Maksim Maydanskiy: Lagrangian submanifolds from reduction

Lagrangian submanifolds, and tori in particular, arise in both classical and modern symplectic topology (from Arnold–Liouville description of finite-dimensional integrable systems, to Strominger–Yau–Zaslov picture of mirror symmetry).

Lagrangians with nice properties like exactness or monotonicity are of particular interest, and subject of fair amount of recent work. In this talk, I will explain a method of constructing such Lagrangian submanifolds coming from (singular) reduction; I will outline how this construction reproduces various Lagrangians in the literature, starting with vanishing cycles in a model Lefschetz fibration, and including the infinitely many tori in R⁴ constructed by Auroux, tori of Chekanov–Schlenk, and others.