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Explore Serre's thin set conjecture through this 54-minute mathematical lecture that examines upper bounds for counting rational points on thin sets in projective space. Learn about the distinction between thin sets of type I, which arise from subvarieties and are well-understood through dimension growth results, and the more challenging thin sets of type II, corresponding to images of ramified dominant finite covers of projective space. Discover how the determinant method applies to analyzing thin sets of type II, with insights drawn from collaborative research involving Tijs Buggenhout, Raf Cluckers, and Tim Santens. Gain a comprehensive overview of the current state of research on counting rational points on thin sets and understand the mathematical techniques used to approach this important conjecture in algebraic geometry and number theory.
