*The primary source is the seminal 1963 differential-topology article, "Groups of homotopy spheres," by Michel Kervaire and John Milnor.*

Professor Khan will present a proof of J P Serre's celebrated 1951 theorem, that **the stable homotopy groups of spheres are finite**.

This is a key background fact used in the seminar's primary source. Moreover, the title of our primary source is a deliberate pun on that subject, *homotopy groups of spheres!*

Serre's proof is a novel example of using the algebraic-topology tools of homotopy fibers and of spectral sequences. (Similarly later, in 1954, R Thom used these tools to calculate the oriented cobordism groups up to dimension 7.)

(For continuity, here's a link to the previous talk.)