AMS-Simons Travel Grant

My research interest lies in the mathematics of data, an emerging field that integrates various mathematical concepts to elucidate the fundamental principles of data science in practice. For example, high-dimensional probability offers valuable insights into understanding data structures in high dimensions, which, in turn, sheds light on other fields where such data arises. Specifically, I have been working on three different topics within this domain: randomized algorithms, graph-related models, and multifidelity methods. The tools I employ reside at the intersection of applied probability, statistics, and computational math. I will provide a brief summary of each of these topics and offer more details in the subsequent section. For randomized algorithms, my work primarily concerns randomized numerical approximation, which involves designing random sampling and projection techniques (e.g., sketching) to reduce the size of the original problem and obtain approximate solutions. Regarding graph-related models, I have been focusing on pairwise comparison models, commonly used for modeling sports competition and social choice, the planted clique model, which is central to the study of statistical-computational gaps, and archetypal analysis for extreme pattern detection. Finally, in the area of multifidelity methods, my research centers on uncertainty quantification for forward multifidelity models.