Defining records (maxima, extremes, etc.) marks in higher dimensions d is very ambiguos, but there are three obvious definitions coming from dimension d = 1. Two of them, weak (other names: Pareto points, efficient or admissible solutions, etc.) and strong (other names: ideal points, multiple maxima, etc.) have been studied at some extent, and will be briefly reviewed and compared with the classical records. The third, recursive, definition (chain records) is more subtle for d > 1 but looks very promising, as it has very large generality, applied appeal and some curious mathematics properties. The talk will focus on general properties of the chain records and on the special situations where the occurences of such records can be efficiently counted.
This work is in progress, partly joint with Charles Goldie.