James Borger University of Chicago Plethystic algebra Friday 27th August, 12:05-12:55pm, Carslaw 175. I will describe what appears to be the beginnings of a new chapter in algebra, having the same relation with commutative algebra and algebraic geometry that representation theory has with linear algebra. Witt vectors, lambda rings, and symmetric functions - things which have always been used in commutative algebra - live quite naturally in this world. I will describe the theory to the extent (small) that it is known, and say something about the many directions in which it is ripe for development, in addition to some precise open questions.