My research interest lies in the intersection of Commutative and Computational Algebra, Combinatorics and Algebraic Statistics.

Algebraic coding theory, arithmetic of finite fields, applications of algebra and algebraic geometry to coding theory.

orthogonal polynomials, approximation theory, random matrix theory.

Integer partitions from a combinatorial perspective, partition generating functions, Rogers-Ramanujan generalizations, q-series, enumerative combinatorics.

Computational Number Theory, Arithmetic of Elliptic Curves, Arithmetic of Hyperelliptic Curves, Diophantine Equations, Arithmetic Dynamical Systems

Complex analysis in multi-variables, pluripotential theory, operator theory

mathematical analysis of nonlinear partial differential equations, nonlinear dispersive and hyperbolic waves, water waves, stability of solitary waves, fractional differential equations.

Function Fields and Algebraic Curves over Finite Fields: Rational points of curves, automorphisms, towers of function fields and their asymptotic properties, Drinfeld modular curves; Coding Theory: Algebraic Geometry Codes; Finite Galois Geometry and Cryptographically significant functions (particularly quadratic functions, their nonlinearity distribution) their applications to Coding Theory and their interaction with Algebraic Curves over Finite Fields; Boolean functions and functions from F_{p^n} to F_p: Functions with high nonlinearity, Bent functions (and their connections to coding theory, cryptography, finite geometry, difference sets), (Modified) Planar functions, Almost Perfect Nonlinear functions; Permutations: (Vectorial) Permutations over finite fields.

Applied probability, statistics, stochastic processes, optimal stopping, stochastic optimal control with applications in finance and engineering

Several Complex Variables, Holomorphic Dynamics and Complex Geometry

Partial differential equations;pseudo-differential operators; functional analysis.

Uniformly distributed sequences; finite fields and applications; pseudo random numbers.