On the uniformity of unlikely intersections Hang Fu, National Taiwan University Host: Paul Fili NOTE THE SPECIAL TIME! Contact Paul Fili for the Zoom link.

Abstract: In this talk, we will discuss some recent progress in the uniformity of unlikely intersections. We will introduce some applications of Arakelov-Zhang pairing and take the following result as a concrete example. Fix $d\geq2$ and let $f_{t}(z)=z^{d}+t$ be the family of polynomials parameterized by $t\in\mathbb{C}$. Then there exists a constant $C(d)$ such that for any $a,b\in\mathbb{C}$ with $a^{d}\neq b^{d}$, the number of $t\in\mathbb{C}$ such that $a$ and $b$ are both preperiodic for $f_{t}$ is at most $C(d)$. This result can be seen as an analog of DeMarco-Krieger-Ye and as a uniform version of Baker-DeMarco.

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