We studied binomial edge ideals, which are at the intersection of graph theory and abstract algebra. Our focus was the multidegrees of these ideals, which contain valuable geometric information. We proved algebraic results that allowed us to write a closed formula for the multidegree of the binomial edge ideal of…

Let $E$ be an elliptic curve defined over a number field $K$, $p$ a rational prime, and $\Lambda(\Gamma)$ the Iwasawa module of the cyclotomic extension of $K$. A famous conjecture by Mazur states that the $p$-primary component of the Selmer group of $E$ is $\Lambda(\Gamma)$-cotorsion when $E$ has good ordinary…