Academic Projects

Master’s Thesis in Applied Mathematics and Computation

Thesis title: Semilinear Wave Equations on Decelerated Expanding FLRW Spacetimes.

• Thesis
• Extended Abstract

Geometric Quantization

A research project done as part of the master’s in mathematics at IST on geometric quantization and complex Hamiltonian flows.

• Geometric Quantization

Mathematical Foundations of Machine Learning

Set of notes and code implementations exploring statistical learning theory [1], machine learning [2], and the neural tangent kernel [3].

• Mathematical Foundations of Machine Learning - Notes
• Mathematical Foundations of Machine Learning - Code

Manifold Learning

Two projects related to manifold learning done in the courses “Mathematics for Machine Learning” and “Nonlinear Optimization” at IST.

• “Manifold Learning in the context of Partially Labelled Classification” - Report
• “Manifold Learning in the context of Partially Labelled Classification” - Code
• “A Duality View of Spectral Methods for Dimensionality Reduction” - Report

Feature Selection

A project related to feature selection via information theory done in the course “Mathematics for Machine Learning” at IST.

• Feature Selection - Report
• Feature Selection - Code

Collaborative Filtering

A project related to collaborative filtering for a movie recommendation system done in the course “Mathematics for Machine Learning” at IST.

• Collaborative Filtering - Report
• Collaborative Filtering - Code