1. Basic Mathematics:

　　Clabi-Yau Equation, L^2-upconversion, Symplectic and Symplectic Topologies, Cross-permeability of Topological, Order and Logical Structures, Hopf Algebra, Quantum Group Representation Theory and Correlation Problem, Structure Theory of Finite Group and General Group, Operator Semigroup Theory, Operator Algebra Structure, Classification and its application in Dynamical Systems, Geometric Properties of Analytic Functions, Soliton Theory and Integrable Systems.

2. Computational Mathematics:

　　Numerical Algebra, Exact Solutions of Nonlinear Partial Differential Equations, Numerical Solutions of Differential Equations and Biological Mathematics, Computational Techniques in Modern Communication, Computability Theory.

3. Probability and Mathematical Statistics:

　　Biological Population Dynamics, Probability Theory and Stochastic Processes, Mathematical Statistics Theory and Application, Financial Mathematics, Biostatistics, etc.

4. Applied Mathematics:

　　Bose-Einstein Condensation, Superconducting Ginzburg-Landau Model and Mean Curvature Flow, mathematical model of differential equations describing Population Diffusion and Infectious Disease Transmission, Cryptography and Information Security, Theoretical Computer Science, Mathematical Modeling.

5. Operational Research and Cybernetics:

　　Error Correction Coding Theory and Cryptography, theory and method of decision based on uncertain information, Nonlinear Differential Inclusion Theory and its application in Optimal Control, Nonlinear Stochastic Systems, Dynamic Analysis and Control of Complex Networks, Neural Networks.

6. Mathematics Teaching:

　　The research focus is on Mathematics Curriculum and Pedagogy. The Mathematics Curriculum focuses on the theory and practice of mathematics courses and the comparison of mathematics courses around the world. Mathematics Pedagogy mainly centers on the theory and practice of mathematics teaching.

7. Computational Science Theory:

　　Artificial Intelligence and Intelligent Systems, Cloud Computing and Big Data Technology, Network and Information Security, Intelligent Control Technology.

8. Complex Systems and Complex Network Dynamics and Control:

　　- studying Nonlinear Climate Dynamics, exploring the occurrence and development of climate events and finding effective ways to predict and detect such events;

　　- studying extreme weather events in complex systems, studying both general and local characteristics of extreme events and their association with global warming, finding out how sub-extreme events can indicate extreme events and working on the pre-warnings and predictions of record-breaking events;

　　- conducting research on Statistical Physics of complex systems and mathematical statistics methods with the characteristics of complex climate systems;

　　- making research on photoelectromagnetism of complex systems, exploring the electronic sequence transfer, spin-sequence transfer and change in complex systems, doping systems, passivation systems and finding the correlation between electrical, magnetic, and optical interactions between systems, and possible approaches to optimization.