
Dynamical systems and Differential Equations 


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. 

Algebra 


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. 

Geometry 


Methods of Local and Global Differential Geometry. Nonlinear and fully
nonlinear 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. 

Topology 


General topology, Algebraic topology, Geometric topology, Pointfree topology,
Domain theory, Fuzzy topology, Differential topology and topological
dynamics, geometric and network topology, lowdimensional manifolds
including knot theory and connections with Kleinian groups, Topological
quantum field theories. 

Analysis and its Applications 


Linear and nonlinear 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. 

Mathematical Physics 


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

Probability and Statistics 


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

Computer Science, Software Modeling and Information Technology 


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. 

Numerical Analysis and Scientific Computing 


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. 

Control Theory and Optimization 


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

BioMathematics 


Modelling of Biological and Biomedical systems, Population Dynamics,
Mathematical Biology, BioInformatics. 