1. Analysis Research Team
This research area primarily focuses on operator theory, operator algebra, and harmonic analysis. The faculty is mainly composed of young academic talents, with all members holding doctoral degrees from renowned universities both domestically and internationally.

2. Algebra Research Team
This research area primarily studies Lie theory, homological algebras and K-theory, as well as the theory of group invariants. The team has a balanced composition and close international exchange and cooperation, achieving influential research results in the representation and classification of modular Lie hyperalgebras and Hom-type algebras, ideal approximation theory, and the theory of modular invariants of groups.

3. Geometry and Topology Research Team
This research area primarily focuses on singularity theory and its applications, noncommutative geometry, and calibrated geometry. The team members' work on singularity theory and its applications, noncommutative geometry, and the Dirichlet problem for minimal surface equations has a significant academic impact both domestically and internationally.

4. Computational Mathematics Research Team
This research direction is driven by practical problems in the fields of science and engineering. It studies mathematical modeling, analysis and computation for practical problems with real-world background and application prospects; it studies fast algorithms and theoretical analysis for scientific computing adapted to large-scale problems; and it studies mathematical theories, new methods and technologies for digital imaging and image processing.

5. Dynamics Systems Research Team
The research focuses primarily on the theory and applications of dynamical systems, including the dynamics theory of Hamiltonian systems, the theory and applications of infinite-dimensional dynamical systems, and dynamical system methods and applications in mathematical physics.

6. Biomathematics Research Team
The university has a comprehensive talent training system, and its research directions cover population dynamics, infectious disease dynamics, grassland ecosystem dynamics, etc. The research tools involve ordinary differential equations, functional differential equations, stochastic differential equations, reaction-diffusion equations, etc., making it an interdisciplinary field.

7. Partial Differential Equations Research Team
Primarily focused on semiconductor partial differential equations, the center continuously develops research in biological partial differential equations, fluid mechanics, dynamics, wave equations, and other related fields, making it one of the well-known partial differential equation centers in China.

8. Cybernetics Research Team
The main research areas are distributed parameter system control, stochastic system control, and inverse problems. All faculty members in the team possess independent research directions and capabilities, and have made a series of significant research achievements in the fields of distributed parameter system control, stochastic system control, and inverse problems.

9. Mathematics Education Research Team
Team members in this research area have made significant contributions to the formulation and revision of the compulsory education mathematics curriculum standards and the general high school mathematics curriculum standards, as well as to the formulation of professional standards for mathematics teachers and standards for the training of mathematics education teachers. They have also achieved a series of results in major national education policy decisions. Team members have in-depth research experience in comparative mathematics education between China and Japan, and in teacher pedagogy.