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

Category theory, K-theory, intersection theory; homotopy type theory and computer formalization of mathematics; mathematical physics.

Algebraic Geometry

Algebraic geometry, intersection theory, singularities, mathematical physics.

Geometric Topology

Low Dimensional Topology/Geometry, Projective Geometry.

Algebraic Topology, Algebraic Geometry

Homological stability, moduli spaces, arithmetic statistics, homotopy theory, algebraic combinatorics.

Geometry

Infinite 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.

Geometry and Topology

Optimal Transport, Metric Geometry, Topological Data Analysis.

Geometry and Topology

Geometry of symmetric spaces, buildings and non-positively curved spaces; geometric group theory; dynamical systems and ergodic theory of semisimple groups; random walks on groups.

Complex Analysis

Quasiconformal mappings, Dirac and Clifford analysis, financial mathematics.

Analysis

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

Analysis

Partial differential equations, harmonic analysis, functional analysis, mathematical theory of fluid mechanics, instabilities of incompressible flows.

Analysis

Harmonic Analysis, Complex Analysis, Potential Theory.

Algebraic geometry and combinatorics

Algebraic geometry and combinatorics, including motivic integration, tropical geometry, and their applications to singularities, hyperplane arrangements, and matroids.