Computational and experimental research on continuous/discontinuous dynamical systems. Sliding motion, Filippov systems and control, bifurcations and singularities. Hamiltonian systems and dynamical systems of geometric origin, Strange attractors and chaotic dynamics, biological systems, neuroscience, climate modeling, data assimilation, engineering applications, networks, Infinite dimensional dynamical systems and PDE, and pattern formation.

Hopf algebras. Homotopy theory and homological algebra. Algebraic Ktheory, Category theory. Groups (finite, infinite, algebraic) and their representations. Rings and module theory. Computational aspect of algebra and applications.

Methods of Local and Global Differential Geometry. Non-linear and fully non-linear geometric PDE. Geometric flows. Geometric structures on manifolds. Symplectic, Riemannian and metric geometry. Geometric aspects of group theory. Conformal geometry, discrete and distance geometry General Relativity.

General topology, Algebraic topology, Geometric topology, Point-free topology, Domain theory, Fuzzy topology, Differential topology and topological dynamics, geometric and network topology, low-dimensional manifolds including knot theory and connections with Kleinian groups, Topological quantum field theories.

Linear and non-linear functional analysis. Classical analysis. Real and Complex analysis in one and several variables, potential theory, Harmonic analysis., operator algebras, Banach algebras, Banach spaces. Metric geometry and applications. Geometric measure theory.

Quantum mechanics. Quantum field theory including gauge theories. General relativity. Statistical mechanics and random media. Integrable systems. Supersymmetric theories. String theory. Fluid dynamics.

Stochastic processes, Interacting particle systems, Random media, Random matrices, Stochastic networks, Stochastic geometry, Statistical inference, High-dimensional data analysis, Spatial methods.

Image Processing, Databases, Intelligent Manufacturing Inspection, Complexity theory and design and analysis of algorithms. Formal languages. Computational learning. Algorithmic game theory. Cryptography. Coding theory. Semantics and verification of programs. Symbolic computation. Quantum computing. Computational geometry, computer vision.

Design of numerical algorithms and analysis of their accuracy, stability, and complexity. Approximation theory. Applied and computational aspects of harmonic analysis. Numerical solution of algebraic, functional, stochastic, differential, and integral equations. Grid generation and adaptivity.

Minimization problems. Controllability, observability, stability. Robotics. Stochastic systems and control. Optimal control. Optimal design, shape design. Linear, non-linear, integer, and stochastic programming. Applications.

Modelling of Biological and Biomedical systems, Population Dynamics, Mathematical Biology, Bio-Informatics.