Hopf algebras and quantum groups, applications to representation theory, combinatorics and integrable systems.
Group theory: structural properties and finite subgroups of simple algebraic groups, black box groups and non-deterministic methods. Combinatorics: discrete geometries and configurations arising from homogeneous spaces. Model theory: groups of finite Morley rank.
Ordinary and modular representation theory of finite groups, especially global-local properties; module categories of blocks of finite groups and related algebras
Free Lie algebras, representation theory, semigroup theory, tropical algebra and geometry.
Combinatorial and geometric group theory, semigroup theory, formal languages and automata, computational complexity, parallel processing, cryptography, and interactions between the above.
Lie Theory: classifications of finite dimensional simple Lie algebras, enveloping algebras, primitive ideas, finite W-algebras, Modular Representation Theory of Reductive Lie Algebras, Invariant Theory of Algebraic Groups.
The Ziegler spectrum of an associative ring, representations of algebras and quivers, structure and complexity of categories of modules and other additive categories.
Finite simple groups, amalgams of groups and completions of amalgams, group geometries, point-line collinearity graphs of sporadic simple groups, coxeter groups, commuting graphs and cages.
Non-commutative algebra, non-commutative algebraic geometry, rings of differential operators.
Lie Algebras: Group actions on free Lie algebras. Group Theory: Homological methods in group theory, combinatorial group theory, equations over groups.
Representation theory and cohomology of groups, homological algebra, profinite groups, group actions on rings, group actions on topological spaces, homotopy theory, and invariant theory.