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Explore a mathematical seminar where Carlo Pagano from Concordia University discusses the undecidability of Hilbert's 10th problem through the lens of additive combinatorics. This February 2025 Colloque des sciences mathématiques du Québec presentation examines how Pagano and Peter Koymans combined Green-Tao's theorem with 2-descent techniques to prove that Hilbert's 10th problem is undecidable over any finitely generated infinite commutative ring. The talk provides a gentle introduction to this breakthrough result, which extends Matiyasevich's 1970 proof of undecidability for Z without requiring the BSD conjecture. Discover the fascinating intersection of mathematical logic, number theory, and additive combinatorics in this one-hour presentation that resolves a long-standing mathematical challenge.
