We worked with Georges Dupret on a model that is able to distinguish the attractiveness (how likely a user is going to click on it) of paper and the position effect (how likely is it that the user will even consider this document, i.e. look at the snippet). This work is described in a SIGIR paper (missing reference).
We developed with Hugo Zaragozza a predictive model for navigational queries (missing reference), where the aim is to predict the document the user will click on along with the confidence we have for this prediction; the confidence is important if one wants to automatically redirect (for example) the user to the page he wanted to browse to when typing their query.
My last project aimed at modeling a whole search session (from the first query string to the last click, including reformulations) using layered Bayesian networks (missing reference). The main potential applications of this work are the estimation of user satisfaction and of the relevance of documents (based on a single interaction between the user and the search engine).