Number theory and arithmetic geometry: elliptic curves and the Birch and Swinnerton-Dyer conjecture, Euler systems and Selmer groups, special cycles on Shimura varieties; mathematical foundations of cryptology and applied cryptography: curve-based cryptography, complexity of computing discrete logarithms, hard-to-compute bits, secure multiparty computation and applications.

Analytic Number Theory, Analytic properties of Automorphic forms and their representations, Ergodic theory on arithmetic homogeneous spaces.

Pure Mathematics. Emphasis on Geometry, Group Theory, Analysis, Dynamical systems.

The main focus of the Chair of Algebraic Geometry is the classification theory of higher dimensional algebraic varieties, including exploring its connections to adjacent fields such as commutative algebra, arithmetic geometry and complex geometry.

Amin Shokrollahi has worked on a variety of topics, including coding theory, computational number theory and algebra, and computational/algebraic complexity theory. He is best known for his work on iterative decoding algorithms of graph based codes.

Subgroup structure of semisimple linear algebraic groups and the related finite simple groups of Lie type. Representation theory of semisimple linear algebraic groups and finite reductive groups. Properties of unipotent elements in semisimple algebraic groups.

Theory of automorphic forms, applications of automorphic forms to harmonic analysis and differential equations, packing problems, optimal configuration of points in geometric spaces.