Differential Geometric

Differential geometry provides powerful mathematical tools for analyzing and modeling complex systems, particularly those involving shapes, curves, and transformations in high-dimensional spaces. Current research focuses on applying these tools to diverse areas, including the development of more interpretable graph neural networks, improved robotic control algorithms using Lie group and algebra methods, and the creation of more accurate and reliable data visualization techniques through geometric autoencoders. These advancements offer significant improvements in areas such as machine learning explainability, robotics, and data analysis, leading to more robust and insightful models and applications.