About me

I am currently a research assistant at Universidad Católica de la Santísima Concepción (UCSC) and GIANuC² under the supervision of professor Sergio Caucao, funded by ANID-Chile through Project FB210005: Centro de Modelamiento Matemático, and working on a project entitled A Posteriori Error Analysis for Stationary and Time-Dependent Problems in Fluid Mechanics. I hold an undergraduate degree in Mathematical Engineering (Ingeniería Civil Matemática) and am currently pursuing research in the analysis and numerical approximation of partial differential equations, with particular emphasis on mixed finite element methods.

My research is motivated by physical models arising in porous media flow, transport phenomena, poroelasticity, and fluid mechanics, where mathematical structure, stability, and approximation properties play a fundamental role. I am particularly interested in time-dependent problems, whose rich analytical structure and broad range of physical applications provide a compelling framework for the study of partial differential equations and numerical analysis. In this sense, coupled multiphysics problems also offer a rich set of models and pose several mathematical challenges.

Complex physical models often lead naturally to implementations that can become prohibitively expensive. Several approaches have been proposed in the literature to address this; in particular, I am interested in the analysis of a posteriori error estimators, which provide a powerful analytical tool for developing efficient adaptive algorithms that lead to significantly cheaper numerical simulations.

Alongside this line of research, I am also interested in PDE-constrained optimization problems under uncertainty, particularly within Rockafellian frameworks and risk-averse formulations. My interests in this area include control theory, optimization, and the calculus of variations, approached from the perspective of functional analysis and partial differential equations. I am especially drawn to problems that connect different areas of mathematics and reveal structural relationships that enable both rigorous analysis and effective computation.

I would like to express my sincere gratitude to my collaborators, whose guidance, generosity, and mathematical insight have been fundamental to my development as a researcher: Harbir Antil, Sean P. Carney, Sergio Caucao, Gabriel N. Gatica, Ricardo Ruiz-Baier, and my friend Benjamín Venegas.

On a more personal note, I am Chilean, and as is customary in the Spanish-speaking world, my full name consists of two surnames: Alonso Javier Bustos Barría. Outside of mathematics, I enjoy listening to music—particularly jazz, progressive rock, and classical music. My favorite musician is John Coltrane, and I also play the guitar.

I am also deeply interested in literature, and my favorite writer is Jorge Luis Borges. One passage I particularly enjoy comes from his short story Funes el memorioso:

Era el solitario y lúcido espectador de un mundo multiforme, instantáneo y casi intolerablemente preciso.

The story portrays a man endowed with a prodigious memory, capable of recalling every detail of his experience, yet rendered unable to generalize or abstract. Condemned to an overwhelming precision, he inhabits a world that he cannot forget.