Number Theory:

• Diophantine Equations (homogeneous equations over number fields)
• Prime Distribution (prime values of systems of univariate sequences)
• L-functions (special values at integer arguments and non-trivial zeroes)

Functional Analysis:

• Operator Algebras (hyperinvariant subspaces of operators)
• Non-linear Operators (fixed points of self-maps; recurrent operator theory)

Convex & Discrete Geometry:

• Discrete Geometry (inscription of polytopes on topological manifolds)
• Convex Geometry (separation and illumination of convex sets)