Differential geometry -- Global differential geometry -- Symmetric spaces.
Group theory and generalizations -- Representation theory of groups -- Hecke algebras and their representations.
Harmonic analysis.
Linear and multilinear algebra; matrix theory -- Basic linear algebra -- Clifford algebras, spinors.
Nonassociative rings and algebras -- Lie algebras and Lie superalgebras -- Automorphisms, derivations, other operators.
Quantum theory -- Groups and algebras in quantum theory -- Symmetry breaking.
Several complex variables and analytic spaces -- Complex spaces with a group of automorphisms -- Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras.
Several complex variables and analytic spaces -- Holomorphic fiber spaces -- Twistor theory, double fibrations.
Symmetric spaces.
Topological groups, Lie groups -- Lie groups -- Representations of Lie and linear algebraic groups over local fields.
Topological groups, Lie groups -- Lie groups -- Semisimple Lie groups and their representations.