Faculty research interests in our department (ordered and grouped based on AMS Subject Classification)
Mathematical Logic and Foundations
K. Eisentraeger Hilbert's Tenth Problem
J. Reimann Logic, Computability, Algorithmic Information Theory and Randomness
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
S. Katok Automorphic Forms
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
N. Higson K-theory, Representation Theory
J. Morton Algebraic Geometry, Computational Complexity
A. Ocneanu Classical and Quantum Groups
K. Schwede Algebraic Geometry, Commutative Algebra
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
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
F. Rodriguez-Hertz Dynamical Systems, Ergodic Theory
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
J. Morton Algebraic Geometry, Tropical Geometry
Y. Pesin Riemannian Geometry
A. Petrunin Singular Geometry, Topology, Combinatorial Geometry
F. Rodriguez-Hertz 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
J. Morton Covariance Matrices, Cumulant Tensors
A. Novikov Stochastic Differential Equations
Y. Pesin Probability and Statistics
T. Reluga Probability and Biology
S. Simpson Algorithmic Randomness
A. Templeman Probability, 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 Surfaces, Reactive Flows
L. Berlyand Complex Fluids
A. Bressan Swimming Motions in Fluids
Q. Du Complex Fluids, Bose-Einstein Condensates
D. Henderson Nonlinear Waves
K. Jenssen Compressible Flows, Combustion
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
Biology, Economics, Optimization
A. Belmonte Cooperative Cell Motion
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
J. Miller Epidemic Modeling
T. Reluga Population Biology
L. Vaserstein Operational Research, Game Theory