Operator theory and algebraic geometry

Operator geometry and algebraic gravity

An algebraic formulation of general relativity is proposed. The formulation is applicable to quantum gravity and noncommutative space. To investigate quantum gravity we develop the canonical formalism of operator geometry, after reconstructing an algebraic canonical formulation on analytical dynamics. The remarkable fact is that the constraint equation of the gravitational system is algebraical...

Complex Geometry and Operator Theory

One of the principal goals of spectral theory for operators is to find unitary invariants which are local relative to the spectrum. Multiplicity theory provides a complete set of such invariants for normal operators on (complex) Hilbert space. For general operators on finite-dimensional Hilbert space a nilpotent operator is attached to each point of the spectrum and these "local operators" toge...

Operator Theory and Complex Geometry

Number-theory and Algebraic Geometry

The previous speaker concluded his address with a reference to Dedekind and Weber. It is therefore fitting that I should begin with a homage to Kronecker. There appears to have been a certain feeling of rivalry, both scientific and personal, between Dedekind and Kronecker during their life-time; this developed into a feud between their followers, which was carried on until the partisans of Dede...

Algebraic Geometry and Representation Theory

0. Let G be a reductive group over Z. For any field F we can consider the group Gp of F-points on G. At first glance, the groups Gp for different fields F appear to have little in common with each other. I. Gelfand has conjectured that (1) The structure of the representations of GF has fundamental features which do not depend on a choice of F. (2) Moreover, it is possible to define representati...