Multivariable Operator Theory: A Joint Summer Research Conference on Multivariable Operator Theory July 10-18, 1993 University of Washington Seattle (Contemporary Mathematics)

This Volume Contains A Collection Of Papers Presented At The Summer Research Conference On Multivariable Operator Theory, Held In July 1993 At The University Of Washington In Seattle. The Articles Contain Contributions To A Variety Of Areas And Topics Which May Be Viewed As Forming An Emerging New Subject. This Subject Involves The Study Of Geometric Rather Than Topological Invariants Associated With The General Theme Of Operator Theory In Several Variables. Developments Have Occurred In Several Different Directions, With The Aid Of A Variety Of Techniques, And Many Advances Have Been Made Through Cross-pollination Among Different Areas Of Mathematics. The Goal Of The Conference, And Of This Volume, Is To Spur Discussion Of The Connections Among The Various Approaches And New Directions For Research. Explicit Formulae For Taylor's Functional Calculus / D.w. Albrecht -- A Survey Of Invariant Hilbert Spaces Of Analytic Functions On Bounded Symmetric Domains / Jonathan Arazy -- Homogeneous Operators And Systems Of Imprimitivity / Bhaskar Bagchi And Gadadhar Misra -- Duality Between [actual Symbol Not Reproducible] On Domains With Nondegenerate Corners / David E. Barrett -- Commutative Subspace Lattices, Complete Distributivity And Approximation / Kenneth R. Davidson -- Models And Resolutions For Hilbert Modules / R.g. Douglas -- Positivity, Extensions And The Truncated Complex Moment Problem / Lawrence Fialkow -- Torsion Invariants For Finite Von Neumann Algebras / Donggeng Gong And Joel Pincus -- Algebraic K-theory Invariants For Operator Theory / Jerome Kaminker -- Fundamentals Of Harmonic Analysis On Domains In Complex Space / Steven G. Krantz -- Spectral Picture And Index Invariants Of Commuting N-tuples Of Operators / R.n. Levy. Raúl E. Curto ... [et Al.], Editors. Includes Bibliographical References. Ideas and techniques from the theory of integrable systems are playing an increasingly important role in geometry. Thanks to the development of tools from Lie theory, algebraic geometry, symplectic geometry, and topolgoy, classical problems are investigated more systematically. New problems are also arising in mathematical physics. A major international conference was held at the University of Tokyo in July 2000. It brought together scientists in all of the areas influenced by integrable systems. This book is the first of three collections of expository and research articles. This volume focuses on topology and physics. The role of zero curvature equations outside of the traditional context of differential geometry has been recognized relatively recently, but it has been an extraordinarily productive one, and most of the articles in this volume make some reference to it. Symplectic geometry, Floer homology, twistor theory, quantum cohomology, and the structure of special equations of mathematical physics, such as the Toda field equations—all of these areas have gained from the integrable systems point of view and contributed to it. Many of the articles in this volume are written by prominent researchers and will serve as introductions to the topics. It is intended for graduate students and researchers interested in integrable systems and their relations to differential geometry, topology, algebraic geometry, and physics.