Conference Summary: The spectrum of differential operator and its applications
Date: August 10-15, 2025
Location: Tianyuan Mathematics Research Center, Kunming, China
The Workshop on “The spectrum of differential operator and its applications”was successfully held at the Tianyuan Mathematics Research Center from August 10 to August 15, 2025. This event was co-organized by Prof. Yuan Lou from Shanghai Jiaotong University and Prof. Maolin Zhou from Chern Institute of Mathematics, Nankai University.
Aims:
The goal of the workshop is to discuss the spectrum theory of differential operators, which is an important tool to study linear and nonlinear equations and plays a key role to understand the behaviors of solutions of evolution equations.
Topics:
The conference covered a wide range of topics, including but not limited to:
· The asymptotic behaviors of the principal eigenvalues of elliptic and parabolic operators
· The relationship between spectrum gap and coefficients
· The application of spectrum theory on semi-linear equations
· The application of spectrum theory on fluid mechanics (linear and nonlinear stability)
The workshop included 21 talks, panel discussions, group discussion of young researchers, and free discussions, facilitating both technical depth and informal idea exchange.
Participants:
25 researchers from institutions across China participated in the conference from different majors: elliptic and parabolic PDEs, probability theory and SDEs, geometry analysis, numerical analysis and modeling. Attendees included experts and young researchers from institutions such as:
· University of Science and Technology of China
· Shanghai Jiaotong University
· Nankai University
· Beijing Institute of Technology
· Tianjin University
· Anhui University
· The Hong Kong Polytechnic University
· Institute of Applied Mathematics, Chinese Academy of Sciences
· The Hong Kong University of Science and Technology
· Northwestern Polytechnical University
· The Chinese University of Hong Kong (Shenzhen)
· Lanzhou University
· South China University of Technology
· Sun Yat-sen University
· Innovation Academy for Precision Measurement Science and Technology, CAS
· Hangzhou Normal University
· Xiangtan University
Summary:
The workshop fostered a vibrant environment for academic exchange and collaborative exploration. It provided a comprehensive overview of current advances and future trends in spectral theory and its applications to PDEs, geometry, simulation, and modeling. Participants gained new insights, discovered research synergies, and laid the groundwork for future collaborations.
The organizers extend their gratitude to all speakers and participants. They expressed the hope that this workshop will inspire more profound collaborations and further advancements in this field.