We start by reviewing the Standard Model, its spectrum, symmetries, representations, and Lagrangian. Then, we consider the Grand Unified Theories extensions, in particular the SU(5) GUT, the SO(10) GUT, and other (bigger) groups. Then, we consider the Minimal Supersymmetric Standard Model (MSSM) and Minimal Supergravity, and new low-energy string (supergravity) constructions.

The issue of denotation for syntax theories is examined. A natural semantics for the syntax theory of the previous chapter is defined.

A Mori fibre space of relative dimension two is a del Pezzo fibration. We address the problem of finding a good representative in each equivalence class of threefold del Pezzo fibrations. In the case of degree at least three, Corti realised a standard model embedded anti-canonically into a projective space bundle. We explain the construction by Kollár for degree three as a semistable model. The stability theory completes the existence of standard models for degree two and one. Mori and Prokhorov proved that the multiplicity of a fibre is bounded by six. We also discuss the rationality problem of del Pezzo fibrations to a rational curve. The total space is always rational when the degree is at least five. We exhibit Alexeev's work for degree four. He established a criterion for rationality in terms of topological Euler characteristic. The lower degree case is treated from the point of view of birational rigidity. Pukhlikov proposed the K2-condition and proved that it is sufficient for birational rigidity. We compare it with Grinenko's K-condition. For a fibration of degree one from a smooth threefold, the K-condition turns out to be equivalent to the birational superrigidity.

This chapter scans the range of possibilities now open for emergency operations planning. The embedded case study describes use of the cloud, artificial intelligence, and the “internet of things.”