Research Areas
Algebra:
- Ezra (Bud) Brown: number theory, cryptography, combinatorics, history of mathematics, expository mathematics
- Edward Green: computational algebra (noncommutative Groebner bases, algorithms, computer implementation), representation of finite dimensional algebras (quotients of path algebras, representation of graphs with relations), homological algebra (Koszul algebras, Ext algebras and Yoneda algebras, homological conjectures for finite dimensional algebras)
- Peter Linnell: algebra, group rings of finite or infinite groups
- Nicholas Loehr: bijective and algebraic combinatorics
- Charles Parry: number theory, field extensions
- Mark Shimozono: algebraic combinatorics, representation theory, algebraic geometry
Analysis:
- James Holub:
- John Rossi: complex analysis, potential theory
Control And Systems Theory:
- Joseph A. Ball: multidimensional system theory, multivariable operator theory, robust control theory
- John A. Burns: optimal control theory; ordinary and functional differential equations; approximation, control, identification and optimization of functional and partial differential equations; aeroelastic control systems, fluid/structural control systems; smart materials; optimal design
- Martin V. Day: stochastic processes, differential games and control problems in fluid or risk-sensitive/large deviations limit of queueing networks
- Terry L. Herdman: Volterra integral equations, ordinary and functional differential equations, applied mathematics, aeroelastic control systems, weakly singular integral equations
- David L. Russell: ordinary and partial differential equations, systems theory, elasticity, mathematical modeling, control theory
Geometry and Topology:
- William Floyd: low-dimensional topology, geometric group theory, discrete conformal geometry, discrete dynamical systems
- Peter Haskell: index theory, analysis on manifolds
- Frank Quinn: low-dimensional manifold topology
Differential Equations and Applications: Partial Differential Equations
- David Y. Gao: complementarity, duality and global optimization
- Werner Kohler: wave propagation in random media
- Jong U. Kim: stochastic differential equations
- Michael Renardy: nonlinear partial differential equations, non-Newtonian fluids, free surface flows, stability and bifurcation
- Robert C. Rogers: physics of continua, elasticity, electromagnetism, thermodynamics, phase transitions in fluids and solids, ferromagnetism
- Shu-Ming Sun: surface waves, soliton theory, Korteweg-de Vries equation
- Michael Williams: diffusion and transport theory
Mathematical Biology / VBI:
- Reinhard Laubenbacher: Mathematical tools for reverse-engineering of biochemical networks, large-scale microsimulation of human immune response to viral pathogens, computational algebra models for Bayesian networks, mathematical foundation of computer simulation
- Henning Mortveit, mathematics of simulations
Mathematical Physics
- William Greenberg: statistical mechanics
- George Hagedorn: Born-Oppenheimer approximation, computational chemistry
- Martin Klaus: inverse scattering, nonlinear optics
Mathematics Education:
- Gwendolyn Lloyd: mathematics teacher development, K-12 mathematics curriculum design and enactment
- Anderson Norton: psychological development of mathematics in K-12 students
- C. Wayne Patty: outreach in mathematics education and technology
Numerical Computation:
- Slimane Adjerid: numerical analysis, scientific computing, finite elements, a posteriori error estimation and adaptivity, singularly perturbed partial differential equations
- Christopher Beattie: scientific computing, eigenvalue computation, Krylov-based approximation methods.
- Jeff Borggaard: computational tools for optimal design and control of nonlinear partial differential equations
- Serkan Gugercin: approximation and control of large scale dynamical systems, singular-value-decomposition-based and Krylov-based approximation methods, Krylov-based controller reduction for large-scale systems
- Traian Iliescu: large eddy simulation of turbulent flows
- Tao Lin: immersed finite-element techniques
- Yuriko Y. Renardy: modeling and analysis of fluids, interfaces and amorphous polymers
- James Turner: computational mathematics, algorithms and grid computing
- Peter Wapperom: computational fluid dynamics, numerical methods, viscoelasticity, non-equilibrium thermodynamics
- Lizette Zietsman: computational methods for control and optimization of distributed parameter systems