时间：2026年1月5日（周一）15:00-16:30
地点: E14-212
腾讯会议：721-541-849
报告人：Linglingzhi Zhu, Georgia Institute of Technology
报告人简介：Linglingzhi Zhu is currently a Postdoctoral Fellow at the H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology. He received the Ph.D. degree in Operations Research from The Chinese University of Hong Kong in 2024. Previously, he received the M.S. degree in Computational Mathematics in 2020 and the B.S. degree in Mathematics in 2017 from Zhejiang University. His research interests include mathematical optimization and its applications in machine learning, signal processing, and statistics.
讲座主题：Rotation Group Synchronization via Quotient Manifold
讲座摘要：Rotation group synchronization is a fundamental inverse problem that arises in applications such as graph realization, computer vision, and robotics. In this talk, we focus on the least-squares estimator of rotation group synchronization with general additive noise. Departing from the standard approach of utilizing the geometry of the ambient Euclidean space to study phase/orthogonal group synchronization, we adopt an intrinsic Riemannian approach to study rotation group synchronization. Benefiting from a quotient geometric view, we prove the negative definiteness of the quotient Riemannian Hessian around the optimal solution to the orthogonal group synchronization problem. Consequently, the Riemannian local error bound property holds and can be applied to analyze the convergence properties of various Riemannian algorithms. Furthermore, improved estimation results of the spectral and least-squares estimator are derived, which guarantee the tightness of orthogonal group synchronization for solving the rotation group version under certain noise level.
