Technion Ritt's Theorem Seminar CHANGE IN TIME Hello all, In light of the department party, we'll be starting this week's seminar at1250hrs on Wednesday in 232 Amado. This week we'll discuss the statement of Ritt's theorems and start the group and Galois theory needed to prove them. The below is a copy from the previous announcement. -Ben Weiss ------------------------------------------- Hello all, Starting next week, the seminar will be meeting at 1230 hours on Wednesdays in 232 Amado. For the next couple weeks we will be starting fresh, and going over the group theory, Galois theory, and geometry needed to prove Ritt's theorem classifying all pairs of polynomials $f$ and $g$ such that f \circ g = g \circ f. For the most part, I will be following a preprint of Peter Muller and Michael Zieve available on the Arxiv (follow that link for the paper). After that, we will discuss how to apply the techniques to a myriad of problems including some recent results in geometry and arithmetic dynamics such as: 1) Classifying equations F(X) = G(Y) with infinitely many integer solutions or infinitely many rational solutions; 2) Showing that for any polynomial $f \in Q[X]$, for all but finitely many rational numbers $r$ we have that there are at most 6 rational preimages in $f^{-1}(r).$ All are welcome, the seminar is being designed with as minimal prerequisites as possible. -Ben Weiss --------------------------------------------------------- Technion Math. Net (TECHMATH) Editor: Michael Cwikel <techm@math.technion.ac.il> Announcement from: Benjamin Weiss <weiss@tx.technion.ac.il>