Research & Software

Computational notes, exact algebraic algorithms, and software implementations focusing on discrete homology, geometric representation learning, and non-commutative algebra.

Research Interests

Algebraic Topology of Discrete Sequences

• Formulation and evaluation of $fr$-codes (derived functors of limits over categories of free presentations of groups) to analyze the structure of discrete sequences.
• Computational implementations of the non-commutative Magnus expansion in free group rings to identify syntactic and logical coherence.

Geometric & Graph Representation Learning

• Non-Euclidean and hyperbolic graph embeddings (specifically, Poincaré and Lorentz models) for representing hierarchical networks, taxonomies, and linguistic structures with minimal metric distortion.
• Geometric Graph Neural Networks (GNNs) and the integration of topological features into message-passing architectures.