Algebra: Commutative Algebra, Algebraic Geometry, Algebraic Number Theory, Classical Groups, Algebraic Manifolds, Moduli of Algebraic Manifolds and Hodge Theory.

Analysis: Convex Analysis and Nonsmooth Optimization, Fractals and Wavelets, Harmonic Analysis, Operator Algebra.

Applied Analysis: Applied Partial Differential Equations, Financial Engineering, Fluid Dynamics, Mathematical Physics, Mathematical Biology, Nonlinear Evolution Equations.

Computational Mathematics: Numerical Analysis, Equations and Linear Algebra, Image Processing, Optimization, Inverse Problems.

Geometric Analysis: Differential Geometry, Several Complex Variables, Nonlinear Analysis on Manifolds.