About me

I am a mathematics PhD student at George Mason University, where I began my studies in Fall 2026. I work as a research assistant with Professor Harbir Antil at the Center for Mathematics and Artificial Intelligence. My research focuses on the analysis and numerical approximation of partial differential equations, with emphasis on finite element methods.

I am particularly interested in developing mathematical tools, drawing on functional analysis, convex analysis, and optimization, to design and analyze numerical methods for partial differential equations. My current research explores the interplay between convex duality and finite element methods, particularly in the development of a posteriori error estimates, as well as the analysis and discretization of parabolic problems.

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 tells of a man with an extraordinary memory who can recall everything he experiences but cannot generalize or think abstractly.