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Explore groundbreaking mathematical research in this Members' Colloquium lecture where Elon Lindenstrauss presents collaborative work with Amir Mohammadi, Zhiren Wang, and Lei Yang on quantitative results related to the Oppenheim Conjecture. Learn about the developments since Margulis's 1980s proof, focusing on indefinite ternary quadratic forms and their behavior at integer points. Discover how algebraic coefficients in these forms relate to asymptotic distributions in R^3, supported by new quantitative equidistribution results for unipotent flows and upper bound estimates from Eskin-Margulis-Mozes and Wooyeon Kim. Delve into advanced mathematical concepts including integral forms, volume asymptotes with power saving error terms, and the dense distribution of quadratic form values in R.
