UM Faculty of Science and Technology project awarded funding from NSFC Key Program

The project ‘Study of Nonlinear Partial Differential Equations with Intrinsic Geometric Structures’, led by Gui Changfeng, chair professor and head of the Department of Mathematics in the Faculty of Science and Technology (FST) at the University of Macau (UM), has been awarded funding from the Key Program of the National Natural Science Foundation of China (NSFC). Yang Wen, associate professor in the same department, also contributed to the project. This is the first time that an FST project has received such funding, representing a significant breakthrough for UM in basic research.

UM has secured funding from NSFC for a total of 25 projects this year. The funded projects fall under various categories, including the Key Program, the General Program, and the Youth Scientists Fund (Categories A, B, and C). Among these is the project ‘Study of Nonlinear Partial Differential Equations with Intrinsic Geometric Structures’, which focuses on partial differential equations that have a strong connection to geometry, including the Allen-Cahn equation and mean field equations. The study will delve into the qualitative behaviour of their solutions, and address cutting-edge issues such as the classification of stable solutions to the Allen-Cahn equation, sphere covering inequality for high-dimensional mean field equations, and the uniqueness of solutions. The UM research team anticipates that the project’s outcomes will significantly enhance the understanding of the geometric structures underlying complex natural phenomena, drive academic progress in the field of nonlinear elliptic equations, and potentially lead to greater breakthroughs in both theoretical research and practical applications.

Prof Gui has long been dedicated to the study of nonlinear partial differential equations and related geometric problems. He has made significant contributions to the field, particularly in areas such as the Allen-Cahn equation, the conjecture of the best constant in the Moser-Trudinger inequality, the De Giorgi conjecture, and the Gibbons conjecture. He has published over 90 papers in leading mathematics journals. Furthermore, Prof Gui has led multiple national-level research projects, and has been selected for national talent programmes and overseas high-level talent recruitment programmes. He is an inaugural fellow of the American Mathematical Society, a Simons Fellow in Mathematics, and a fellow of the American Association for the Advancement of Science. He has also received numerous awards, including the Best Paper Award from the IEEE Signal Processing Society and the Pacific Institute for the Mathematical Sciences (PIMS) Research Prize.

Prof Yang specialises in the study of nonlinear elliptic partial differential equations. His notable work includes the classification of stable solutions to Liouville-type equations, the local mass classification of blow-up solutions to Toda systems, and the uniqueness of lump solutions to the Kadomtsev-Petviashvili equation. He has published over 60 papers in prestigious international journals. Prof Yang has also led and participated in multiple projects funded by NSFC and the Ministry of Science and Technology’s Key R&D Program.

Gui Changfeng

Yang Wen