- Groups of large cardinality, countably recognizable properties of groups, characteristic subgroups, immersion properties of subgroups, automorphisms of groups, inertial properties of infinite.
- PDEs, topological and variational methods in nonlinear analysis, control theory, dynamical systems, conservation laws, geometric measure theory, symmetrization techniques, function spaces, BV and Sobolev mappings, models in continuum mechanics, thin structures, homogenization techniques for composite materials, shape optimization, geometric analysis, evolutions of geometric structures.
- Combinatorial optimization, probability and statistics
- Shortest path and flux problems in networks, computationally hard problems in combinatorial optimization, stochastic arrangements in reliability theory, neural models, dynamic models for motor proteins.
- Algebraic geometry: varieties with just one singular point,
Cohen-Macaulay varieties, Hilbert polynomials, Hilbert functions.
Combinatorial geometry: classification of flocks, translation generalized quadrangles, finite semifields.
Topology: cohomology of commutative Hopf algebras, invariant theory.
- Mathematical physics
- Construction and development of mathematical models (PDEs, autonomous and non autonomous ODEs) to describe real world phenomena, quantitative and qualitative analysis of models by using analytical and numerical approaches: linear and nonlinear stability, asymptotic behaviour of solutions, existence of absorbing sets in phase space.
- Numerical analysis and data mining
- Algorithms and solvers for numerical optimization, methods for multivariate data interpolation and approximation, design and analysis of numerical methods for differential and integral equations, reduced order methods, numerical approaches in data mining, learning methodologies for data analysis and image processing.
- Scientific computing
- High performance computing: hardware-software architectures, algorithms, software for GPU computing.