I will discuss homological mirror symmetry from the perspective of Lagrangian skeleta and constructible sheaves following Fang, Liu, Treumann, and Zaslow.  I will discuss an extension to the non-proper setting and, if time permits, a relation to Morse theory and variation of geometric invariant theory quotients.

This is joint work in progress with Ballard, Diemer, Katzarkov, Kerr, and Kontsevich.