Major reseach areas:

Theory of algebraic numbers. Non-regularities in the distribution of primes and prime ideals. In particular a new method of estimating from the number of sign changes of error terms occurring in number theory.
Explicit formulae, in particular K-functions and their applications, Riemann zeta function and Dirichlet L-functions, concentrated mainly on random graphs theory.
Spaces of continuous, harmonic and holomorphic functions and the associated spaces of measures. Splitting theory for spaces of distributions and smooth functions. Factorisation of Montel operators.
Theory of LS-spaces, non-archimedean Banach spaces and locally convex spaces. Actions of compact Lie groups on topological spaces. Differential and integral equations in Banach spaces. Logic in artificial intelligence (autoepistemic logic, logic of information processing, action logic, linear logic).
Mathematical linguistics (categorial grammar, automata). Philosophy of mathematics. History of logic.
Real methods in mathematical analysis and function spaces and their applications.
Algebraic number theory. Algebraic K-theory. Algebraic geometry. Cryptological algorithms. Data security.