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Explore a 55-minute mathematics lecture examining Hilbert's tenth problem over rings of integers, delivered by Ari Shnidman from The Hebrew University of Jerusalem at the Institute for Advanced Study. Delve into groundbreaking research demonstrating that for every quadratic extension of number fields K/F, there exists an abelian variety A/F of positive rank whose rank remains constant when changed to base K. Learn how this finding, combined with Shlapentokh's work, proves the impossibility of creating an algorithm to determine whether polynomial equations with multiple variables over the ring of integers R of any number field have solutions in R. Discover the collaborative research results achieved with Levent Alpöge, Manjul Bhargava, and Wei Ho in this joint Princeton University and Institute for Advanced Study number theory seminar.
