Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:	王玉超,上海大学
Inviter:	葛力明教授
Title:	Almost prime points on unirational varieties
Language:	Chinese
Time & Venue:	2023.07.11 14:30-16:30 南楼N802
Abstract:	In this talk, we generalise the definition of the saturation number introduced by Bourgain, Gamburd and Sarnak to investigate the distribution of rational points on unirational varieties whose coordinates have few prime factors. We prove that there exists an integer $r$ such that rational points for which the product of the coordinates has at most $r$ prime factors form a Zariski dense subset, provided that the variety has one rational point. Moreover, we may obtain rather small bounds for $r$ for several special cases. Our approach relies on the circle method, the weighted sieve and unirationality arguments.