Speaker: Robert Guralnick, USC

Nov. 24, 4:00-4:50 in MS 5148

Rational Functions that are Bijective modulo infinitely many primes

Let R be the ring of integers in a number field and f(x) a rational function over R such that f is bijective on projective 1-space over R/P for infinitely many primes P of R. I will discuss joint work with Peter Mueller and Jan Saxl on classifying such rational functions. This was studied by Schur for f an integral polynomial and also by Fried. The case of rational functions is considerably more difficult. It is related to the notion of exceptional maps between varieties which I will discuss as well.