On Rado's Boundedness Conjecture

Rado's Conjecture and Ascent Paths of Square Sequences

Gonality of Dynatomic Curves and Strong Uniform Boundedness of Preperiodic Points

Fix d ≥ 2 and a field k such that char k d. Assume that k contains the dth roots of 1. Then the irreducible components of the curves over k parameterizing preperiodic points of polynomials of the form z + c are geometrically irreducible and have gonality tending to ∞. This implies the function field analogue of the strong uniform boundedness conjecture for preperiodic points of z + c. It also h...

On Robson's Convergence and Boundedness Conjecture Concering the Height of Binary Search Trees

$n$-factorization Property of Bilinear Mappings

In this paper, we define a new concept of factorization for a bounded bilinear mapping $f:Xtimes Yto Z$, depended on  a natural number $n$ and a cardinal number $kappa$; which is called $n$-factorization property of level $kappa$. Then we study the relation between $n$-factorization property of  level $kappa$ for $X^*$ with respect to $f$ and automatically boundedness and $w^*$-$w^*$-continuity...

Uniform Boundedness of Rational Points and Preperiodic Points

We ask questions generalizing uniform versions of conjectures of Mordell and Lang and combining them with the Morton–Silverman conjecture on preperiodic points. We prove a few results relating different versions of such questions.