Research

Modern Analysis

Research interest by our Modern Analysis group includes work on: Semifinite and purely infinite von Neumann algebras, C*-algebras of real rank zero, K-theory of C*-algebras, classical and Ko-valued Fredholm Index, structure of multiplier algebras, homotopy of the unitary group of C*-algebras, groups and quantum group actions on C*-algebras, spectra, invariant derivations, cross products, Kadison-Singer extension problem, ideals, traces and commutators on Hilbert spaces, arithmetic means and majorization theory, wavelets and frames.

Another primary area of focus for the modern analysis group is Geometric Analysis. This area includes research in geometric function theory on Riemann surfaces, quasiconformal mappings in R^n and in metric spaces, geometry of domains in metric spaces and connections to Gromov hyperbolicity, analysis and potential theory on metric spaces, geometric measure theory, and generalization of Riemannian and conformal structures, as well as hyperbolic and quasihyperbolic geometry.

The group's research has been funded by the National Science Foundation. The group holds regular weekly research seminars.

Faculty

Herb Halpern, von Neumann algebras.
Victor Kaftal, operator algebras, operator theory.
Costel Peligrad, operator algebras.
Gary Weiss, operator algebras, operator theory, harmonic analysis.
Shuang Zhang, operator theory K-theory, homotopy theory, Fredholm index theory.

Ersin Deger (Visting 2007-08), complex analysis, several complex variables, potential theory
David Herron, geometric function theory, quasi-conformal mappings, hyperbolic geometry, potential theory.
Vidur Malik (Visting 2007-08), hyperbolic geometry, Kleinian groups, Teichmuller theory
Dave Minda (Taft Professor), Classical complex analysis, Riemann surfaces, quasi-conformal mapping.
Nages Shanmugalingam, analysis on metric spaces, potential theory, geometric function theory

Pando Georgiev (Adjunct), analysis on Banach spaces, non-smooth analysis

 

 

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