Professor Du Jinyuan from the School of Mathematics and Statistics at Wuhan University visited Macau University of Science and Technology on the afternoon of October 16, 2025. He was warmly received by Professor Qian Tao, Director of the Macao Centre for Mathematical Sciences at Macau University of Science and Technology, and Associate Professor Xiao Xuanxuan, Assistant Director of the Macao Centre for Mathematical Sciences.
Professor Du Jinyuan specialized in complex and hypercomplex boundary value problems, including theoretical and applicable computational methods in fractional calculus. His primary research focuses on numerical methods for singular integral equations and their applications in elasticity and fracture mechanics. He has made significant contributions to the mechanical quadrature of Cauchy-type singular integrals, building upon the work of renowned experts in numerical quadrature for singular integrals, such as Hunter, Paget, Elliott, and the Erdogan mechanics school. His research achievements in mechanical quadrature of singular integrals and numerical solutions of singular integral equations have substantially advanced both the theoretical and practical aspects of the discipline. Additionally, Professor Du supervises graduate students and contributes to academic service through organizations such as the Chinese Mathematical Society, supporting progress in mathematical physics and engineering applications.
Professor Du Jinyuan delivering a presentation.
Professor Du systematically introduced the Hilbert boundary value problem for regular functions on hyperplanes, where the solutions exhibit arbitrary integer orders of growth or decay (positive, negative, or zero) at infinity. A complete solution to the problem, along with explicit closed-form conditions for solvability, is rigorously derived. Even when restricted to the classical complex plane, the case of negative order is entirely novel. These results are achieved through two key components: (1) The Hilbert boundary value problem is transformed into a Riemann boundary value problem via the Clifford symmetric extension method, employing numerous innovative geometric techniques. This represents the core focus and primary contribution of the work, effectively initiating the study of geometric Clifford function theory. (2) The complete resolution of the Riemann boundary value problem is presented in the companion paper, which is another collaborative work of ours. While this also marks a significant advancement in Clifford boundary value problems, it does not involve geometric methods and thus stands solely as a breakthrough in Clifford analysis concerning boundary value problems.
A group photo of Professor Du Jinyuan (right), Professor Qian Tao (center) and Professor Wang Jianzhou (left)
