Algebraic characterizations in complex differential geometry

Complex Analysis and Algebraic Geometry

The theme of these four lectures is roughly "the history of, and some recent developments in, the study of algebraic geometry by analytic methods". Since this topic is much too broad I have chosen to isolate one particular analytic tool, the local notion of residue and subsequent global residue theorem, and will attempt to illustrate some ways in which residues may be used in both classical and...

Numerical Algebraic Geometry and Differential Equations

In this paper we review applications of numerical algebraic geometry to differential equations. The techniques we address are direct solution, bootstrapping by filtering, and continuation and bifurcation. We review differential equations systems with multiple solutions and bifurcations.

Model Theory and Differential Algebraic Geometry

An Algebraic Model of Transitive Differential Geometry

One of the basic assumptions that is frequently made in the study of geometry (or physics) is that of homogeneity. I t is assumed that any point can be moved into any other by a transformation preserving the underlying geometrical structure (e.g., by a Euclidean motion in Euclidean geometry, an inhomogeneous Lorentz transformation in special relativity, etc.). The problem we shall treat in this...

Reprinted from Complex Analysis and Algebraic Geometry