|Location:||Space Science Lab, Room 105|
There are several analogies between discrete and continuous mathematics that influence our thinking and understanding. For a very basic example, take the the Boolean lattice of subsets of a finite set with its continuous analog the measurable subsets of the unit interval.
A general setting for such analogs, suggested by matroid theory and inspired by von Neumann’s work on "continuous geometries" from 1936, will be discussed. It is based on work from the 1980’s, much of it joint with L. Lovász, on continuous matroids, including continuous analogs of partitions and of field extensions.