The following core faculty members have active research interests in pure mathematics and teach most program courses.
Arithmetic algebraic geometry, applications of elliptic curves in cryptography.
Algebraic Geometry, Homotopy Theory
K-Theory, intersection theory, category theory, mathematical physics.
Algebraic geometry, intersection theory, singularities, mathematical physics.
Low Dimensional Topology/Geometry, Projective Geometry.
Infinte Dimensional Riemannin Geometry, Shape Analysis, Manifolds of Mappings, Geometric Mechanics, Medical Imaging.
Geometric Group Theory, Conformal Geometry.
Geometric Topology, Dynamical Systems
Foliations, flows and laminations in 3-manifolds; Large scale geometry.
Archimedean geometry, Tropical and Birational Geometry of algebraic varieties.
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.
Automorphisms of complex projective varieties.
Applications of differential topology in computer vision and pattern recognition.
Geometry and Topology
Optimal Transport, Metric Geometry, Topological Data Analysis.
Quasiconformal mappings, Dirac and Clifford analysis, financial mathematics.
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.
Harmonic Analysis, Complex Analysis, Potential Theory.