Mathematics

• Philosophy of Mathematics (ontology, foundations of geometry, and calculus).
• History of Mathematics (geometry: Euclid, Descartes, Hilbert; the 17th and 18th-century calculus)

• Orthogonality and approximate orthogonality in normed linear spaces
• Selected topics in functional equations

Critical point theory

– partial differential equations with p-Laplacian

– hemivariational inequalities

• Quasi-ordinary singularities
• Geometry of polynomial mappings at infinity

• Universal algebra, in particular, its applications in algebraic logic
• Intuitionistic logic and Fregean algebras

• Asympthotic invariants in geometry and algebra
• Objects associated to sets of points in projective spaces

• Norm derivatives and their application in geometry of Banach spaces.
• Selected topics in geometry of operator spaces and spaces of continuous functions.