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Explore a 57-minute mathematics lecture from the Joint Princeton University/Institute for Advanced Study Number Theory series where Ari Shnidman from The Hebrew University of Jerusalem presents groundbreaking research on Hilbert's 10th Problem over rings of integers. Delve into the proof that demonstrates for every quadratic extension of number fields K/F, there exists an abelian variety A/F of positive rank whose rank remains constant when base-changed to K. Learn how this finding, combined with Shlapentokh's work, leads to the significant conclusion that no algorithm exists to determine whether polynomial equations with multiple variables over the ring of integers R of any number field have solutions in R. Understand the collaborative research conducted with Levent Alpöge, Manjul Bhargava, and Wei Ho that contributes to this fundamental advancement in number theory.
