List of Faculty Research Areas

Faculty research interests in our department (ordered and grouped based on AMS Subject Classification)


Algebra and Group Theory

N. Higson K-theory, Representation Theory
J. Huizenga Algebraic Geometry
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


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
A. Mazzucato Elasticity, Inverse Problems
A. Novikov Composites, Martensitic Transitions in Polycrystals


Dynamical Systems and Ergodic Theory

N. Brown Noncommutative Dynamical Systems
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


Fluid Mechanics

A. Belmonte Viscoelastic Fluids, Free Surfaces, Reactive Flows
L. Berlyand Complex Fluids
D. Henderson Nonlinear Waves
K. Jenssen Compressible Flows
M. Levi Ideal Fluids
A. Mazzucato Navier-Stokes and Euler equations, turbulence, mixing
T. Nguyen Navier-Stokes equations, Boundary layer theory
A. Novikov Turbulence
W. Shen granular flow, traffic flow, polymer flooding in two phase flow, reservoir simulation
J. Xu Simulation of Non-Newtonian Fluids


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
J. Case Conformal and CR Geometry
C. Curto Applied Algebra, Topology and Geometry
N. Higson Operator Algebras, K-theory, Noncommutative Geometry
J. Huizenga Algebraic Geometry
V. Itskov Applied Algebraic Topology and Geometry
B. Kalinin Geometry
A. Katok Geometry
S. Katok Hyperbolic Geometry and Fuchsian Groups
M. Levi Differential Geometry and Classical Mechanics
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


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
T. Reluga Population Biology, Ecology and Infectious Disease Modeling

W. Shen PDE models for stems and leaves

 


Mathematical Logic and Foundations

K. Eisentraeger Hilbert's Tenth Problem
J. Reimann Logic, Computability, Algorithmic Information Theory and Randomness


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


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


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. Zikatanov Computational Mathematics, Numerical Analysis


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
L.-C. Li Integrable Systems
A. Mazzucato equations of continuum mechanics (fluid flow and elasticity), inverse problems, harmonic and microlocal analysis
T. Nguyen Navier-Stokes equations, Kinetic theory of gases, Dynamics of nonlinear waves, Boundary layers
A. Novikov Partial Differential Equations, Analysis
W. Shen Hyperbolic Conservation Laws, Relaxation, Partial Differential Equations
Y. Zheng Partial Differential Equations


Probability Theory and Stochastic Processes

J. Conway Probability and Biology
M. Denker Probability and its applications
L.-C. Li Random Matrices
X. Li Modeling and Computations with Stochastic Differential Equations
J. Morton Covariance Matrices, Cumulant Tensors
A. Novikov Stochastic Differential Equations
Y. Pesin Probability and Statistics
T. Reluga Probability and Biology


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
N. Brown Diversity in STEM
J. Li  Mathematical Economics, Finance, Monetary Economics
A. Mazzucato  mathematical finance, option pricing
T. Reluga  Game Theory of Disease Management
W. Shen  differential games and applications, optimal control
L. Vaserstein  Operational Research, Game Theory