Queueing Theory, Applied Probability Models, Stochastic Modelling and Simulation, Stochastic Models in Operations Research and their application in Communication systems, Transportation, Manufacturing, Production and Inventory Systems.

Stochastic analysis of Partial Differential Equations (SPDEs), Weak and Strong Approximation (Numerical analysis) of SPDEs, Wellposedness and Large Deviation theory of SPDEs, Homogenisation of SPDEs

Several Complex Variables; Metric Geometry

Operator theory; Functional analysis

Valuation Theory; Algebraic Geometry; Commutative Algebra.

Numerical Analysis, Scientific Computing, Partial Differential Equations, Domain Decomposition Methods

Number Theory, in particular Analytic Number Theory; Modular Forms; Siegel Modular forms; Hermitian Modular forms; L-functions;

I primarily delve into functional analytic and algebraic topological techniques to understand the existence and multiplicity of solutions to linear/nonlinear elliptic PDEs.

Control Theory Linear Algebra & Matrix Theory Observer design Differential-Algebraic Equations (Descriptor Systems) Design of Input and Output Feedback

My research interest is primarily in Number Theory. In particular, Hypergeometric functions; Elliptic curves; Modular forms; Distributions to Algebraic Varieties over random finite fields; Kloosterman sums.

Variational Inequalities, Complementarity Problems, Optimization Techniques, Mathematical Analysis, Functional Analysis

Combinatorial Commutative Algebra; Commutative Algebra

Algebra

Numerical Methods to Partial Differential Equations, Computational Fluid Dynamics

Complex Dynamics; Fractals; Independence polynomials and Independent fractals of graphs

Complex Analysis, Geometric Function Theory, Harmonic Mappings in the Plane