Stochastic Analysis and Statistical Genetics
My dissertation, co-advised by Fei Xue and Jing Wang, applies stochastic methods to Statistical Genetics. I am developing a general linkage disequilibrium fourth moments (LD4M) method that applies to any polygenic linear model and estimates the polygenicity of a trait in a population, that is, how many genetic variants contribute to it. Using tools from Martingale Theory, I extend the model beyond the Gaussian setting, allowing non-Gaussian distributions for both the errors and the variables. In the Gaussian case, I proved Random Matrix Theory results computing the moments of general Wishart distributions, and used Chatterjee’s second-order Poincaré inequality to show that the regression coefficient is asymptotically normal. A first paper from this project, Inferring the efficient number of true signals using high-dimensional summary-level data, written with F. Xue and B. Zhao, appeared in 2026.
Combinatorics and Number Theory
Ever since my Olympiad days, I have been drawn to elementary problems with connections to deep mathematics. I have worked on counting lattice paths, the subject of my paper Lattice paths in corridors and cyclic corridors in Contributions to Discrete Mathematics, as well as on polygonal numbers and the dynamics of quadratic sequences. My recent preprint with S. Rodríguez and G. Salazar, Perfect squares in reciprocal-sum sequences and primes that are inert in quadratic fields, continues this line of work, and further work is in preparation.
As an undergraduate at Universidad Nacional de Colombia, I did research on combinatorial lattice paths and Experimental Number Theory with R. Flórez, J. L. Ramírez, and V. Moll. In spring 2021, as a UREP-C Research Scholar at Purdue, I surveyed recent progress on the Generalized Baues Conjecture under the direction of Manuel Rivera.
Machine Learning and AI
I am interested in new Machine Learning methods and their applications across fields. In summer 2025 I worked at Outlier, training AI systems on mathematical reasoning and proofs, and I have studied how well Large Language Models can write formal proofs in Statistics (arXiv:2606.23666). I am currently an AI Research Intern at Blue Wave AI Labs, where I work on Numerical Optimization and on neural network models for anomaly detection in nuclear energy.