Algebras with polynomial identities, Integrable equations

Complex Geometry and Analysis, Hodge Theory, Non-commutative Geometry, Homological Mirror Symmetry

Modal logic, Boolean function complexity.

Endomorphism semirings, Matrix semirings, Derivations in semirings, Combinatorics, Stochastic processes.

Type-theoretic approaches to information theory and information processing, Dependent-Type Theory of Situated Information, Type-Theory of Algorithms, Recursion Theory, Computational Syntax, Automata Theory, Computational Semantics, Computational Syntax-Semantics Interface, Computational Linguistics, Type-Theoretic Grammars, Constraint Based Lexicalized Grammar (CBLG), Artificial Intelligence

Group algebras and Abel groups, modules and associative rings, algebraic theory of matrices.

Algebra: Theory of Associative Rings: fields; field extensions; Galois theory - maximal p-extensions, absolute Galois groups; central simple algebras; Brauer groups of fields - structure and invariants; valuation theory. Number Theory - local class field theory.

Representation theory of Lie algebras and Lie groups, applications to Invariant theory, infinite-dimensional Lie algebras, momentum maps, geometric quantization and applications to physics.

String theory, AdS/CFT correspondence, lattice gauge theories, Monte Carlo simulations, financial mathematics.