  This note is based on a talk given at String-Math 2012 in Bonn, on a joint
paper with Ed Segal. We exhibit derived equivalences corresponding to certain
Grassmannian flops. The construction of these equivalences is inspired by work
of Herbst-Hori-Page on brane transport for gauged linear sigma models: in
particular, we define 'windows' corresponding to their grade restriction rules.
We then show how composing our equivalences produces interesting
autoequivalences, which we describe as twists and cotwists about certain
spherical functors. Our proofs use natural long exact sequences of bundles on
Grassmannians known as twisted Lascoux complexes, or staircase complexes. We
give a compact description of these. We also touch on some related
developments, and work through some extended examples.
