Finding polygon overlays of point data

We already have all the data we need to identify the parent state of each airport. The dt dataset includes the geo-coordinates of the locations, and we managed to render the states as polygons with the map function. Actually, this latter function can return the underlying dataset without rendering a plot:

> str(map_data <- map('state', plot = FALSE, fill = TRUE))
List of 4
 $ x    : num [1:15599] -87.5 -87.5 -87.5 -87.5 -87.6 ...
 $ y    : num [1:15599] 30.4 30.4 30.4 30.3 30.3 ...
 $ range: num [1:4] -124.7 -67 25.1 49.4
 $ names: chr [1:63] "alabama" "arizona" "arkansas" "california" ...
 - attr(*, "class")= chr "map"

So we have around 16,000 points describing the boundaries of the US states, but this map data ...

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