I am interested in mathematical theories and their applications for understanding the shapes and dynamics of data, with a particular focus on optimal transport theory. Optimal transport characterizes differences and correspondences between distributions through the minimum cost of transporting one distribution to another. My recent work focuses on analyzing the mathematical properties of regularized optimal transport and developing computational methods applicable to real-world data.

In applications, I am interested in shape data analysis and single-cell data analysis. For shape analysis, I develop methods that combine similarities between shapes with values of shape functionals, such as area and energy, to visualize the corresponding landscapes. For single-cell analysis, I use optimal transport theory to connect data from cell populations observed at different times and infer the dynamics of cell differentiation. I am also involved in collaborative research that integrates imaging data acquired using different measurement techniques to characterize drug distributions and their dynamics.

In addition, I work on shape optimization and inverse problems involving partial differential equations. Through both theoretical analysis and the development of methods, I seek to understand the shapes and dynamics of data.