University of Washington

Department of Mathematics


Algebraic Geometry

Algebraic Topology

Combinatorics and Discrete Geometry

Complex Analysis

Differential Geometry

Current Research

Ergodic Theory and Symbolic Dynamics

Geometric Measure Theory

Inverse Problems

The classical theory of differential equations is concerned with "forward problems": given a differential equation, find a solution. But in many real-world situations, one has to go in the reverse direction: given some information about the solutions to a differential equation, find the unknown coefficients in the governing equation. The Mathematics Department has a strong group working on various aspects of inverse problems. Professors
Gunther Uhlmann and John Sylvester study various kinds of tomography, which is a powerful method for probing the world around us by directing energy in the form of waves or electric currents at an object and observing the energy after it has interacted with the object. Professor Ken Bube works on inverse problems related to seismic exploration of the earth. Professors Jim Morrow and Ed Curtis study how to determine the structure of an electrical network from measurements of voltage and currents at its boundary terminals.

For more information, see the home page of the Inverse Problems Group.

Mathematical Physics

Noncommutative Algebra

Number Theory

Current Research

  • Cryptography

    Numerical Analysis

    Current Research

  • Neutron transport
  • Numerical methods and software for conservation laws

    Optimization and Variational Analysis

    Applications of optimization, including stochastic optimization, are emphasized in projects which combine theory and computation in cooperation with nearby industries such as Boeing.

    At the UW we have an interdisciplinary program in theoretical, numerical, and applied optimization. The core faculty are Professors Jim Burke, and Terry Rockafellar. Current research activities of this group include collaborative activities in the Departments of Statistics (numerical methods for robust statistics), Bioengineering (population analysis and biomedical imaging), Computer Science and Engineering (Markovian decision processes), Finance (portfolio optimization), and the School of Fisheries (hydro-power optimization). Most of these projects have graduate student involvement.

    Partial Differential Equations

    Probability

    Representation Theory of Lie Groups and Lie Algebras