*From fluids to combinatorics and vice versa via Optimal Transport theory*
A comprehensive mathematical description of fluids like water goes back to Leonard Euler in the middle of the 18th century. If we think at a discrete level, for instance in terms of pixels, the motion of water looks very much like a very fast succession of permutations exchanging pixels, a little like a "melting rubik cube". We will discuss this analogy in more details, in connection with the mathematical theory of optimal transportation and its numerous applications.
Reference URL: https://www.math.unipd.it/~lcaraven/colloquia/colloquia_files/20250130_Brenier.html