Faculty Research Areas

Mathematical Logic and Foundations

J. Clemens Logic, Set Theory
K. Eisentraeger Hilbert's Tenth Problem
S. Simpson Logic, Foundations, Computability

Number Theory and Combinatorics

G. Andrews Partitions, Number Theory, Applications
D. Brownawell Number Theory
K. Eisentraeger Cryptography, Number Theory, Arithmetic Geometry
W. Li Number Theory, Representation Theory, Coding Theory, Spectral Graph Theory
G. Mullen Finite Fields, Combinatorics
M. Papikian Algebraic Number Theory, Arithmetic Geometry
J. Sellers Number Theory, Partitions, Enumerative Combinatorics
S. Simpson Ramsey Theory
L. Vaserstein Number Theory
R. Vaughan Analytic Number Theory
W. Waterhouse Number Theory
A. Yee Partition Theory, Enumerative Combinatorics

Algebra and Group Theory

E. Formanek Algebra, Ring Theory
N. Higson K-theory, Representation Theory
A. Ocneanu Classical and Quantum Groups
L. Vaserstein Classical Groups over Rings, Algebraic K-Theory
W. Waterhouse Algebra, Algebraic Geometry, Affine Group Schemes
P. Xu Algebra and Quantum Groupoids
Y. Zarhin Algebraic Geometry

Mathematical Physics

L.-C. Li Integrable Systems
A. Ocneanu Topological and Quantum Field Theory
M. Stienon Higher Structures, Groupoids, Stacks
A. Wade Poisson Geometry
P. Xu Quantization, Stacks

Partial Differential Equations

L. Berlyand Partial Differential Equations, Calculus of Variations
A. Bressan Nonlinear Hyperbolic Systems, Conservation Laws
K. Jenssen Conservation Laws, Compressible Flow, Combustion
L.-C. Li Integrable Systems
C. Liu Evolution Equations, Calculus of Variations, Phase Field Methods
A. Mazzucato Harmonic and Microlocal Analysis, Inverse Problems
V. Nistor Analysis on Singular Spaces
A. Novikov Partial Differential Equations, Analysis
W. Shen Hyperbolic Conservation Laws, Relaxation, Partial Differential Equations
Y. Zheng Partial Differential Equations

Dynamical Systems and Ergodic Theory

D. Burago Dynamical Systems
A. Katok Dynamical Systems, Ergodic Theory
S. Katok Dynamical Systems and Applications to Analysis and Number Theory
M. Levi Dynamical Systems and Applications to Physics and Engineering
Y. Pesin Dynamical Systems, Ergodic Theory, Dimension Theory, Statistical Physics
O. Sarig Ergodic Theory, Probability
G. Swiatek Dynamical Systems
S. Tabachnikov Dynamical Systems
A. Tempelman Ergodic Theory, Statistics
K. Wysocki Hamiltonian Dynamics

Functional Analysis

J. Anderson Operator Theory
N. Brown Operator Algebras
P. Baum Operator Algebras, K-Theory
N. Higson Operator Algebras, K-theory, Noncommutative Geometry
A. Ocneanu Operator Algebras
J. Roe Operator Algebras, Index Theorems, Noncommutative Geometry

Geometry and Topology

P. Baum Algebraic Topology
D. Burago Riemannian Geometry
A. Banyaga Symplectic Topology, Contact Geometry
A. Katok Geometry
S. Katok Hyperbolic Geometry and Fuchsian Groups
L.-C. Li Poisson Geometry
Y. Pesin Riemannian Geometry
A. Petrunin Singular Geometry, Topology, Combinatorial Geometry
J. Roe Coarse Geometry, Topology
M. Stienon Poisson Manifolds, Categories
S. Tabachnikov Symplectic Geometry, Differential Geometry and Topology, Knots
A. Wade Differential Geometry
K. Wysocki Symplectic and Contact Topology
P. Xu Poisson Geometry
Y. Zarhin Algebraic Geometry

Probability Theory and Stochastic Processes

M. Denker Probability and its applications
Q. Du Statistical Mechanics
L.-C. Li Random Matrices
A. Novikov Stochastic Differential Equations
Y. Pesin Probability and Statistics
T. Reluga Probability and Biology
O. Sarig Probability
S. Simpson Algorithmic Randomness
A. TemplemanProbability, Ergodic Theory

Numerical Analysis

J. Brannick Computational Fluid Dynamics and Chromodynamics
Q. Du Numerical Analysis, Scientific Computation
X. Li Computational Mechanics
V. Nistor Numerical Analysis, Partial Differential Equations
W. Shen Numerical Simulation
J. Xu Computational Analysis, Numerical Methods, Multigrid
L. Zikatanov Numerical Analysis, Partial Differential Equations

Deformation of Solids / Material Science

A. Belmonte Fragmentation, Dynamic Buckling
L. Berlyand Homogenization Theory, Composites
W. Cao Material Science
Q. Du Complex Elastic Solids
X. Li Multiscale Modeling in Crystals
C. Liu Nonlinear Elasticity, Mixtures, Fluid-Structure Interactions
A. Mazzucato Elasticity, Inverse Problems
A. Novikov Composites, Martensitic Transitions in Polycrystals

Fluid Mechanics

A. Belmonte Viscoelastic Fluids, Free Surface Flows, Turbulence
L. Berlyand Complex Fluids
A. Bressan Swimming Motions in Fluids
Q. Du Complex Fluids, Bose-Einstein Condensates
D. Henderson Nonlinear Waves
M. Levi Ideal Fluids
C. Liu Complex Fluids, Liquid Crystals, Electrorheological Fluids
A. Mazzucato Navier-Stokes Equation, Turbulence
A. Novikov Turbulence
J. Xu Simulation of Non-Newtonian Fluid
Y. Zheng Compressible Flows

Biology, Economics, Optimization

L. Berlyand Biological Suspensions
A. Bressan Control Theory, Optimization, Differential Games
Q. Du Biological Membranes
J. Li Mathematical Economics, Finance, Monetary Economics
C. Liu Biological Membranes, Electro-kinetic Fluids
T. Reluga Mathematical Biology, Disease Dynamics
L. Vaserstein Operational Research, Game Theory