Department of Algebra and Logic

Algebra.

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.

(Complex) algebraic geometry, (nonabelian) Hodge theory and mathematical physics.

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

Combinatorial and computational ring theory, noncommutative algebra, algebras with polynomial identity, automorphisms and derivations of polynomial and free algebras, commutative and noncommutative invariant theory, group representations, theory of symmetric functions, group algebras, and coding theory.

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

Non-commutative algebra and applications for quantum groups, non-commutative geometry, symbolic computation

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

Soliton theory, Soliton interactions.

Temporal logic, probability logic, real-time systems, model checking, formal methods and theoretical computer science in general.

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

Algebra.

Modal logic, Boolean function complexity.

Algebraic geometry: surface theory, Algebra: associative algebras, theory of finite group representations, Artin braid group representations, Combinatorics: census problems. Mathematical Chemistry: isomerism in organic cemistry, Mathematical Economics: sets of preferences, utility functions.

Abstract and axiomatic recursion theory; Romanization of Cyrillized languages and re-Romanization of English; Antarctic place naming, geographic surveying and mapping; foreign and security policy, European and Atlantic integration; self-determination, minority rights, immigration policies.

Logics for space and time, modal logic.

Algebra.

Coding theory, query problems, covering problems.

Algebra, Semigroup Theory, Transformation Semigroups, Universal Algebra, Clone Theory, Varieties of algebraic structures, discrete functions.

Algebras with polynomial identities, Integrable equations

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

Algebra.

Algebra.

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