# Research Areas

Algebra:

- Ezra (Bud) Brown: number theory, cryptography, combinatorics, history of mathematics, expository mathematics
- Peter Linnell: algebra, group rings of finite or infinite groups
- Nicholas Loehr: bijective and algebraic combinatorics
- Leonardo Mihalcea: algebraic geometry, algebraic combinatorics, geometric representation theory
- Daniel Orr: algebra and combinatorics related to Lie theory
- Mark Shimozono: algebraic combinatorics, representation theory, algebraic geometry

Analysis:

- 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
- Terry L. Herdman: Volterra integral equations, ordinary and functional differential equations, applied mathematics, aeroelastic control systems, weakly singular integral equations

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

- 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

Mathematical Biology / VBI:

- Matthias Chung: Scientific computing, computational biology, inverse problems, applied dynamical systems
- Stanca Ciupe: Mathematical modeling, mathematical biology, dynamical systems
- 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

- Alexander Elgart: adiabatic behavior in quantum mechanics, Anderson localization
- George Hagedorn: Born-Oppenheimer approximation, computational chemistry
- Martin Klaus: inverse scattering, nonlinear optics

Mathematics Education:

- Estrella Johnson: teaching and learning of undergraduate mathematics, particularly in inquiry-oriented classroom settings; mathematical activities of teachers and students; characteristics of successful college calculus programs
- Anderson Norton: psychological development of mathematics in K-12 students
- Megan Wawro: teaching and learning of undergraduate mathematics, particularly linear algebra; analyzing mathematical development at the individual and collective levels

Numerical Analysis and Scientific Computing:

- 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
- Julianne Chung: scientific computing, inverse problems, image processing
- Matthias Chung: scientific computing, computational biology, inverse problems, applied dynamical systems
- 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
- Pengtao Yue: sicentific computing, fluid mechanics
- Lizette Zietsman: computational methods for control and optimization of distributed parameter systems