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.
![Amod Agashe](../Images/agashe.jpg)
Algebraic Geometry, Homotopy Theory
Category theory, K-theory, intersection theory; homotopy type theory and computer formalization of mathematics; mathematical physics.
![Ettore Aldrovandi](../Images/aldrovandi.jpg)
Algebraic Geometry
Algebraic geometry, intersection theory, singularities, mathematical physics.
![Paolo Aluffi](../Images/aluffi.jpg)
Geometric Topology
Low Dimensional Topology/Geometry, Projective Geometry.
![Sam Ballas](../Images/ballas.jpg)
Algebraic Topology, Algebraic Geometry
Homological stability, moduli spaces, arithmetic statistics, homotopy theory, algebraic combinatorics.
![Oishee Banerjee](../Images/banerjee.jpg)
Geometry
Infinite Dimensional Riemannin Geometry, Shape Analysis, Manifolds of Mappings, Geometric Mechanics, Medical Imaging.
![Martin Bauer](../Images/bauer.jpg)
Geometric Topology
Geometric Group Theory, Conformal Geometry.
![Phil Bowers](../Images/bowers.jpg)
Geometric Topology, Dynamical Systems
Foliations, flows and laminations in 3-manifolds; Large scale geometry.
![Sergio Fenley](../Images/fenley.jpg)
Geometric Topology
Topology of 3-manifolds, group actions, A-category classification.
![Wolfgang Heil](../Images/heil.jpg)
Algebraic Geometry, Computational Algebra
Computer algebra and algorithms to solve differential equations, computations with algebraic curves.
![Mark van Hoeij](../Images/hoeij.jpg)
Dynamical Systems
Automorphisms of complex projective varieties.
![Kyounghee Kim](../Images/kim.jpg)
Differential Topology
Applications of differential topology in computer vision and pattern recognition.
![Eric Klassen](../Images/klassen.jpg)
Geometry and Topology
Optimal Transport, Metric Geometry, Topological Data Analysis.
![Tom Needham](../Images/needham.jpg)
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.
![Thang Nguyen](../Images/nguyen.jpg)
Complex Analysis
Quasiconformal mappings, Dirac and Clifford analysis, financial mathematics.
![Craig Nolder](../Images/nolder.jpg)
Analysis
Harmonic Analysis, specifically generalized Radon transforms and time-frequency analysis.
![Richard Oberlin](../Images/roberlin.jpg)
Analysis
Partial differential equations, harmonic analysis, functional analysis, mathematical theory of fluid mechanics, instabilities of incompressible flows.
![Wojciech Ozanski](../Images/ozanski_t.jpg)
Analysis
Harmonic Analysis, Complex Analysis, Potential Theory.
![Alexander Reznikov](../Images/reznikov_t.jpg)
Algebraic geometry and combinatorics
Algebraic geometry and combinatorics, including motivic integration, tropical geometry, and their applications to singularities, hyperplane arrangements, and matroids.
![Jeremy Usatine](../Images/usatine_small.jpeg)