Book Review: Gauge field theory and complex geometry

Gauge Field Theory in terms of complex Hamilton Geometry

On the total space of a G−complex vector bundle E is defined the gauge transformations. A gauge complex invariant Lagrangian determines a special complex nonlinear connection for which the associated Chern-Lagrange and Bott complex connections are gauge invariant. The complex field equations are determined with respect to these associated gauge complex connections. By complex Legendre transform...

The Geometry / Gauge Theory

of the Dissertation The Geometry/Gauge Theory Duality and the Dijkgraaf–Vafa Conjecture

Gauge theory, calibrated geometry and harmonic spinors

We establish connections between different gauge-theoretical problems in high and low dimensions. In particular we show that higher dimensional asd equations on total spaces of spinor bundles over low dimensional manifolds can be interpreted as Taubes-Pidstrygach’s generalisation of Seiberg-Witten equations. By collapsing each fibre of the spinor bundle to a point, we relate solutions of Taubes...

Gauge Field Theory Models

Quasicrystals and geometry: a Book Review

Penrose tilings (Fig. 1) are beautiful. They also suggest significant new mathematics, so it is about time someone wrote a book about them which is readable (in fact, eminently readable) by mathematicians. The book, Quasicrystals and geometry, by Marjorie Senechal, has an even broader goal: to present certain developments in crystallography from the past decade. The developments were generated ...