Geometry and complexity of partition bijections

The study of partition identities has a long history going back to Euler, with applications ranging from Analysis to Number Theory, from Enumerative Combinatorics to Probability. Partition bijections is a combinatorial approach which often gives the shortest and the most elegant proofs of these identities. These bijections are then often used to generalize the identities, find "hidden symmetries", etc. In the talk I will present a modern approach to partition bijections based on the geometry of random partitions and complexity ideas.