Areas of Study

My graduate disciplines sit where pure mathematics meets modern computation: the structures of algebra and analysis, and the methods that turn data into understanding.

Artificial Intelligence

Machine learning, neural networks, and natural language processing. Exploring how models learn from data, how their predictions are evaluated, and the mathematics behind intelligent systems.

Group Theory

Groups, symmetries, and the structures that describe transformations. Studying how abstract patterns connect geometry, algebra, and computation, with an interest in symmetry-aware approaches to machine learning.

Data Science

Statistical inference, exploratory analysis, and predictive modeling. Turning raw data into reproducible analyses, testing assumptions, and communicating findings that support informed decisions.

Linear Algebra

Vector spaces, matrix decompositions, eigenvalues, and linear transformations. The foundation for understanding embeddings, dimensionality reduction, and the computations at the heart of modern AI and data science.

Real Analysis

Limits, continuity, convergence, and the rigorous foundations of calculus. Studying how precise definitions and proofs explain the behavior of functions, sequences, and the methods used in mathematical modeling.

Graph Theory

Networks, connectivity, paths, and combinatorial structures. Exploring how relationships can be modeled and analyzed, from algorithmic problems to network data and graph-based machine learning.

Topology

Continuity, connectedness, compactness, and the structure of spaces. Investigating properties preserved under continuous transformations, with an interest in how shape and structure inform the analysis of data.