Algebraic number theory, valuation theory and commutative algebra

Infinite-dimensional Lie algebras and Algebraic combinatorics

Number Theory

Commutative Algebra, Algebraic Combinatorics

Homological methods and categories in commutative algebra, affine algebraic geometry, algebraic K-theory

Algebra, Geometry, Algebraic and Complex Geometry

Linear and Nonlinear PDEs, Isoperimetric problems, weighted Sobolev inequalities.

Riemannian geometry, Geometric analysis, Representations of real Lie groups, Geometric quantization.

General Mathematics

Infinite-dimensional Lie algebras and Algebraic combinatorics

Graphs and matrices

Fractal Interpolation and Approximation, Shape Preserving Fractal Interpolation, Geometric Modelling, Fixed Point Theory, Fractal Radial Basis, Wavelets

Complex analysis, Functional Spaces, Special Functions

Harmonic Analysis, Time -frequency Analysis, Mathematical sampling theory and data sciences, Solutions of operator equations

Approximation Theory, Sampling Operators

Functional Analysis, Matrix Theory

Numerical Linear Algebra, Computational Mathematics, Machine Learning, Fast Algorithms

Functional Analysis, Free Convexity, Quantum Information Theory.

Operator Algebra, Operator Theory, Quantum Information theory.

Functional analysis, Operator Theory

Nonlinear Analysis-nonsmooth analysis and Optimization

Several Complex Variables

Analysis of Partial Differential Equations, Multiscale Analysis (Homogenization) of PDEs, Optimal Control of PDEs

General Mathematics

Infinite-dimensional Lie algebras and Algebraic combinatorics

Combinatorics on words, Bio-molecular computing, Theory of codes

Graph Theory, Combinatorics, Graph Ideals

Automata Theory, Theory of codes

Cryptology

Approximation Algorithms

Probability Theory, Representation theory of finite groups, Algebraic Combinatorics, and Statistical Physics

Theory of Computation, Complexity Theory

Linear and Nonlinear PDEs, Isoperimetric problems, weighted Sobolev inequalities.

Fractal Interpolation and Approximation, Shape Preserving Fractal Interpolation, Geometric Modelling, Fixed Point Theory, Fractal Radial Basis, Wavelets

Non-linear Differential Equations

Fluid Mechanics

Differential and Integral Equations, Wave-Structure Interactions

Development of meshfree numerical schemes to partial differential equations originated from fluid dynamics.

Computational Fluid Dynamics, Convective Heat And Mass Transfer

Analysis of fractional functional DE, Mathematical Study of ferromagnetic systems, Neural network and differential equations

Numerical Linear Algebra, Computational Mathematics, Machine Learning, Fast Algorithms

Computational PDE, Mathematical Modeling and Numerical Simulation

Analysis of Partial Differential Equations, Multiscale Analysis (Homogenization) of PDEs, Optimal Control of PDEs

Riemannian geometry, Geometric analysis, Representations of real Lie groups, Geometric quantization.

Algebraic Geometry

Differential and algebraic topology and their interactions with differential geometry

Algebraic Topology, Geometric Topology, Differential Geometry, Convex Geometry, K-Theory

Geometric Group Theory, Low dimensional Topology

Algebraic Topology, Algebraic Geometry

Algebra, Geometry, Algebraic and Complex Geometry

Stochastic Partial Differential Equations, Probability Theory

Time Series, Statistical Learning, Subordinated Stochastic Processes, Applied Probability, Stein Method

Game Theory

Probability Theory, Representation theory of finite groups, Algebraic Combinatorics, and Statistical Physics

Subdata selection, screening experiments, design of experiments, rank aggregation problem, data science and interdisciplinary research