There Are Infinitely Many Elliptic Curves Over the Rationals of Rank 2

Explore a number theory lecture where David Zywina from Cornell University proves that there are infinitely many elliptic curves over the rationals with rank 2. Learn about the Mordell-Weil group E(Q) as a finitely generated abelian group and discover how explicit models and 2-descent techniques are used to determine the ranks of these curves. The proof relies on a theorem by Tao and Ziegler to establish the infinitude of such elliptic curves. If time permits, the speaker also discusses recent work on rank stability. This joint Princeton University/Institute for Advanced Study Number Theory seminar is scheduled for April 10, 2025, at 3:30pm in Simonyi 101 with remote access available.