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Graph Theory, Combinatorics, Complex Networks
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Mathematical Teaching, Biomathematics
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Functional Analysis, Operator Algebras, Noncommutative Geometry, Quantum Information Theory
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Geometric Representation Theory, Hall Algebra, Quantum Groups, Canonical Basis, Category Theory, Schur-Weyl Duality, Characteristic Sheaves
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System Modeling and Prediction, Biomathematics
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Convective Heat Transfer, Numerical Methods, Partial Differential Equations
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Applied Mathematics and Computational Mathematics, mainly including Mathematical Physics Equations and their Numerical Solutions, Optimization Theory and Numerical Algorithms
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Nonlinear Functional Analysis and its Application
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Quantum Information and Computing, Conducting Scientific Research Projects at the Intersection of Mathematics and Quantum Physics
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Mathematical Teaching
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Nonlinear Evolution Equations and Infinite Dimensional Dynamical Systems
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Biomathematics, Deep Learning
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Geometric Representation Theory and its Application in Quantum Information, specifically Quantum Groups and their Representation Theory, Quantum Network Research, Quantum Resource Theory, Quantum Key Distribution, Quantum Communication
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Mathematical Teaching
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Iwasawa Theory
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Algebra, Mathematical Teaching
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Biomathematics
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Mathematical Teaching, Probability Statistics, Biomathematics
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Low-Dimensional Topology
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Graph Theory, Combinatorics, Complex Networks
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Applied Mathematics
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Nonlinear Vibration, Numerical Computing, Quantum Information, Physical Information Neural Network
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Partial Differential Equations
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Ramsey Theory, Extreme Graph Theory
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Algebraic and Geometric structures of scattering amplitudes in both field and string theories, the BCJ and KLT relations, aiming to uncover the underlying algebraic structures that enhance the efficiency of gravity and gauge theory calculations, q-deformed Lie algebras, string amplitudes, and loop-level calculations, contributing to post-Minkowskian gravity and gravitational wave research,theoretical understanding and practical applications in physics
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Representation Theory and its Connection with Symplectic/Algebraic Geometry
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Representation Theory of Algebraic Groups, Geometric Methods of Representation Theory
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Quantum Information and Quantum Computing
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Nonlinear System Control, Multi-agent System Collaborative Control
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Machine Learning, Intelligent Optimization Algorithm, Complex Network Algorithm and Application
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Differential Equations and Dynamical Systems
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Wave Equation Inversion
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Graph Theory, Combinatorics, Complex Networks
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Signal Processing, Teaching Research
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Partial Differential Equations in Fluid Mechanics, including: Global Existence of Weak Solutions to Fluid Mechanics Equations; Energy Conservation of Weak Solutions to Fluid Mechanics Equations; Existence and Stability of Steady Vortex Solutions
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Geometric Representation Theory, Quantum Group, Cluster Algebra
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Operator algebras, Free Probability Theory, Set Theory, Functional Analysis
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Lie Algebra and its Applications
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Lie (Super) Algebra and its Representation Theory
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Complex Systems
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Probability Theory, Random Process, Infinitely Divisible Process, Financial Mathematics
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Differential Equations and Dynamical Systems
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Group Behavior of Multi-agent Systems, Kinetic Equations
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Multi-dimensional and High-dimensional Time Series Model Testing, Cointegration Analysis, Biostatistics
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