Wash U Graduate Program in Mathematics : The Faculty and Its Research

A significant measure of outside recognition of the mathematical activities at Washington University is the grant support held by its faculty. In the past five years, several dozen research and research-related projects conducted by Washington University faculty were funded by both federal and private agencies. These have included research grants, grants to purchase computing equipment, grants to run conferences, grants to develop educational projects, grants to develop software and algorithms, and grants to develop collaborations with engineering and other departments. Also the Washington University mathematics faculty are frequent speakers and visitors at other universities around the world.

We now summarize just a few of the research activities that receive grant support:

• Studies of unsolved problems in complex function theory and other problems in analysis where symmetrization can be expected to play a role: developing a comprehensive and unified theory of symmetrization starting from a ``master inequality"; applying these ideas to problems involving Bloch's theorem, quasiconformal mapping, and singular integrals.
• Problems in differential geometry and topology: foliations of 3-manifolds by surfaces, the asymptotic behavior of leaves in the case of hyperbolic 3-space, theory of levels and the topology of knot complements, Anosov flows, and the generalized Poincare-Bendixson Theory.
• Theory of functions of several complex variables: Hardy spaces, the Nevanlinna class, boundary limits along curves, and the theory of Lipschitz and Bloch spaces. Applications to regularity theory for the d-bar operator on weakly pseudoconvex domains using the language of invariant metrics; boundary uniqueness theory; automorphism groups of pseudconvex domains.
• Theoretical models and data analysis to be used to study intragenic recombination in bacteria and other aspects of population dynamics that can be inferred from statistical analysis of DNA sequences.
• Wavelet theory is a new mathematical subject intersecting harmonic analysis, geometry, operator theory, numerical and signal analysis.
• Boundary behavior of Poisson integrals and Hardy spaces associated to Riemannian symmetric spaces.

A more comprehensive list of research projects can be found under Faculty Research Projects.
Here is a partial list of other recent faculty activities:

• R. Rochberg recently gave a principal lecture at a regional meeting of the American Mathematical Society.
• S. Krantz and G. Weiss have each received the Chauvenet prize for mathematical expository writing.
• A. Baernstein and J. Jenkins have been invited speakers at the International Congress of Mathematicians.
• J. Jenkins, S. Krantz, M. Taibleson, and G. Weiss are authors of widely known monographs on conformal mapping, several complex variables, harmonic analysis on local fields, and harmonic analysis in Euclidean space, respectively.
• G. Weiss organized a year long session on harmonic analysis at the Mathematical Sciences Research Institute in Berkeley.
• S. Krantz organized a three-week American Mathematical Society Summer Research Institute on the subject of Several Complex Variables and Complex Geometry.
• S. Krantz was awarded the Beckenbach Book Prize for his book Complex Analysis: The Geometric Viewpoint.
• John McCarthy was an organizer of the program "Holomorphic Spaces" at MSRI, and has served on the Council for the American Mathematical Society. He has written a monograph on interpolation, and a textbook on mathematical thinking. He frequently gives public lectures on mathematics.

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