Applied Mathematics Research Center of Sun Yat-sen University Institute of Advanced Studies Hong Kong Successfully Hosts Workshop on “Interdisciplinary Research in Applied Mathematics”

On the morning of December 17, 2025, the Applied Mathematics Research Center of Sun Yat-sen University Institute of Advanced Studies Hong Kong (SYSUIASHK)successfully held “Interdisciplinary Research in Applied Mathematics” workshop, marking the Center’s second academic seminar since its establishment.The workshop invited Professor Yuan Yaxiang, Academician of CAS, Vice President of the China Association for Science and Technology, and Research Fellow at the Academy of Mathematics and Systems Science, as well as Professor Qi Yuanwei from The Hong Kong University of Science and Technology.Professor Yao Zheng’an, Director of the Applied Mathematics Research Center, presided over the meeting.Gao Yi, Director of the General Affairs Office of SYSUIASHK, first introduced the Institute’s overall development to the invited experts. The two scholars then delivered keynote academic presentations, followed by lively exchanges and discussions among participants.

Professor Qi Yuanwei first presented the Recent Progress on the Gatenby and Gawlinski Model of Cancer Invasion. In this work, Professor Qi and his collaborators studied a reaction–diffusion system modeling tumor invasion. The model was proposed by the renowned biologist and cancer specialist Gatenby and his collaborators. The underlying partial differential equation system features cross-diffusion terms and density-dependent degenerate diffusion coefficients. Professor Qi and his collaborators proved the existence and smoothness of solutions to the associated initial–boundary value problem under no-flux boundary conditions. More importantly, they rigorously established the existence of traveling wave solutions, providing valuable insights into the dynamical behavior of cancer invasion.

Academician Yuan Yaxiang then delivered a lecture entitled Optimization on Product Manifolds under a Preconditioned Metric. Since optimization on Riemannian manifolds depends critically on the choice of metric, understanding how the performance of Riemannian optimization methods varies under different metrics—and how to skillfully construct metrics to accelerate these methods—is of significant interest. To this end, Academician Yuan and his collaborators proposed a general framework for optimization problems on product manifolds equipped with preconditioned metrics and developed corresponding Riemannian optimization algorithms. In general, the metric is constructed via an operator designed to approximate the diagonal blocks of the Riemannian Hessian of the cost function. Academician Yuan and his collaborators proposed three specific operator design strategies: exact block-diagonal preconditioning, left–right preconditioning, and Gauss–Newton-type preconditioning. More specifically, they tailored new preconditioned metrics for canonical correlation analysis and truncated singular value decomposition, and adapted the proposed Riemannian methods accordingly. These approaches were shown to accelerate existing Riemannian optimization algorithms. In addition, they applied Gauss–Newton-type preconditioning to solve tensor ring completion problems. Numerical experiments across these applications confirmed that a well-designed metric can indeed accelerate Riemannian optimization methods.

Following the presentations, participating experts and scholars engaged in in-depth roundtable discussions. Academician Yuan and Professor Qi also offered valuable and constructive suggestions for the Center’s long-term development from different perspectives. They agreed that the Center should fully leverage Sun Yat-sen University’s geographical advantages and rich resources in the Guangdong–Hong Kong–Macao Greater Bay Area, actively utilize Hong Kong’s unique position as an international platform, and strive for greater achievements in talent recruitment and cultivation, frontier scientific research, and deep integration of industry, academia, and research. They emphasized contributing more substantially to the country’s high-quality development in related fields.

Guest Profiles

Professor Yuan Yaxiang is a Research Fellow at the Academy of Mathematics and Systems Science, an Academician of the Chinese Academy of Sciences, an Academician of the World Academy of Sciences, a Corresponding Member of the Brazilian Academy of Sciences, a Founding Fellow of the American Mathematical Society, a Fellow of the Society for Industrial and Applied Mathematics, and an Honorary Member of the London Mathematical Society. He currently serves as a Standing Member of the National Committee of the Chinese People’s Political Consultative Conference and Vice Chairman of the China Association for Science and Technology. He previously served as President of the Chinese Mathematical Society, President of the Operations Research Society of China, President of the International Council for Industrial and Applied Mathematics, and Vice President of the International Federation of Operational Research Societies. His honors include the Second Prize of the National Natural Science Award of China, the TWAS Prize in Mathematics, the Ho Leung Ho Lee Scientific and Technological Progress Award, the Chen Sheng-Shen Prize and Hua Luogeng Prize of the Chinese Mathematical Society, the Su Buchin Prize of the China Society for Industrial and Applied Mathematics, and the SIAM Prize for Distinguished Service. He has also been recognized as one of China’s “Top Ten Outstanding Youths”.

Professor Qi Yuanwei is an internationally recognized scholar in partial differential equations, with primary research interests in nonlinear reaction–diffusion equations, traveling wave solutions, and their applications in mathematical biology. He received his bachelor’s degree from the Department of Mathematics at Peking University in 1982, his master’s degree from the Chinese Academy of Sciences in 1985, and his PhD from the University of Oxford in 1990.