My name is Xi Wang (王溪). I am now a Postdoctoral Research Assistant EE&T, University of New South Wales, under the supervision of Professor Victor Solo. Prior to this, I obtained Bachelor’s degree in Mathematics and Applied Mathematics from the University of Chinese Academy of Sciences in 2018, and Ph.D. degree in Operational Research and Cybernetic, at the Academy of Mathematics and Systems Science, Chinese Academy of Sciences, under the supervision of Professor Yiguang Hong. I was also a visiting student at the Australian Centre for Field Robotics, University of Sydney, under the supervision of Associate Professor Guodong Shi during 2022-2023.

Research Insterest

My research interests primarily focus on fundamental Riemannian optimization and Riemannian numerical analysis. These two areas aim to extend classical optimization and numerical computation techniques to curved spaces, or namely, Riemannian manifolds.

Riemannian optimization explores how to formulate and solve optimization problems when the search space is a manifold rather than a Euclidean space. This is particularly important in applicationssuch as low-rank matrix recovery, pose estimation, and machine learning, where data naturally resides on nonlinear geometric structures.

Riemannian numerical analysis, on the other hand, focuses on the design and analysis of numerical schemes that respect the underlying manifold geometry, particularly for differential equations evolving on manifolds. Riemannian numerical analysis includes developing integrators for manifold-valued ODEs and SDEs that preserve geometric properties such as constraints and symmetries, which is essential for the accurate simulation and control of systems on Riemannian manifolds. Typical applications include modeling the attitude dynamics of rigid bodies on the Lie group ${\rm SO}(3)$, as well as simulating diffusion processes on curved biological surfaces.

A central theme in both areas is the exploitation of the manifold’s geometric structure to design more accurate, stable, and efficient algorithms. By leveraging tools from differential geometry, such as exponential maps, retractions, parallel transport, and curvature, we can avoid embedding distortions, enforce constraints intrinsically, and gain deeper theoretical insights into algorithmic behavior.

In my future research, I aspire to develop Riemannian approaches for applications in quantum computing, machine learning, and biomedical data analysis.