Asymptotic period relations for Jacobian elliptic surfaces

We find an asymptotic description of the period locus of simply connected Jacobian elliptic surfaces and of the period locus of hyperelliptic curves. The two descriptions are essentially the same, and are given by the alkanes of organic chemistry.Comment: The use of the Minimal Model Program has been clarified, as has the Torelli theorem for special elliptic surface

Siegel modular forms and the gonality of curves

There is no stable Siegel modular form that vanishes on the trigonal locus in every moduli space of curves.Comment: This version takes into account Yamada's correction of Fay's formula for the period matrix of a certain degenerating family of curve

"Del Pezzo surfaces as Springer fibres for exceptional groups"

We show that simultaneous log resolutions of simply elliptic singularities can be constructed inside suitable stacks of principal bundles over elliptic curves. In particular, we give a direct geometrical construction of del Pezzo surfaces from the corresponding exceptional simple algebraic groups.Comment: This is a re-written version of "From exceptional groups to del Pezzo surfaces and simultaneous log resolutions via principal bundles over elliptic curves". It contains 2 figures. This version corrects one of the figure

Hot Routes: Developing a New Technique for the Spatial Analysis of Crime

The use of hotspot mapping techniques such as KDE to represent the geographical spread of linear events can be problematic. Network-constrained data (for example transport-related crime) require a different approach to visualize concentration. We propose a methodology called Hot Routes, which measures the risk distribution of crime along a linear network by calculating the rate of crimes per section of road. This method has been designed for everyday crime analysts, and requires only a Geographical Information System (GIS), and suitable data to calculate. A demonstration is provided using crime data collected from London bus routes