Research Units

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Mean Curvature Flow in the Heisenberg Group

Geometric Partial Differential Equations Unit

Analysis of partial differential equations is a very rich mathematics subject, which is broadly applied in a large variety of fields of science. It is particularly important to study nonlinear PDEs that arise in geometry and many related areas. The Geometric Partial Differential Equations Unit aims to develop new analytic methods to understand behavior of solutions to various geometric evolutions and explore solvability of nonlinear equations in general geometric settings such as sub-Riemannian manifolds and metric spaces. Our research is motivated by numerous applications in material sciences, crystal growth, image processing and is also closely connected with topics in optimal control, game theory and machine learning, etc.
Quing Liu

Qing Liu

Associate Professor

MLDS Unit

Machine Learning and Data Science Unit

In the machine learning and data science (MLDS) unit, we focus on developing fundamental machine learning algorithms and solving important scientific problems using machine learning. We are currently interested in statistical modeling for high-dimensional data including kernel and deep learning models and geometric machine learning algorithms, including graph neural networks (GNN) and optimal transport problems. In addition to developing ML models, we focus on developing new machine learning methods to automatically find a new scientific discoveries from data.
Makoto Yamada

Makoto Yamada

Associate Professor

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