Generalised Complex Geometry in Thermodynamical Fluctuation Theory

Generalised Complex Geometry in Thermodynamical Fluctuation Theory

We present a brief overview of some key concepts in the theory of generalized complex manifolds. This new geometry interpolates, so to speak, between symplectic geometry and complex geometry. As such it provides an ideal framework to analyze thermodynamical fluctuation theory in the presence of gravitational fields. To illustrate the usefulness of generalized complex geometry, we examine a simp...

Generalised Geometry for M-Theory

Generalised geometry studies structures on a d-dimensional manifold with a metric and 2-form gauge field on which there is a natural action of the group SO(d, d). This is generalised to d-dimensional manifolds with a metric and 3-form gauge field on which there is a natural action of the group Ed. This provides a framework for the discussion of M-theory solutions with flux. A different generali...

Generalised Complex Geometry and the Planck Cone

Complex geometry and symplectic geometry are mirrors in string theory. The recently developed generalised complex geometry interpolates between the two of them. On the other hand, the classical and quantum mechanics of a finite number of degrees of freedom are respectively described by a symplectic structure and a complex structure on classical phase space. In this letter we analyse the role pl...

Model Theory and Complex Geometry

Model theory is a branch of mathematical logic whose techniques have proven to be useful in several disciplines, including algebra, algebraic geometry and number theory. The last fifteen years have also seen the application of model theory to bimeromorphic geometry, which is the study of compact complex manifolds up to bimeromorphic equivalence. In this article I will try to explain why logic s...

Operator Theory and Complex Geometry