3/31/2024 0 Comments Lectures in basic number theoryThe goal of the course will be to understand and calculate the group of all rational points on an elliptic curve (i.e., calculate its torsion and rank), and a number of more refined invariants (such as the order of the Shafarevich-Tate group). Elliptic curves are central in modern number theory, e.g., they were essential in the proof of Fermat’s Last Theorem. The surprising feature of elliptic curves is that their points can be made into an abelian group, and this group is finitely generated when we focus on points with coordinates in the rational numbers lying on an elliptic curve with rational coefficients. This course will be an introduction to elliptic curves which, roughly speaking, are smooth cubic curves in the projective plane with at least one rational point (turns out they have a simple model of the form y^2=x^3+ax+b). Videos of the lectures will be posted to YouTube. **In Spring 2021, the mode of instruction for this class will be distance-learning.**ĭistance learning here means that there will be live-stream lectures on Tuesdays and Thursdays 11-12:15 (live-stream is only available for UConn students), but the lectures and attendance are not mandatory.
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