What sets the fragility of a glass-forming liquid
In plain words
Some liquids, such as molten silica, slow down smoothly as they approach the glass point, while others, such as many organic liquids and polymers, slow down abruptly; this steepness is called fragility. Why liquids differ so much is not known.
Precise statement
The kinetic fragility m = d log10(tau_alpha) / d(T_g/T) evaluated at $T = T_g$ ranges from about 20 for SiO2 to above 150 for some polymers. Identify the microscopic determinants of $m$ (softness of the repulsion, network connectivity, vibrational anharmonicity, the heat-capacity jump $\Delta C_p$ at $T_g$) and give a predictive relation for $m$ tested across a set of chemically different liquids.
What would settle it
A relation predicting m from microscopic or thermodynamic inputs that holds within experimental error across a large database of molecular, network, polymeric and metallic glass formers.