Dual complex characterizes how components of a divisor intersect each other. We will sketch the recent progress on using minimal model program to study it, with applications in various natural settings.
Links:
[1] http://www.mpim-bonn.mpg.de/de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/de/node/3444
[3] http://www.mpim-bonn.mpg.de/de/node/6228