About me

I hold an undergraduate degree in Mathematical Civil Engineering and am currently pursuing research in the analysis and numerical approximation of partial differential equations, with particular emphasis on mixed finite element methods. My work is motivated by physical models arising in porous media flow, transport phenomena, and fluid mechanics, where mathematical structure, stability, and approximation properties play a central role.

Recently, my research has focused on mixed formulations for fluid mechanics problems, leading to finite element methods with established well-posedness and convergence properties. In addition, I am investigating a posteriori error analysis for mixed finite element methods, as well as coupled problems in poroelasticity, with the aim of developing reliable numerical schemes that respect the underlying variational and operator structure of the problem.

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

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.