List of Faculty Research Areas

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

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
L. Vaserstein Number Theory
R. Vaughan Analytic 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
L. Vaserstein Classical Groups over Rings, Algebraic K-Theory
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 Hyperbolic Conservation Laws, Nonlinear Wave Equations, Models of Traffic Flow on Networks
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
T. Nguyen Partial Differential Equations
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
B. Kalinin Dynamical Systems and Ergodic Theory
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
V. Sadovskaya Dynamical Systems and Ergodic Theory
S. Tabachnikov Dynamical Systems

Functional Analysis

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
C. Curto Applied Algebra, Topology and Geometry
V. Itskov Applied Algebraic Topology and 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
P. Xu Poisson Geometry
Y. Zarhin Algebraic Geometry

Probability Theory and Stochastic Processes

J. Conway Probability and Biology
M. Denker Probability and its applications
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

Numerical Analysis

J. Brannick Computational Fluid Dynamics and Chromodynamics
J. Harlim Numerical Analysis
X. Li Computational Mechanics
W. Shen Numerical Simulation
J. Xu Computational Analysis, Numerical Methods, Multigrid
L. ZikatanovComputational Mathematics and Numerical Analysis

Deformation of Solids / Material Science

A. Belmonte Fragmentation, Dynamic Buckling
L. Berlyand Homogenization Theory, Composites
W. Cao Material Science
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
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 Fluids

Mathematical Biology

A. Belmonte Cooperative cell motion, biological fluid dynamics, evolutionary games
L. Berlyand Biological Suspensions
A. Bressan Free Boundary Problems Modeling Tissue Growth
J. Conway Infectious Disease Modeling
C. Curto Theoretical and Computational Neuroscience, Neural Network Theory and Neural Coding
V. Itskov Theoretical Neuroscience, Neural networks and Learning
C. Liu  Biological Membranes, Electro-kinetic Fluids
T. Reluga Ecology and Infectious Disease Modeling

Social Science, Economics, Optimization

A. Belmonte  Game Theory Dynamics
L. Berlyand Social networks
A. Bressan Optimal control, Differential Games and Applications to Economics and Finance
J. Li  Mathematical Economics, Finance, Monetary Economics
L. Vaserstein  Operational Research, Game Theory