Technion
 
Ritt's Theorem Seminar
 
CHANGE IN TIME
 
Hello all,
 
     In light of the department party, we'll be starting this week's
seminar at 1250  hrs 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
 
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Technion Math. Net (TECHMATH)
Editor: Michael Cwikel   <techm@math.technion.ac.il> 
Announcement from: Benjamin Weiss   <weiss@tx.technion.ac.il>