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.
