Research
My main research interests until now have revolved around various fields of applied mathematics, and I am now orienting myself more towards Machine Learning.
Current Work - Internship at INRIA, Sophia-Antipolis, France
I am currently pursuing a research internship at INRIA, at the intersection of Applied Mathematics, Machine Learning, and Optimal Transport. More precisely, my work focuses on generalizing entropic optimal transport to the broader class of f-divergence–regularized frameworks, with applications in machine learning. The first part of the internship concerns establishing theoretical guarantees, while the second part will focus on designing and implementing efficient algorithms for accelerated computation of Wasserstein distances. An INRIA research report is available here .
Three-semester PDE research project - MICS laboratory, CentraleSupélec, France
I met my advisor, Anna Rozanova-Pierrat, of the MICS laboratory during my first year of studies at CentraleSupélec. After a few exchanges, she suggested we started working together on a PDE research project, along with a few fellow students. The main idea behind all the work produced throughout these three semesters was to generalize existing PDE/Functional Analysis theories and results, that were developed exclusively on smooth boundary domains to rough boundary domains. During the first semester, the research focused on the Stokes system for fluids in domains with potentially rough, typically fractal boundaries. The study established the well-posedness of the problem with Dirichlet boundary conditions. Then during my second year at CentraleSupélec, further work explored theoretical properties of unusual Sobolev spaces, expanding general results like the Hodge decomposition to rough boundary domains. Below are the reports for each semester. Only the most recent one is written in English, as it was prepared with a view toward potential publication:
Last semester report (PDF)
Last semester slides (PDF)
Second semester report (PDF)
First semester report (PDF)
PDE/Modeling project - CentraleSupélec, France
This project was carried out during the PDE course, in my first year of studies at CentraleSupélec. The teachers offered the opportunity to the willing students to choose a problem of their own, model it with PDEs, and then apply the methods seen in class to solve it. I chose to model the growth of a spy network using a system of partial differential equations, established its well-posedness, and analyzed the influence of various parameters through numerical (finite elements) solutions.
Project report (PDF)
Jupyter Notebook
Transport and diffusion of a pollutant within an aquifer - Lycée International de Valbonne, France
Measured the coefficients of an existing PDE model through experiments. Developed a discrete numerical model based on the measured coefficients and conducted simulations.