Chatchai Noytaptim, Department of Pure Mathematics, University of Waterloo
"Equidistribution of small points and GCD of iterated polynomials"
In 2006, Favre-Rivera-Letelier, Baker-Rumely, and Chambert-Loir independently proved equidistribution theorems of points of small height. These equidistribution results have many applications in dynamical unlikely intersection problems. In this (expository) talk, I discuss a result of Hsia and Tucker in which they show that, under nice conditions, there are finitely many irreducible factors of the greatest common divisor of iterates of polynomials. A crucial step in the proof—in the case the degree of both polynomials is greater than 1—is to apply the equidistribution theorems to obtain dynamical relations of two polynomials (namely, Call-Silverman canonical height and Julia set).
MC 4063