About me
Currently...
I'm Gabriel Pinochet-Soto, a 27-year-old graduate student at Portland State University. I'm pursuing my Ph.D. in Mathematical Sciences; I began in Fall 2021.
Prior Education
Previously, I obtained my Master and Bachelor degrees in Mathematics at Pontificia Universidad Católica de Valparaíso. I also participated in IMPA's summer school in 2019 and attended the Second NGSolve user meeting in 2018. I've completed internships at ANL and LLNL.
Research Interests
I like math. I like (most of) analysis. My current research interests include functional analysis, numerical analysis, and numerical methods for differential equations. During my bachelor's, I focused on numerical methods for production-destruction models. My master's research centered on numerical methods for resistivity measurements in axisymmetrical settings.
Current Research
-adaptivity, error estimation
DWR method for non-self-adjoint problems
(Time-harmonic) Maxwell equations
Helmholtz equation
PML methods
Eigenvalue problems
FEAST solver
DPG-based discretizations
Other topics:
FEM and implementation
Block solvers, saddle-point problems
Matrix-free methods and preconditioners
Multilevel methods and application
Encoder-decoder-based projectors/interpolators
JAX-based autodifferentiation
Personal Interests
Opinioated bits of myself...
Favorite Theorems
My current favorite Theorems are:
Grothendieck's characterization of compact sets in normed spaces
Banach's fixed point principle
Arzelà-Ascoli Theorem
My favorite proofs are:
Urysohn’s Lemma proof, by indexing separating sets with dyadic numbers.
Undecidability of the Halting problem, by a Cantor's diagonal-like argument.
Side Projects
To learn more about...
Complexity theory
Quantum complexity theory, quantum computing, quantum algorithms
Machine learning, artificial intelligence, neural networks
Implementations: automatic differentiation, low-level programming
Functional analysis, tensor products, linealization...
To learn more programming languages and paradigms...
Write "super useful" software and "safe" projects...
[ ] A shell
[ ] A FEM library
[ ] A programming language
[ ] A rubber-ducky
[ ] A NAS
To complete the projects above!
Personal Life
Sometimes, I do have a life out of school. I enjoy playing guitar, writing songs and poetry, reading comics, watching shows, and listening to music while biking around the waterfront. I've been residing in Portland, Oregon, for more than three years. Prior to Portland, I lived in Viña del Mar, Rio de Janeiro, Hayward, and Livermore.
Contact
email: gpin2 at pdx dot edu
instagram: at homeomorfismo