Generating families on Lagrangian cobordisms:

Generating families (generating functions) for exact Lagrangian or Legendrian submanifolds provides a finite dimensional approach to understanding nonclassical invariants of the submanifolds. Given an exact Lagrangian cobordism between Legendrians in 1-jet bundles, we prove that a generating family linear at infinity on the Legendrian at the negative end extends to a generating family linear at infinity on the Lagrangian cobordism, when the necessary formal obstructions vanish. If time permits, we will discuss an analogous result for microlocal sheaves and formulate an (optimistic) conjecture between microlocal sheaves and generating families.