The following core faculty members have active research interests in pure mathematics and teach most program courses.

Number Theory

Arithmetic algebraic geometry, applications of elliptic curves in cryptography.

Algebraic Geometry, Homotopy Theory

K-Theory, intersection theory, category theory, mathematical physics.

Algebraic Geometry

Algebraic geometry, intersection theory, singularities, mathematical physics.

Geometric Topology

Low Dimensional Topology/Geometry, Projective Geometry

Geometry

Infinte Dimensional Riemannin Geometry, Shape Analysis, Manifolds of Mappings, Geometric Mechanics, Medical Imaging

Geometric Topology

Geometric Group Theory, Conformal Geometry.

Geometric Topology, Dynamical Systems

Foliations, flows and laminations in 3-manifolds; Large scale geometry.

Geometric Topology

Topology of 3-manifolds, group actions, A-category classification.

Algebraic Geometry, Computational Algebra

Computer algebra and algorithms to solve differential equations, computations with algebraic curves.

Dynamical Systems

Automorphisms of complex projective varieties.

Differential Topology

Applications of differential topology in computer vision and pattern recognition.

Complex Analysis

Quasiconformal mappings, Dirac and Clifford analysis, financial mathematics.

Analysis

Harmonic Analysis, specifically generalized Radon transforms and time-frequency analysis.

Geometric Topology, Number Theory

Character varieties, arithmetic orbifolds, congruence subgroups, Artin's primitive root conjecture

Analysis

Harmonic Analysis, Complex Analysis, Potential Theory