CARLOS ÁVILA
Computer Science Engineer. Educator. Based in El Salvador.
RESEARCH
ENGINEERING
TEACHING
I build systems and break down equations for a living.
Background in software engineering and mathematics education.
Research interests: applied mathematics, topology, and their applications to machine learning.
AI & NLP
Language Modeling
Education
Math Didactics
Technical Stack
Full Stack (JS, TS, Next, Spring)
SeniorPython
SeniorLinux
SeniorApplied Mathematics
AdvancedDevOps & Cloud
Intermediate// Elsewhere
Academic Background/ Education & Research
Degree
Computer Science Engineering
Universidad Centroamericana José Simeón Cañas (UCA)
Thesis Research
Geometric Framework of Topological Data Analysis for Text-Based Machine Learning
Application of Topological Data Analysis (TDA) to extract geometric features from natural language vector embeddings.
Recognitions
National Champion
Huawei ICT Competition 2023-2024 (Cloud Track)
Jun 2024Presidential Scholarship
Becas FANTEL - Academic Excellence
Merit-basedMath Schools & Specialized Certifications
EMALCA Honduras 2025
Universidad Nacional Autónoma de Honduras
Focus Areas & Coursework
- High-Dimensional Statistics
- Integer Optimization Applied to Humanitarian Logistics
- Introduction to Control Theory
- Introduction to Statistical Learning
CIMPA School El Salvador 2024
Submanifold Theory and Geometric Analysis
Focus Areas & Coursework
- Differential Operators on Riemannian Manifolds
- Geometric Analysis on Surfaces
- Introduction to Differential Geometry of Surfaces
- Introduction to Finsler Geometry
- Introduction to Lorentzian Geometry of Curves and Surfaces
- Recent Advances in Lorentzian Geometry
EMALCA Costa Rica 2024
Universidad de Costa Rica (UCR)
Focus Areas & Coursework
- An Introduction to Elliptic Curves
- Introduction to Dynamical Systems
- Numerical Stability and an Application of an Earth Dam
- Plane Algebraic Curves
Huawei Certified ICT Associate
Artificial Intelligence (HCIA-AI)
EMALCA El Salvador 2023
Universidad de El Salvador
Focus Areas & Coursework
- Introduction to Data Science: Linear Regression
- Introduction to Error-Correcting Codes Theory
- Linear Optimization: Models and Solution Methods
- Numerical Solution of Partial Differential Equations
- An Introduction to Differential Geometry of Curves and Surfaces
Professional Experience
Software Implementation Technician
EcoPortal (New Zealand) · Remote
Technical configuration and deployment of SaaS solutions for international enterprise clients. Remote production environment management.
High School Math Teacher
Escuela Americana
Instruction of Algebra I & II aligned with international standards (AERO). Curriculum development focused on critical thinking and problem-solving.
Teaching Assistant
UCA El Salvador
Teaching Assistant for Calculus I, II, III, Differential Equations, and Numerical Analysis at the Department of Mathematics.
Lecturer
UCA El Salvador
Lecturer for Logic and Mathematics, Mathematics for Engineering, and Mathematics for Economics at the Department of Mathematics.
Research Study Assistant
UCA El Salvador / Florida International University
Programming, software design, database management, and QA for the collaborative research project on civil society capacity building.
Automation Engineer
Power[GI] (El Salvador) · Remote
Engineering scripts and bots for internal workflow optimization.
Data Analyst
True North Land (United States) · Remote
Data processing and business intelligence generation for the US real estate sector.
SelectedProjects
Theory applied. Systems built.
Geometric Framework of TDA for Text-Based Machine Learning
Undergraduate thesis applying Topological Data Analysis to extract geometric features from natural language vector embeddings. Developed at Universidad Centroamericana José Simeón Cañas under the supervision of Dr. Yoceman Sifontes.
Naive Bayes Stroke Predictor
Probabilistic model to predict stroke likelihood using Bayesian probability. Categorizes variables such as age, glucose levels, and health conditions to identify risk factors. Developed from scratch in Python as part of the AI course at Pontificia Universidad Javeriana.
Parametric Curves & Bézier Curve Modeling
Researched and modeled 2D/3D parametric curves and Bézier splines using Python, implementing Lagrange interpolation and Hermite cubic polynomials to analyze computational trade-offs.
Notes
Occasional thoughts on math, code, and the spaces between.
Contact
Available for consultation on software architecture, AI integration, and educational technology.