The talks will focus on half-BPS boundary conditions for 3d N=2 gauge theories that preserve 2d N=(0,2)

supersymmetry. I will review (and extend) the classification of such boundary conditions and the BPS local

operators living on them, which form chiral algebras. I define a half-index that counts boundary local operators,

or equivalently computes a character of the boundary chiral algebra. With the help of the half-index and some

physical intuition, I will identify the action on boundary conditions of some basic dualities, including ``mirror

symmetries'' and level-rank dualities. This in turn leads to a definition of duality interfaces. (Work in progress

with D. Gaiotto and N. Paquette.)