Two roads between algebra and geometry, one Saturday. At one, a new course opens on commutative algebra: rings, ideals and modules, where prime ideals become points and the spectrum of a ring turns algebra into a space you can look at. At three, the geometric group theory course runs the other way, reading a group through the geometry it acts on, and presses on toward Cannon’s conjecture: must a hyperbolic group whose boundary is a 2-sphere act geometrically on hyperbolic 3-space?