Abstract: The dynamical uniform boundedness conjecture (UBC) of Morton and Silverman is one of the major motivating problems in arithmetic dynamics. The conjecture asserts that the number of rational preperiodic points for a rational function of degree $d \ge 2$ is bounded above by a constant depending only on $d$. The UBC is still wide open, even in the simplest case $d = 2$, but a great deal of progress has been made. There have been a few recent results in this direction under the hypothesis that the abc conjecture is true. After a brief introduction to the abc conjecture, we will discuss an application toward UBC. This includes joint work with Wade Hindes (Texas State).
Mathematics Seminars and Colloquia