• He has experience in international collaboration with counterparts in countries such as China (Hong Kong), Brazil, Spain, and France 

In December 2018, Patrick Vega Román obtained at the University of Concepción, UdeC, the academic degree of Doctor in Applied Sciences with mention in Mathematical Engineering, after defending his thesis 'Adaptive and High Order Hybridizable Discontinuous Galerkin Methods in Fluid Mechanics' in which he had the co-direction of Weifeng Qiu from the City University of Hong Kong (China) and UdeC researchers Manuel Solano Palma and Rodolfo Araya Durán, current director of the Center for Research in Mathematical Engineering, CI²MA.   

In this regard, Professor Solano commented that "I am happy to see how Patrick has evolved over time. He was always very hardworking and dedicated in research, but when I met him as a student, he was disorderly with his academic responsibilities. However, over time he has been able to overcome this shortcoming. In fact, in recent years he has had an important academic growth".   

"Based on work and his impetus to generate new knowledge, "the academic added, "he has published articles in excellent journals, has organized thematic sessions in different conferences and has also built an important collaboration network of national and international researchers".   

Previously, in 2014, also at CI²MA, but under the direction of Prof. Rodolfo Rodríguez Alonso, Patrick had developed his graduate thesis to obtain the professional degree of Civil Mathematical Engineer from UdeC. More recently, at the beginning of this semester, Dr. Vega joined the Department of Mathematics and Computer Science (DMCC) of the Faculty of Science of Universidad de Santiago de Chile (USACH). This, he details, "through a job offer on the DMCC website of the USACH, which I came to through an advertisement on the website of the Mathematical Society of Chile (SOMACHI)".   

"It is always very gratifying to see how our graduates are influencing the mathematical development of the country. It is certain that Patrick will be able to develop a fruitful academic career at Universidad de Santiago", emphasized the director of CI²MA, Dr. Rodolfo Araya Durán.   

"After graduating", Patrick continued, "I continued my collaboration with my thesis advisers through my participation in the MATH-AmSud project 'Photovoltaic Solar Devices in Multiscale Computational Simulations (PHOTOM)', whose national coordinator was Diego Paredes, also a researcher at CI²MA", he explains and adds that "after participating in WONAPDE 2019, I also presented at the second workshop of the PHOTOM project, which brought together the Brazilian, Chilean and French counterparts and took place at the Inria Sophia Antipolis - Méditerranée center, Valbonne, France".   

This 2019 experience, details Patrick, "motivated me to apply for a postdoctoral position at that center, to work on a posteriori error estimates for discretizations of Maxwell's equations and related models with Théophile Chaumont-Frelet and Stéphane Lanteri, joining the Atlantis team, whose research activities focus on modeling and numerical methods for computational wave-matter interactions at the nanoscale".  

In the meantime, Patrick worked "teaching mathematics and programming courses at Universidad Católica de la Santísima Concepción and Universidad Andrés Bello. Once in France, I worked for a year and a half on a posteriori error estimates for discretizations of Maxwell's equations at high frequency and model from of nanophotonics, which gave rise to three scientific papers and the start of a couple more".   

"In June 2021", he details, "after concluding my stay at the Inria center, I joined the Institute of Mathematics (IMA) of the Pontificia Universidad Católica de Valparaíso (PUCV), with funding from an internal call of that university, to work with Ignacio Muga on residual minimization methods. My work as part of the Numerical Analysis Research Group (IMA Numerics) allowed me to diversify my research topics and networks, through my work with Ignacio Muga and Sergio Rojas (also part of IMA Numerics), the award of a FONDECYT postdoctoral project, and a three-month stay at the University of the Basque Country with the group of Professor David Pardo". 

"As a result of this period of work," he explains, "we published two articles in SIAM Journal on Numerical Analysis, one proceeding and submitted a paper for publication, in addition to four works in progress. In parallel to my postdoctoral research in France and Chile, I participated as a reviewer in the Journal of Scientific Computing and SIAM Journal on Numerical Analysis, I taught (at PUCV and Universidad Técnica Federico Santa María) and participated in the organization of events (a thematic session at the XLVIII Mathematics Week at PUCV and the periodic seminar Caleta Numérica). In addition, during my stay at PUCV, motivated by Ignacio Muga, I began my incursion into the resolution of partial differential equations using artificial neural networks".   

Among his new obligations at USACH, in addition to scientific research, Dr. Vega teaches the Linear Algebra course for undergraduate courses, which is compatible with the co-organization of thematic sessions of numerical analysis in two different conferences: "the XLIX Mathematics Week of the PUCV and the XCI SOMACHI meeting at the Faculty of Sciences of the U. of Chile", in addition to the co-organization of a mini-symposium of WONAPDE 2024, which will be held at the UdeC". At the same time, Patrick details that "during the next year I will probably be a graduate faculty member of the Master‘s and Doctorate programs in Science with a mention in Mathematics of the DMCC".  

Patrick emphasizes that this incorporation is his first experience in a state institution "and, obviously, for me, it is an honor to join an institution with the historical and symbolic value of the former Universidad Técnica del Estado (UTE), which to this day is recognized for its excellence and for the promotion of social equity, inclusion and pluralism at the service of the country and the construction of a democratic, equitable and sustainable society".