I know that smoking negates the fast, and write because, as I arrive and leave school, I have to pass a group of smokers. I hold my breath and try to pass them by as fast as possible, but sometimes I have to take a breath while I am still among them. That’s when I inhale some of their smoke. Does this invalidate my fast?

Although one is not permitted to smoke during the fast, that does not apply to passively inhaling smoke from those around you. There is no need for you to hold your breath.