Analytic number theory algebraic number theory Diophantine analysis, transcendental number theory, model and module function theory, number theory application.

Keywords algebraic group theory, group representation theory, Lie group, Lie algebra, algebraic group, canonical group, homology algebra, algebraic K theory, Kac-Moody algebra,

Ring theory, algebra (separable algebra), ontology, coding theory and method, and research on order structure.

Keywords geometric global differential geometry, algebraic geometry, manifold analysis, Riemannian manifold and Lorenz manifold, homogeneous space and symmetric space,

Harmonic mapping and its application in theoretical physics, submanifold theory, Young-Mills field and fiber bundle theory, symplectic manifold.

Topological differential topology, algebraic topology, low-dimensional manifold, homoethics theory, singular catastrophe theory, point set topology.

Keywords function theory, multiple complex variable function theory, complex manifold, complex dynamic system, simple complex variable function theory, real method of harmonic analysis in Rn,

Harmonic analysis and function approximation theory of noncompact semisimple Lie groups.

Functional analysis Nonlinear functional analysis, operator theory, operator algebra, functional equation, space theory, generalized function.

Functional differential equation of ordinary differential equation, characteristic and spectrum theory and its inverse problem, qualitative theory, stability theory, bifurcation theory,

Keywords chaos theory, singular perturbation theory, differential equation in complex domain, dynamic system,

Partial differential equations, nonlinear elliptic (and parabolic) equations, reaction, diffusion and other application fields in physical mechanics of continuous media,

Partial differential equations in geometry and mathematical physics, microscopic local analysis and general partial differential operator theory,

New methods and concepts in research, mixed equations and other singular equations,

Nonlinear waves, nonlinear evolution equations and infinite dimensional dynamic systems.

Gauge field theory of mathematical physics, classical theory and quantum theory of gravitational field theory, soliton theory, statistical mechanics,

Mathematical problems such as continuum mechanics.

Keywords probabilistic Markov process, stochastic process, stochastic analysis, random field, martingale theory, limit theory, stationary process,

The application of probability theory in harmonic analysis, geometry and differential equations, and the probability theory problems in physics, biology and chemical management.

Keywords mathematical logic and mathematical foundation recursive theory, model theory, proof theory, axiomatic set proof,

Application of mathematical logic in artificial intelligence and computer science.

Combinatorial mathematics combinatorial counting, combinatorial design, graph theory, linear computational geometry, combinatorial probability method.

applied mathematics

Keywords mathematical statistics sampling survey and sampling method, experimental design, time series analysis and its algorithm research, multivariate analysis and its algorithm research,

Keywords data analysis and graphic processing, nonparametric statistical method, basic work of applied statistics, statistical linear model,

Parameter estimation method, statistical theory and method of stochastic process, Monte Carlo method (statistical simulation method).

Keywords operational research linear and nonlinear programming, integer programming, dynamic programming, combinatorial optimization, stochastic service system, game theory, fixed point algorithm,

Stochastic optimization, multi-objective programming, nondifferentiable optimization, reliability theory.

Keywords cybernetic finite-dimensional nonlinear system, distributed parameter system control theory, stochastic system control theory, optimal control theory and algorithm,

Parameter identification and adaptive control, algebraic and geometric methods of linear system theory, control calculation method, differential game theory,

Robust control.

Several interdisciplinary subjects of information theory and application, economic mathematics, biological mathematics, uncertain mathematics theory, fractal theory and its application.

Keywords computer mathematics foundation, solvability and computability, machine proof, computational complexity, VLSI mathematics foundation,

Computer network and parallel computing.