  We introduce a model based on Ordinary Differential Equations to describe how
two mutually exclusive groups progress through a career hierarchy, whether in a
single organization, or in an entire economic sector. The intended application
is to gender imbalance at the top of the academic hierarchy in European
Universities, however, the model is entirely generic and may be applied in
other contexts also. Previous research on gender imbalance in European
universities has focused on large-scale statistical studies. Our model
represents a point of departure, as it is deterministic (i.e. based on Ordinary
Differential Equations). The model requires a precise definition of the
progression rates for the different groups through the hierarchy; these are key
parameters governing the dynamics of career progression. The progression rate
for each group can be decomposed into a product: the proportion of group
members at a low level in the hierarchy who compete for promotion to the next
level a given year, multiplied by the in-competition success rate for the group
in question. Either of these two parameters can differ across the groups under
consideration; this introduces a group asymmetry into the organization's
composition. We introduce a glass-ceiling index to summarize this asymmetry
succinctly. Using case studies from the literature, we demonstrate how the
mathematical framework can pinpoint the proximate cause of the glass ceiling in
European academia.
