyt-type research projects and form postgraduate academic cloisters, both Master and Doctorate, with CNA accreditation level”, explains Gatica. He also emphasizes that, “according to Sergio's academic and scientific training, it is expected that during the first year of insertion he will be incorporated into the academic staff of the Master's program in Applied Mathematics of the UCSC as a member of the cloister. In addition, he should apply to the Fondecyt 2020 Initiation research funding. In the medium term, the intention is him to collaborate by teaching and supervisinggraduation projects in his line of research, as well as byincreasing the scientific productivity of the UCSC. Finally, we hope Sergio, from his expertise, to collaborate us in the elaboration and implementation of a doctoral program project in the line of numerical analysis of EDP (doctorate program in collaboration with UdeC and UBB), which will allow us to give a choice of continuity of scientific training to our students of the Master program and to all of those who wish to opt for our institutional seal for the realization of these studies”, the UCSC academician details.

“This is the third insertion project in the line of Numerical Analysis that we have applied and won in UCSC with former students of the UdeC Doctorate (Abner Poza in 2012 and Jessika Camaño in 2014 preceded it), which on the one hand shows the high competitive level of graduates of the Doctorate program in Applied Sciences with mention in Mathematical Engineering from UdeC, as well as how successful it has been for the UCSC to incorporate young academics of excellence through Conicyt's insertion programs, opportunity that is undoubtedly appreciated and that as an institution we have taken advantage of our postgraduate programs and students in general”, Gatica emphasizes.

Caucao emphasizes that, given the high competitiveness in projects financed by CONICYT, “I consider the awarding of this new project as a great honor and recognition of the work done during my Master's studies at the Universidad del Bío-Bío and Doctorate in UdeC, in addition to my work as a postdoctoral student at both the Center for Research in Mathematical Engineering (CI²MA) and Pittsburgh. Undoubtedly, the high scientific productivity achieved in my doctoral training under the supervision of professors Gabriel Gatica and Ricardo Oyarzúa, the participation in national and international conferences thanks to the funding of my Conicyt scholarship for postgraduates studies in Chile, Department of Mathematical Engineering and Graduate Office of the UdeC, in addition to my work as a postdoctoral fellow at CI²MA in 2018 and as a co-advisor, together with Professor Gabriel Gatica, were crucial for the award of the project”.

The project recently awarded by Caucao considers financial support to perform research stays at the Department of Mathematics, University of Pittsburgh, as well as to participate in national and international conferences. “All this in order to maintain academic and research ties with Professor Ivan Yotov and the University of Pittsburgh. My expectations when startingmy position at UCSC are to develop cutting-edge research and fulfill the research objectives proposed in my insertion project; perform teaching and supervise undergraduate and graduate thesis. In particular, I’m interested in addressing the problems proposed in the project with students of the UCSC Master of Applied Mathematics program. In addition, I hope to contribute to the interdisciplinary and collaborative work with academics of the UCSC and other national and international universities”,  the researcher explains.

In addition to the postdoctoral activities that he currently carries out, Caucao participates as co-director of the student of the PhD program in Applied Mathematics at the UBB, Segundo Villa, in collaboration with Ricardo Oyarzúa, program director, who explains that “the fact that Sergio will work at UCSC is an example that crowns the permanent collaboration of academics from the three universities in the CI²MA. This is because he obtained the Master degree in Mathematics at the UBB, then the Doctorate degree at the UdeC and will now begin as a researcher at the UCSC. The latter, and the fact that he is in Pittsburgh, working with Ivan Yotov, opens up a huge range of new research topics that, for example, will allow him to supervise Master thesis there at UCSC. In addition, it contributes to the idea of definitively shaping the joint doctoral program between the three universities”.

As for the co-supervision of Villa's thesis, Oyarzúa details that “this will allow Segundo, who is now starting his thesis, to perform a research stay in Pittsburgh to work with Sergio and Ivan Yotov. We all work on nonlinear coupled problems in fluid mechanics, such as Navier-Stokes coupled with heat equations, or with poroelasticity”, the UBB academician says.