Colloquium

In bijective combinatorics, one seeks to prove that two sets have the same size by constructing an explicit one-to-one correspondence between them. We will introduce this subject by surveying some remarkable bijections involving lattice paths and Catalan numbers. In particular, we describe a surprising relationship between Catalan structures and the Central Limit Theorem from probability theory. If time allows, a brief introduction to quantum Catalan numbers will also be given.