Title: Uniform bounds on torsion of elliptic curves in geometric isogeny classes
Speaker: Tyler Genao (OSU)
Abstract: A celebrated result of Merel (1996) proved there exists an absolute bound on all torsion groups of elliptic curves over number fields of a fixed degree. On the other hand, any geometric isogeny class of elliptic curves ("geometric" meaning defined over a fixed algebraic closure of $\mathbb{Q}$) will contain $j$-invariants of arbitrarily large degree over $\mathbb{Q}$. It may be surprising, then, that torsion groups from geometric isogeny classes are still "uniformly behaved" in several ways.
In this talk, we will discuss new results on polynomial bounds for torsion from geometric isogeny classes of elliptic curves, as well as "typical boundedness" of torsion from the collection of geometric isogeny classes with at least one rational $j$-invariant.
URL associated with Seminar: https://research.math.osu.edu/numbertheory/
