- Series
- Number Theory
- Time
- Wednesday, November 11, 2026 - 3:30pm for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Abbey Bourdon – Wake Forest University – bourdoam@wfu.edu – https://users.wfu.edu/bourdoam/
- Organizer
- Cruz Castillo
In 1996, Merel showed that for any elliptic curve defined over a number field $F$ of degree $d$, the size of the torsion subgroup is bounded by a constant $B(d)$ that depends only on $d$. It is conjectured that one can choose $B(d)$ to be polynomial in the degree $d$. For the special class of elliptic curves with $j$-invariant in $\mathbb{Q}$, polynomial bounds were first established by Clark and Pollock in 2018. In this talk, I will discuss recent improvements to these bounds that are essentially optimal for the exponent of the torsion subgroup.